4) Prove:
A) 1/(1+ xᑫ⁻ᵖ + xʳ⁻ᵖ) + 1/(1+ xᵖ⁻ᑫ + xᑫ⁻ʳᑫ) = 1
B) If aˣ = m, aʸ = n and a²= (mʸˣ)ᶻ then show that xyz = 1.
C) If 64ˣ =48 ʸ = 36ᶻ then prove 1/x + 1/z = 2/y.
D) If 2ᵃ = 3ᵇ = 12ᶜ then prove that ab = c(a+ 2b).
E) If pˣ = qʸ = rᶻ then prove pqr = 1.
F) If aˣ = bʸ = cᶻ and b² = ac, then prove 1/x + 1/z = 2/y.
G) If (3.6)ᵖ =(.36)ᑫ = (1)ʳ then prove 1/p = 1/q + 1/r.
H) If x¹⁾ᵃ = y¹⁾ᵇ = z¹⁾ᶜ and xyz = 1 then prove a+ b + c= 0.
I) If x² = y³ then prove (x/y)³⁾²+ (y/x)²⁾³ = x¹⁾² + y⁻¹⁾³.
J) If xʸ = yˣ then prove that (x/y)ˣ⁾ʸ = xˣ⁾ʸ ⁻¹ .
M) If x¹⁾³ + y¹⁾³+ z¹⁾³ = 0 then prove that (x + y+ z)³ = 27 xyz.
N) If x= 2¹⁾³ + 2⁻¹⁾³ then prove 2x³ = 6x +5.
O) a= 5 - 5²⁾³ - 5¹⁾³ then prove a³ - 15a² + 60a = 20
TEST PAPER- 1
1) Attempt all (1 x3= 3)
a) If cosecθ = 13/12, then the value of tanθ is
i) 12/5 ii) 5/12 iii) 5/13 iv) 5/12
b) If tanA = x/y, then cosA is
i) x/√(x²+ y²) ii) y/√(x²+ y²) iii) (x²- y²)/√(x²+ y²) iv) (x²- y²)/(x²+ y²)
c) secθ=
i) hypotenuse/base ii) perpendicular/base iii) base/hypotenuse/base iv) none
2) Answer any 2 (2 x2=4)
a) Given A is an acute angle and cosecA=√2, find the value of (2sin²A + 3 cot²A)/(tan²A - cos²A).
b) If cot θ= 15/8, then find the value of (2sin²θ+ 3 cosθ)/(5 sinθ - 3 cos²θ).
c) If sinθ = 12/13, then find tan²θ - sec²θ.
3) If tanθ= p/q, find the value of (p sinθ - q cosθ)/(p sinθ + q cosθ).
4) If sinx = √3/2 then value of {(2+ 2 sinx)(1- tanx)}/{(1+cotx)(2- 2 cosecx)}.
Compound Intrest and Circle mean-median-mode, trigonometry , Simultaneous equation, Pythagorean
1) The boundary of the shaded region in the given diagram consists of 3 semi circular areas.
Calculate
a) the length of the boundary.
b) The area of the shaded region.
2) A horse is tetherd to one corner of a square plot of side 42m, by a rope 35m long. Find 
a) What area it can graze ?
b) What area will be left ungrazed ?
3) Find the mean and median of 3.2, 3.4,4,3.8,4.7,3.74.2,3.8,3,3.5
4) Calculate the area of the shaded part of the semi circle in the adjoining diagram,
given BC= 20cm, AC= 12cm (π=3.142).
5) Evaluate: sin²60+ cos²30+ tan²30. sin90.
6). Verify: tan60= 2 tan30/(1- tan²30).
7) ABCD represents a flower bed if OA= 28m and OD=21m, find 
a) the area of the flower bed,
b) the perimeter of the flower bed.
8) If A= 60 and B= 30. Show that
a) cos(A+ B)= cosA cosB - sinA sinB
Sin(A+ B)= sinA cosB + sinB cosA.
9) If Rs 50000 amount to Rs 73205 in 4 years, find the rate of compound interest payable yearly.
10) Evaluate: sin90 cos90 tan45.
11) Prove (2,-2),(8,4),(5,7),(-1,1) are the vertices of a rectangle.
12) A race track is in the form of a circular ring whose inner circumference is 440 and outer circumference is 506m. Find the width of the track and also area of the track.
13) In the given figure
diameter of the biggest semicircle is 216cm, and diameter of the smallest circle is 72cm. Calculate the area of the shaded portion.
14) Find the compound interest on Rs 4000 for 3/2 years at 8% p.a. if interested is compounded semiannually.
15) In a class test, the marks of 30 pupils were 6,5,3,4,5, 5,8,3, 1,4,3,6, 4,5,8, 5,4,2, 3,4,4,7, 4, 2, 5, 4, 7, 9, 8, 10, Draw up a tally chart and frequency table, hence find the mean the median.
16) Evaluate: (sin²60+ cos²45)/(tan²60 - sin90 cos90).
17) The boundary of the shaded region in the given diagram consists of 5 semi circular areas.
Calculate
a) the length of the boundary.
b) the area of the shaded region correct to the nearest square metre.
18) If the points (-5,a),(-1,5) and (7,1) are collinear, find a.
19) A man borrows Rs 5000 at 10% p.a compound interest. At the end of each year he repays Rs 1500. Find how much he still owes after the 3rd year.
20) If sin2x= cos3x, x< 90; find
a) x
b) cos5x
c) sin5x.
21) Evaluate: sin30 cos60 + cos30 sin60.
22) The marks of 24 candidates in mathematics are given below:
45,40,48,11,48,11,50,42,15,29,18,23,23,0,30,2,30,3,15,3,35,12,30,14
The maximum marks are 50. Make a frequency distribution taking class interval 0-10,10-20,........ Draw a histogram.
23) A circular road runs round a circular garden of diameter 14m. If the difference between the circumference of the outer circle and the inner circle is 85m. Find
a) the width of the road.
b) the area of the road.
24) The masses of 20 men, correct to the nearest kg, are as follows:
65, 55,53,66,55,69,63,60,57,70,65,54,56,69,53, 54,63,76,64,52
Draw up a tally chart and a frequency table for the groups 50-55, 55-60 etc. hence find the mean.
25) The coordinates of A, B, C the three vertices of a right angle triangle are (0,3),(-2, k) and (-1,4). If the triangle is right angled at A, find the value of k.
26) From the adjoining diagram,
calculate the value of
a) cosθ b) θ c) Show that: 1/cos²θ - tan²θ= 1.
27) Solve : x - 3y= 3x -1= 2x - y.
28) P and Q are points on the line joining A(-4,3) and B(2,-1) such that AP= PQ= QB. Calculate the coordinates of P and Q.
29) A sum of money amounts to Rs 1331 in 3 years at the rate of 10% p.a compound interest. Find the sum.
30) If the sum of the two sides of a right angled triangle is 17cm and the hypotenuse is 13cm, find the length of the remaining two sides.
31) How many times will the wheel of a car rotate in a journey of 7.7 km, if the diameter of the wheel is 1.96 m ?
32) Evaluate: (sin⁴45+ cos⁴60+ 2 sin²45 cos²60)/(sin⁴30 + tan⁴60 + 2 tan²60 sin²30).
33) The area of a circular ring enclosed between two concentric circles is 286m². Find the diameter of the circles, if their difference is 14m.
34) Show: 2tan60/(1- tan²60) + √3=0.
35) Construct a rectangle ABCD in which AD= 3cm and BD= 6.5cm. measure CD.
36) If tan²x -3=0, find
a) x b) sin(x/2) c) cos(3x/2). sun(3x/2).
37) In the adjoining square of side 4cm, four circles are inscribed.
Calculate the area of the shaded portion.
38) If x= 30; show (sin3x + sinx)/(cos3x + cosx)= tan2x
39) Solve 5y = 2x+ 8; 4y= x +7.
40) Evaluate: (cos⁴60+ 2 sin²60. cos²60+ sin⁴60)/(sin⁴30+ 2 cos²30 sin²30 + cos⁴30) . (sin²90+ cos²90).
41) If x= 30 show that
(Sinx + sin2x)/(1+ cosx + cos2x)= Sin2x/(1+ cos2x)= sin3x/tan2x.
42) Rs 5000 lent out on CI to be compounded annually amounts to Rs 5400 at the end of the first year calculate
a) the amount at the end of the second year.
b) The sum which must be returned at the end of the first year, so that a payment of Rs 2700 at the end of the second year may settle the debt.
43) The area of the shaded region enclosed between two concentric circles is 1039.5 m²
Given A is midpoint of OP (O is centre of the circles), calculate
a) OP
b) By how many metres does the circumference of outer circle, exceed the circumference of the inner circle?
44) Solve: 3x - y= 7; 2x - 3y=0.
45) Calculate mean and median of 3,22,7,15,17,12,10,5,5,15
46) Evaluate: (2 tan 40)/(cot 50) - (cosec61)/(sec29).
47) ABCD is a rectangle. The radius of the semicircles drawn on AD and BC and the radius of the circle drawn in between is the same.
Given that AD= 7cm. Calculate the area of the shaded portion.
48) Find the value of: 3 sin35 sec 55+ 2 cos32 cosec58.
49) Find the mean, median of 3,7,10,6,9,5,7,5,16,7.
50) The hypotenuse of a right angled triangle is 50cm and the longer of the other two sides, exceeds the shorter by 10cm. Calculate
a) the length of the sides.
b) area of the triangle.
51) Evaluate: (sin²60+ tan²60)/(sin²30+ cos²60).
52) The figure compromise of two equal semicircles ABC, CDE and a semi circle AFE. Given AC= 7cm.
Calculate
a) Area of the shaded portion
b) The length of the boundary AFEDCBA.
53) Given A= 30 and B= 60 verify that sin(B- A)= sinB cosA - cosB sinA.
54) Given 2 tanθ = 5 , find the value of
(3 sinθ - 4 cosθ)/(Sinθ + 4 cosθ).
55) The denominator of a fraction is 3 more than the numerator. The sum of the fraction and its reciprocal is 29/10. Find the fraction.
Maths- 4
1) One of the factors of (9x²-1) - (1+ 3x)² is
a) 3+x b) 3- x c) 3x -1 d) 3x +1
2) Which of the following needs a proof?
a) theorem b) axiom c) definition d) postulate
3) An exterior angle of a triangle is 110 and the two interior opposite angles are equal. Each of these angles is
a) 70 b) 55 c) 35 d) 110
4) Two sides of a triangle are of lengths 7cm and 3.5cm. The length of the third side of the triangle cannot be
a) 3.6cm b) 4.1cm c) 3.4cm d) 3.8cm
5) The coefficient of x² in (2x⅖-5)(4+ 3x²) is
a) 2 b) 3 c) 8 d) - 7
6) In triangle ABC and DEF, angle A= angle D, angle B= angle E and AB= EF, then are the two Triangles congruent ? If yes, by which congruence criterion ?
a) yes by AAS b) no c) yes by ASA d) yes by RHS
7) Two lines are respectively perpendicular to two parallel lines. Then these lines to each other are
a) perpendicular b) parallel c) intersecting d) inclined at some acute angle.
8) Is (8/15)³ - (1/3)³ - (1/5)³= 8/75?
9) Evaluate ³√(-1/27)²
10) In an isosceles triangle, prove that the altitude from the vertex bisect the base.
11) Simplify 2√6/(√2+ √3) + 6√2/(√6+ √3)
OR
If (√5+ √3)/(√5- √3)= a - √15 b find the values of a and b.
12) if a= 9 - 4√5, find the value of a - 1/a.
Or
If x= 3+ 2√2, find the value of x²+ 1/x²
13) Find the value of x³+ y³ when x+ y= 5 and xy= 20.
Or
If a+ b+ c = 6, find the value of (2- a)³+ (2- b)³+ (2- c)³ - 3(2- a)(2- b)(2- c).
14) Find the area of a triangle, two sides of which are 18cm and 10cm and the perimeter 42cm.
15) Factorize: x¹² - y¹².
16) In ∆ ABC, right angled at A,
AL is drawn perpendicular to BC prove that angle BAL= Angle ACB.
Maths -3
1) Draw a bar graph for the maximum temperature for 7 days of week in a city.
Day max.tempreture
Monday 29
Tuesday 32
Wednesday 34
Thursday 31
Friday 37
Saturday 39
Sunday 28 (2)
2) A father is 3 times as old as his son in 15 years. He will be only twice as old. Find their present ages. (2)
3) The number of the sticks of 22 Matchboxes is as follows: 57, 58, 63, 61, 60, 59, 58, 60, 61, 58, 59, 59, 60, 61, 65, 63, 64, 65 tabulate these raw scores into a table. (2)
4) The distribution of the weight(in kh) of the students of the class was tabulated as given. draw a histogram:
Weight: no of people
25-27 2
27-29 5
29-31 12
31-33 18
33-35 25
35-37 10
37-39 4
39-41. 1. (3)
5) In a country the men and women in various professions were:
professions men women
Workers 87 63
teachers 54 114
Nurses 43 153
Servants. 39 86
doctors 76 69
Vendors 28. 17
Draw a multiple bar diagram for the above data. (3)
6) Given below are the mass of 27 students in a test :
21, 3, 28,38, 6, 40, 20 , 26, 9, 18,14, 18, 20, 16, 17, 10, 8, 5, 22, 27, 34, 2 ,35, 31, 16, 28, 37
i) using the class interval 1-10, 11- 20.....etc. construct a frequency table.
ii) State the range of these marks.
iii) State the class marks of the third class of the of your frequency table. (3)
7) By joining the following in order, what figure can be obtained: (-3,2),((-5,3),(-5,6) and (-3,5). (3)
8) A sailor goes 8 km downstream in 40 minutes and returns back to the starting point in 1 hour. Find the speed of boat in still water and speed of the current. (3)
9) If the numerator of a fraction is increased by 2 and its denominator decreased by 1, then it becomes 2/3. Again numerator is increase by 1 and denominator increased by 2, then it becomes 1/3. find the fraction. (3)
10) In a rhombus ABCD show that: AB ²+ BC ²+ CD ²+ AD ²= AC ²+ BD ². (4)
11) In an equilateral triangle ABC. If AD perpendicular to BC. Show that 3 AB ²= 4 AD ². (4)
12) Draw a histogram frequency polygon:
height no of boys
140-145 24
145-150 32
150-155 16
155-160 37 (4)
Test Paper-8
Section - A (10 x 1=10)
1) In the given figure,
angle BPC=19°, arc AB= arc BC= arc CD. Then, measure of angle APD is
a) 38° b) 59° c) 57° d) 76°
2) The given figures show two congruent circles with centre O and O'.
Arc AXB subtends an angle of 75° at the centre and arc A'YB' subtends an angle of 25° at the centre O'. Then , the ratio of arc AXB to A'YB' is
a) 3:1 b) 1:3 c) 2 : 1 d) 1:2
3) Greatest chord of a circle is called its
a) radius b) diameter c) chord d) secant
4) In the given figure,
if OA = 5cm, AB= 8cm and OD is perpendicular to AB, then CD is equals to
a) 2 cm b) 3 cm c) 4cm d) 5 cm
5) If a straight line APQB is drawn to cut two concentric circles,
then
a) AP> BQ b) AP= BQ c) AP< BQ d) AQ> PB
6) The radius of a circle is 5cm and the length of one chord is 8cm. The distance of the chord from the centre.
a) 4cm b) 3cm c) 5cm d) 6cm
7) In a quadrilateral ABCD, AB|| DC and AD= BC= 5.5cm, and one of the angles is 80°, then the other angles are
a) 90,90,100 b) 120,80,80 c) 80,100,100 d) 110,85,85
8) Which of the following is not true for a parallelogram ?
a) opposite sides are equal
b) opposite angles are always bisected by the diagonals
d) diagonals bisect each other.
9) ABCD is a rhombus
in which angle BCD= 100, then (x + y) equals to
a) 40 b) 60 c) 80 d) 70
10) Given a trapezium PQRS such that PQ= 12cm, RS= 5cm, PQ|| SR, PS= QR= 8cm, If Ang R = 130°, then angle P is
a) 130 b) 50 c) 150 d) 120
Section - B
(13x4= 52)
11) The given figure 
show the circumcircle of an equilateral triangle. If the radius of the circumcircle is 20cm, find the length of each side of the equilateral triangle.
12) In a circle of radius 7.5cm, AB and BC are two equal chords, 
each of length 9cm. Find the length of the chord AC.
13) Two circles of radii 17cm and 10cm intersect at two points and the length of the common chord is 16cm. Find the distance between their centres.
14) In the given figure,
the straight lines l, m and n are parallel to each other and G is the midpoint of CD. Calculate
a) BG, if AD= 7cm
b) CF, if GE= 2.5cm
c) AB, if AC= 9cm.
d) ED, if FE= 4cm.
15) ABCD is a quadrilateral P,Q,R, S are the midpoints of AB, BC, CD and DA respectively.
If AC= 6cm, BD= 8.6cm, calculate PQ, QR, SR and PS.
16) ABCD and AEFG are two parallelogram.
If Angle C= 58, determine angle F.
17) In the given figure, ABCD is a parallelogram,
AX and CY are respectively the bisectors of opposite angle A and C. If Angle DCB= 80, find the measure of angle DAX.
18) In the given figure ABCD is a parallelogram. E is the midpoint of CD and through D a line is drawn parallel to EB to meet CB produced at G and it cuts AB at F.
Show that
a) AD= (1/2) GC
b) DG= 2EB
OR
Prove that the line segment joining the midpoints of the diagonals of a trapezium is parallel to the parallel sides and equal to half their difference.
19) PQRS is a parallelogram. PO and QO are respectively the angle bisectors of angle P and Q. Line LOM is drawn parallel to PQ.
Prove that
a) PL= QM
b) LO= OM.
20) The base of a right angled triangle is 24cm and its hypotenuse is 25cm. Find the area of the triangle.
21) The area of a triangle is 216cm² and its sides are in the ratio 3:4:5. Find the perimeter of the triangle.
22) If the length and breadth of a rectangular room are each increased by 1m, then the area of floor is increased by 21m². If the length is increased by 1m and breadth is decreased by 1m, then the area is decreased by 7m². Find the perimeter of the floor.
23) A rectangular lawn 60m by 40m has two roads, each 5m wide, running in the middle of it, and parallel to length and the other parallel to breadth. Find the cost of gravelling them at Rs3.60 per m²
24) Find the area of a trapezium ABCD in which AB|| DC, AB= 77cm, BC= 25cm, CD= 60cm and DA= 26cm
TEST PAPER -7
Simplify:
1) (l⁴m⁶/n⁸). (m⁸n⁴/l⁻⁶).(n⁶l⁶/m⁴)².
2) solve:
a) ³√(5/4)ˣ⁺²= 4096/15625. -20
b) 3²ˣ+ 2.3ˣ - 99= 0. 2
c) 3ˣ⁺³ - 3ˣ⁻³= 6552 then find x². 25
3) If x= ³√2 +³√4, what is value of x³ - 6x ?
4) ᵧp/(p+q+r). ᵧq/(p+q+r) ᵧr/(p+q+r).
A) y B) 1 C) 1/y D) y²
5) If a.5²= 2020.20, what is the value of 10⁻³a/10⁴
6) 5ˣ⁺³ - 5 ˣ⁻³ =78120, find x.
A) 4 B) 3 C) 5 D) 6 E) 7
7) If x¹⁾ᵃ = y¹⁾ᵇ = z¹⁾ᶜ and a+b+c= 0, show that xyz = 1
8) 6x + 5y=7x +3y+1=2(x+6y-1). 3,2
9) Find the area of a triangle whose base is 15cm and the corresponding height is 9.6cm. 72
10) solve for c and y
a) 2x+3y= 0, 7x +y= 23.
b) solve: 5x-8y= -4; 2x-7y= 6.
11) A room is half as long again as it is broad. The cost of carpeting the room at ₹18 per m² is ₹972 and the cost of white washing the four walls at ₹6 per m² is ₹1080. Find the dimensions of the room.
12) The base of an isosceles triangle is 24cm and it's area is 192 cm². Find its perimeter.
13) The wheel of a cart making 5 revolutions per second. if the diameter of the wheel be 84cm find its speed in km/hr. give your answer, correct to nearest km.
14) Find the volume, the surface area and the diagonal of a cuboid 12cm long, 4cm wide and 3cm high.
15) Area of a concentric circle ⭕ is 346.5 cm². The circumference of the inner circle is 88cm. Find the radius of the outer circle.
16) A bucket is raised from a well by means of a rope which is wound round a wheel of diameter 77cm. given that the bucket ascends in 1 minute 28 seconds with a uniform speed of 1.1m/s. calculate the number of complete revolutions the wheel makes in raising the bucket. Take π to be 22/7.
Test paper - 6
1) The compound interest on a certain sum of money at 5% p.a for 2 years is 246. Find the simple interest on the same sum for 3years at 6% p.a.
2) What sum of money will amount to ₹ 3630 in two years at 10% p.a. compound interest?
3) Show that the points (3,3),(9,0) and (12,21) are the vertices of a right angled triangle.
4) Find the mean of first five prime numbers.
5) Expand (2x + 1/3x)².
6) A man invests ₹ 5000 for 3 years at a certain rate of interest, compounded annually. At the end of one year it amounts to ₹5600. Find
A) the rate of interest.
B) interest in the 2nd year.
C) The mount at the end of 3rd year.
7) using formula find the value of 124 x 116.
8) expand: (√2 m + √3 n)².
9) Show that (_1,1),(2,3) and (8,11) are collinear.
10) Find the mean of all the factors of 20.
Test paper - 5
1) A pit 7.5 metre long, 6 metres wide and 1.5m deep is a dug in a field in a field. find the volume of soil removed.
2) Find the length of the longest pole that can be placed in an Indoor Stadium 24 metre long. 18 metre wide and 16m high.
3) The Length, breadth and the height of a room are in the ratio of 3:2:1. If volume be 1296m³, find its breadth.
4) The whole surface of a rectangular block is 8788 square cm. If Length, breadth and height are in the ratio of 4:3:2, find its length.
5) Three metal cubes with edges 6cm, 8cm and 10cm respectively are melted together and formed into a single cube. Find the side of the resulting cube.
6) Find the number of bricks, each measuring 25cm x 12.5cm x 7.5cm, required to construct a wall 12m long, 5m high and 0.25m thick, while the sand and cement mixture occupies 5% of the total volume of wall.
7) Seven equal cubes each of side 5cm are joined end to end. Find the surface area of the resulting cuboid.
8) In a swimming pool measuring 90m by 40m, 150 men take a dip. If the average displacement of water by a man is 8 cubic metres, what will be the rise in water level?
9) A closed wooden box measures externally 10cm long, 8 cm broad and 6cm high. Thickness of wood is 0.5 cm. find the volume of wood used.
10) A cuboid of dimension 24cm x 9cm x 8cm is melted and smaller cubes are of side 3cm is formed. Find how many such cubes can be formed?
11) Three cubes each of volume of 216m³ are joined end to end. find the surface area of the resulting figure.
12) The area of of three adjacent faces of a cuboid are are x,y, z. if the volume is V, then V² will be equals to.
Test paper - 4
1) If cotx = 7/7.5, then cosecx is
a) 7.5/4 b) 8/17 c) 17/15 d) 15/17
2) If 2x = secA and tanA= 2/x then the value of 2(x²- 1/x²)²= ?
a) 1/2 b) 1/4 c) 1/8 d) 1/16
3) The value of (sin43° . cos47°+ cos43° sin47°) is
a) 0 b) 1 c) sin4° d) cos4°
4) If tanx = 4/5, then cosx =
a) 4/5 b) 3/5 c) 3/4 d) 5/√41
5) If sinx = 1/√2, then sec2x =
a) 0 b) 1 c) 2 d) none
6) The value of ( tan35/cot55 + cot78/tan12) is
a) 0 b) 1 c) 2 d) none
7) ABC is a triangle. Then sin{(B+ C)/2}=
a) sin(A/2) b) cos(A/2) c) sinA d) cosA
8) The simplest value of cos53°/sin37° is _____.
9) if tan35° tan55°= sinx, then lowest positive value of x will be_____.
10) If cos²x - sin²x = 1/x (x > 1), then cos⁴x - sin⁴x = ____.
11) The value of (sin 12 . cos 18. sec 78. Cosec72) is___.
12) The value of tan 15 tan 45 tan 60 tan 75 is ____.
13) if tanx = 4/5, then x = ____.
14) If sinx =1/2, then cos2x =_____.
15) cosx= √3/2, then sin2x=_____. √3/2
16) The value of (4/sec²x + 1/(1+ cot²x) + 3 sin²x) is ____.
17) If sinx =1/2, then tan2x =___.
18) If sin(x - 30°)= 1/2, then the value of cosx is_____.
19) A person deposited Rs100 in a bank and gets the amount Rs121 after 2 years. The rate of compound interest is____%.
20) If the simple interest for n years at r% p.a. be Rs Pnr/25, then the principle will be Rs____.
21) At same rate percent per annum, the simple interest and compound interest of same principal are same in ____ year.
22) A person depreciates at a certain rate over time is called____.
23) The person who gives loan is called____.
24) Amount of Rs2P per t years at the rate of simple interest r/2% per annum (2P+ ____) Rs.
25) if the ratio of principle and amount for 1 year is 8:9, then the rate of the simple interest per annum is_____.
26) Fixed amount rupee fixed annual interest rate one year compound interest rate and simple interest rate ____.
27) With the passage of time, someone grows at a certain rate , it is called___.
28) if a principal becomes twice of it in 10 years, then the rate of a simple interest for annum is
a) 5% b) 10% c) 15% d) 20%.
29) Interest on Rs a at the simple interest 10% per annum for b months is
a) ab/100 b) ab/120 c) ab/1200 c) ab/10.
30) If the ratio of principal and yearly amounts be in the ratio 25:28, then the yearly rate of interest is
a) 3% b) 12% c) 75/7% d) 8%
31) If the total interest becomes Rs x for any principal having the rate of simple interest of x% per annum for x years then the principal will be
a) Rsx b) Rs 100x c) Rs 100/x d) Rs 100/x²
32) The total interest of a principal in n years, at the rate of simple interest of r% per annum is one/109, the principle will be
a) Rs2p b) Rs4p c) Rs3p d) 5p.
33) If the interest on Rs p at the rate of simple interest of r% per annum in t years is I, then
a) I= prt b) prt I= 100. I c) prt = 100. I d) none.
34) A principal becomes twice of its amount in 20 years at a certain rate of simple interest. At that same rate of simple interest, that principal becomes thrice of its amount in
a) 30 years b) 35 years c) 40 years d) 45 years
35) A sum of Rs400 amounts to Rs480 in 4 years. What will it amount to if the rate of interest is increased by 2% ?
a) Rs484 b) Rs560 c) Rs512 d) none
36) At what rate of percent per annum will Rs2304 amount to Rs2500 in 2 years at compound interest ?
a) 9/2% b) 21/5% c) 25/6% d) 13/3%
37) An amount doubles itself in 5 years with simple interest. What is the amount of interest percent per annum?
a) 10% b) 20% c) 25% d) 30%
38) A person deposited Rs109 in a bank and got the amount Rs121 for 2 years. The rate of compound interest is
a) 10% b) 20% c) 5% d) 21/2%
39) In case of compound interest, the rate of compound interest per annum is
a) equal b) unequal c) both equal or unequal d) none.
40) In case of compound interest
a) The principals remains unchanged each year
b) principal changes in each year
c) principal may be equal or unequal in each year d) none
41) On What sum of money, the difference be
tween the simple interest and compound interest in 2 years at 5% per annum is Rs15 ?
42) A certain sum of money invested at 5% intrest, compounded annually, for 3 years. If the interest computes to Rs2522, determine the principal.
43) In how many years will a sum of Rs800 at 10% per annum compounded semi-annually become Rs926.10 ?
44) Suraj has a fixed deposit in Bank of India of Rs40000 for a period of 3 years. The bank allows a compound interest of 13% compounded half yearly. Find the maturity value.
45) Find the difference between compound and simple intrest at 5% per annum for 4 years on Rs20000.
46) If 4ˣ = 8ʸ then find x/y - 1.
47) Evaluate: (2ᑫ. 6ᵖ⁺¹. 10ᵖ⁻ᑫ . 15ᵖ⁺ᑫ⁻²)/(4ᵖ. 3²ᵖ⁺ᑫ. 25ᵖ⁻¹).
48) If log2= x and log3= y, then find the value for log60.
49) Evaluate: 4 log(8/25) - 3 log(16/125) - log 5.
50) Solve: 3x²- 14x +16=0.
51) Solve: x²- (a+ b)x + ab=0.
52) In ∆ABC, AB=26cm, BC=28cm and the altitude AD=24cm. Calculate AC.
53) The area between two concentric circles is 3168cm². Find the radii of the two circles if
A) their sum is 42cm
B) their difference is 28cm
54) (3+ √5)/(3- √5)= a + b √5, find the value of a and b.
55) If x= 4 +√15. Then find the value of x² + 1/x²
56) Simplify (√11- √7)(√11+ √7)
57) Rationalise: 1/(7+ 3 √2)
58) Rationalise: 5/(3√3+ 2√2).
59) If (2/3)⁶(9/4)⁵=(3/2)ᵐ⁺² then find the value of m
60) simplify: x³ +3 √x³/√x
61) simplify: (√3+ 1)(1- √12)+ 9/(√3+ √12)
Factorization
62) 12x² - 7x +1
63) 2x² + 7x +3.
64) 6x² + 5x -6.
65) 3x² - x - 4
Test paper -3
1) A bar graph is drawn to the scale 1cm= k units, then a bar of length k cm represents
a) 1 unit b) k units c) 2k units d) k² units
2) A bar graph is drawn to the scale of 1 cm = x units. If the length of a bar representing a quantity of 702 units is 3.6cm, then x=
a) 165 b) 175 c) 185 d) 195
3) In figure
bar graph represents sales of two wheelers and four wheelers in a mega city from 2013 to 2016. In which year the difference between the sales of two wheelers and four wheelers is less ?
a) 2013 b) 2014 c) 2015 d) 2016
4) In the figure, the total number of vehicles (two wheelers and four wheelers ) sold in the year 2013 and 2014 is
a) 26100 b) 28500 c) 25100 d) 27500
5) In figure, the maximum difference between sales of two wheelers and that of four wheelers, in any year, in the given period is :
a) 1500 b) 1700 c) 1800 d) 2000
6) In figure, the total number of two wheelers sold in four years is
a) 26000 b) 27000 c) 31000 d) 32000
7) in a bar graph, the height of a bar is 5cm and it represent 40 units . The height of the bar representing 56 units is:
a) 11.2cm b) 5.6cm c) 7cm d) 8cm
8) in a bar graph, length of a bar is 6.4cm and it represent 256 units. The number of units represented by a bar of length 5.3cm is
a) 228 b) 196 c) 212 d) 224
9) In a bar graph, the height of a bar is proportional to the
a) width of the bar b) range of the data c) value of the component d) number of observation in the data.
10) Which one of the following is not the graphical representation of statistical data ?
a) bar graph b)?histogram c) frequency polygon d) cumulative frequency distribution
11) In a frequency distribution, ogives are graphical representation of
a) frequency b) relative frequency c) cumulative frequency d) raw data.
12) A frequency polygon is constructed by plotting frequency of the class interval and the
a) upper limit of the class b) lower limit of the class c) mid value of the class d) any values of the class
13) In a Instagram the area of each rectangle is proportional to
a) the class marks of the corresponding class interval.
b) the class size of the corresponding class interval
c) frequency of the corresponding class interval.
d) cumulative frequency of the corresponding class interval .
14) In the 'less than' type of ogive the cumulative frequency is plotted against
a) the lower limit of the concerned class interval.
b) the upper limit of the concerned class interval .
c) the mid value of the concerned class interval.
d) any value of the concerned class interval.
15) In a histogram the class interval or the groups are taken along
a) y-axis b) x-axis c) both of x-axis and y-axis d) in between x and y-axis .
16) A histogram is a pictorial representation of the grouped data in which class intervals and frequency are represpectively taken along
a) vertical axis and horizontal Axis
b)!vertical access only
c) horizontal Axis only
d) horizontal axis and vertical axis.
17) In a histogram, each class rectangle is constructed with base as
a) frequency b) class intervals c) range d) size of the class
18) Consider the following frequency distribution :
Class interval Frequency
5-10 6
10-15 12
15-25 10
25-45 8
45-75 15
To draw a histogram to represent the above frequency distribution the adjusted frequency for the class 25-44 is
a) 6 b) 5 c) 3 d) 2
19) Figure shows the bar graph of number of boys and number of girls in a school from 2014 to 2017.
In which year the difference between the number of boys and the number of girls was more ?
a) 2014 b) 2015 c) 2016 d) 2017
20) In figure, total number of students in the year 2015 was
a) 1160 b) 1270 c) 1380 d) 1490
21) In figure , the minimum difference between the number of boys and girls in any year in the given period was
a) 90 b) 70 c) 50 d) 30
22) In figure, in which year the number of girls more than the number of boys?
a) 2014 b) 2015 c) 2016 d) 2017
23) In figure , the ratio between the number of student in the year 2016 and 2017 was
a) 107 :145 b) 127 : 145 c) 29 :36 d) 107: 127
CASE STUDY
1) Following bar graph represents the sales of the cold drinks of two companies A and B from 2015 to 2018.
i) The year in which the difference between the sells of two companies was highest, was
a) 2018 b) 2015 c) 2016 d) 2017
ii) Total sales of A and B in the year 2016 was
a) 1160000 b) 1270000 c) 1380000 d) 1490000
iii) The minimum difference between the sales of company A and B in any year in the given period was
a) 90000 b) 70000 c) 50000 d) 300000
iv) In which year was the sales of company B more than the sales of company A?
a) 2015 b) 2016 c) 2017 d) 2018
v) The ratio of the total sales in the year 2017 and that in 2018 was
a) 107 :145 b) 29:36 c) 127: 145 d) 107: 127
2) Read the following bar graph and answer the following questions:
a) 2015 b) 2016 c) 2017 d) 2018
ii) Total number of the vehicles (scooters and cars) sold in the year 2015 and 2016 was
a) 26100 b) 28500 c) 25100 d) 27500
iii) The maximum difference between the sales of scooters and cars , in the given period was
a) 1500 b) 1700 c) 1800 d) 2000
iv) The total number of scooters sold in the 4 years was
a) 26000 b) 27000 c)!31000 d) 32000
v) The ratio between the total number of vehicles sold (scooters and cars) in the year 2016 that in the year 2018.
a) 41: 46 b) 69: 91 c) 147 :182 d) 46: 49
3) Population census in India is conducted every 10 years. The first complete census was taken in 1881 and 15th decennial census taken in 2011. The 16th decennial census was to be conducted in 2021 but due to the COVID it will be taken in 2022. The data obtained from the census of a town has been represented by a bar graph shown in figure. It represents the number of persons living in various age groups in the town. Observe the bar graph and answer the following questions:
a) 2000 b) 2200 c) 2100 d) 1900
ii) How many persons are more in the age group 10 to 15 than in the age group 30 to 35 ?
a) 200 b) 250 c) 300 d) 350
iii) What is the total population of the town ?
a) 6700 b) 6400 c) 7700 d) 6600
iv) What is the number of persons in the age-group of 60-65 ?
a) 900 b) 750 c) 850 d) 800
v) What is the age group of exactly 1200 persons living in the town ?
a) 10 to 15 b) 20-25 c) 30-35 d) 40-45
4) A healthcare survey was done by the State Health and Family Welfare Care Board of the State of Punjab. The data is collected by forming age groups i.e.,10 - 15, 20 -25, 30 -35, 40 -45, 50 -55, 60- 65, 70-75. The overall data from a town is the given below in the form of a bar graph. Read the data carefully and answer the question that follow :
ii) What is the age group of exactly 1200 persons living in the town?
iii) What is the percentage of the youngest age group persons over those in the oldest age group?
iv) What is the total population of the town ?
5) Find the difference between compound and simple intrest at 5% per annum for 4 years on Rs20000.
6) Solve: z + √z = 6/25.
7) (6x+2)/4 + (2x²-1)/(2x²+2) = (10x -1)/4x.
8) Factorize:
a) a⁴- 2a²b² + b⁴
b) x⁴- (y+ z)⁴
9) Evaluate:cos²60. Cos²45. Cos²30.
10) If tanx =a/b, find the value of (a sinx + b cosx)/(asinx - b cosx).
11) A diameter of a circle has the extreme points (7,9) and (-1,-3). Then find coordinates of the centre.
12) 4ˣ⁻¹ = 3. 2ˣ - 8. Find x.
13) If (5⁵ + 0.01)² - (5⁵ - 0.01)²= 5ˣ then x is
14) If log2= 0.3010, log3= 0.4771, log7= 0.8451, find the value of log294.
Test paper -2
1) Evaluate:
a) log5+ log20 + log 24 + log 25 - log 60.
b) log 6+ 2 log 5 + log 4 - log 3 - log 2.
c) 7log(16/15) + 5log(25/24) + 3log (81/80).
d) (log 32)/(log 4).
e) log27)/( log 9).
2) Express (2log 3 - (1/2) log 160 + log 12) as a single logarithm.
3) If log 2 = x, log 3= y and log 7= z, express log(4 ³√63) in terms of x, y and z.
4) Solve:
a) log₁₀x - log₁₀(2x -1)= 1.
b) log₅(x²+ x) - log₅(x +1)=2.
c) log₁₀5+ log₁₀(5x +1)= log₁₀(x +5)+ 1.
5) If log₁₀y + 2 log₁₀x =2, express y in terms of x.
6) If log = 0.3010 and log 3= 0.4771, find the value of
a) log 6.
b) log 48.
c) log √24.
d) log ⁵√108.
TEST PAPER -1
1) Ifx²+ y²+ z²= 40 and xy+ yz + xz= 30, then x+ y+ z is equal to
a) only+10 b) only -10 c) ±10 d) ±70
2) Simplify: (3.59 x 3.59 - 2.41 x 2.41)/(3.59 + 2.41).
3) Factorise: a(a -3) - b(b -3).
4) If x²+ 1/x²= 7, find the value of x + 1/x.
5) If x²+ 1/x²= 83, find the value for x³- 1/x³.
6) Factorise: x²+ x/6 - 1/6.
7) Find the percentage increase in the area of a triangle if each of its side is doubled.
8) The length of the longest rod that can be placed in a room 12m long, 9m broad and 8m high is
a) 15m b) 20m c) 18m d) 17m
9) Given below is the data of mode of transport used by school going students (girls and boys) to go to school.
Mode of transport bus walking bicycle other
Number of girls 100 42 35 120
Number of boys 64 90 130 86
Draw a bar graph to represent the above data.
10) For the following data, draw a histogram and a frequency polygon
Class interval frequency
00-10 13
10-20 20
20-30 15
30-40 12
40-50 5
11) The mean of 20 numbers is 9. If 3 is added to every number what will be the new mean.
12) Find the mean, median, mode of the following marks obtained by 16 students in a class test marked out of 10 marks.
0,0,2,2,3,3,3,4,5,5,5,5,6,6,7,8.
EXPONENTS
EXERCISE - 2(A)
A) 1⁵ B) 5⁰ C) 0⁵ D) 5¹
a) A and B b) B and C c) A and C d) A and D
2) (6⁰ - 2⁰)(6⁰+2⁰)= ?
a) 0 b) 1 c) -1 d) 2
3) The multiplicative inverse of 10⁻¹⁰⁰ is
a) 10 b) 100 c) 10¹⁰⁰ d) 1/10¹⁰⁰
4) The multiplicative inverse of (-4/9)⁻⁹⁹
a) (-4/9)⁹⁹ b) (4/9)⁹⁹ c) (9/-4)⁹⁹ d) (9/4)⁹⁹
5) If 5ˣ = 3125 then the value of 5ˣ⁻³ is
a) 25 b) 125 c) 625 d) 1625
6) The value of (256)⁵⁾⁴ is
a) 512 b) 984 c) 1024 d) 1032
7) The value of 27⁻²⁾³ lie between
a) 0 and 1 b) 1 and 2 c) 2 and 3 d) 3 and 4
8) The value of (32/243)⁻⁴⁾⁵ is
a) 4/9 b) 9/4 c) 16/81 d) 81/16
9) The value of (-1/216)⁻²⁾³ is
a) 36 b) -36 c) 1/36 d) -1/36
10) 120m²n⁻³/60m⁵n⁻² (m ≠0, n≠ 0) when expressed in simplest form becomes
a) 2m³/n b) 1/2m³n c) 2/m³n d) 2n/m³
11) The value of [2 - 3(2- 3)⁻¹]⁻¹ is
a) 5 b) -5 c) 1/5 d) -1/5
12) Evaluate: 5¹⁾⁴ x (125)⁰·²⁵
a) √5 b) 5 c) 5√5 d) 25
13) (256)⁰·¹⁶ x (256)⁰·⁰⁹ =?
a) 4 b) 16 c) 64 d) 256
14) The value of (8⁻¹ - 9⁻¹)⁻¹ ÷ (4⁻¹ - 9⁻¹)⁻¹ is
a) 5 b) 10 c) 14 d) 25
15) If p= (2⁻² - 2⁻³), q= (2⁻³ - 2⁻⁴) and r= (2⁻⁴ - 2⁻²) then the value of 3pqr equal
a) 9/1024 b) -9/2048 c) -63/2048 d) -63/1024
16) (64)⁻¹⁾² - (-32)⁻⁴⁾⁵ =?
a) 1/8 b) 3/8 c) 1/16 d) 3/16
17) (16)⁰·¹⁶ x (16)⁰·⁰⁴ x (2)⁰·² is
a) 1 b) 2 c) 4 d) 16
18) If m,n are positive integers (n > 1) such that mⁿ = 121 then the value of (m -1)ⁿ⁺¹ is
a) 1 b) 11 c) 1000 d) 12321
19) When simplified, (x⁻¹ + y ⁻¹) is equal to
a) (x+y)/xy b) xy c) 1/xy d) xy/(x + y)
20) Which of the following is the same as (-5/7)⁻⁷ ?
a) (5/6)⁻⁷ b) -(5/7)⁻⁷ c) (7/5)⁷ d) (-7/5)⁷
21) The value of 5³ ÷ 5⁻⁴ is
a) 5⁻¹ b) 5⁷ c) 5 d) 5⁻⁷
22) The value of (7⁻¹ - 8⁻¹)⁻¹ - (3⁻¹ - 4⁻¹)⁻¹ is
a) 12 b) 44 c) 56 d) 68
23) Which of the following is not true?
a) 343 x 7ⁿ⁻²= 7ⁿ
b) (2ⁿ)/4 = 2ⁿ⁻²
c) 25(5ⁿ⁻²)= 5ⁿ
d) 4ⁿ⁻¹ = 4ⁿ/4
24) Which of the following is not true to y⁶
a) (√y⁶)² b) ³√y¹⁸ c) (y¹⁾³)¹² d) (y²⁾³)⁹
25) If 3ˣ⁺ʸ = 81 and 81ˣ⁻ ʸ = 3⁸ then the values of x and y are
a) -1.-3 b) -1,3 c) 1,3 d) 3,1
26) When simplified and expressed with negative exponens, the expression (x + y)⁻¹.(x⁻¹ + y⁻¹) is equal
a) x⁻² + 2x⁻¹y⁻¹+ y⁻² b) x⁻¹ y⁻¹ c) x⁻²+ 2⁻¹ x⁻¹ y⁻¹ + y⁻² d) x⁻² + y⁻²
27) By what number should we multiply (-8)⁻¹ so that the product may be equal to (10)⁻¹ ?
a) 4/5 b) 5/4 c) -4/5 d) -5/4
28) If x= 1/{(3/2)⁻² x (2/3)⁻⁴} then the value of x⁻³ is
a) (2/3)¹⁰ b) (2/3)⁻⁶ c) (3/2)⁻¹² d) (3/2)⁸
29) Each of the numbers 1,2,3 and 4 is substituted, in some order for a,b,c and d. The greatest possible value of aᵇ + cᵈ is
a) 14 b) 19 c) 66 d) 83
30) If {(p⁻¹q²)/(p³q⁻²)} ÷ {(p⁶q⁻³)/(p⁻²q³)}= pᵃqᵇ then the value of a+ b, where p and q are different positive primes, is
a) -2 b) -1 c) 0 d) 1
31) If √2ⁿ = 64 then the value of n is
a) 2 b) 4 c) 6 d) 12
32) Out of the following, which one is the greatest?
a) (0.008)¹⁾³ b) 0.01¹⁾² c) 0.2² c) 1/100
33) (343 x 49)/(2 6 x 16 x 81)=?
a) 7⁵/6⁷ b) 7⁵/6⁸ c) 7⁶/6⁷ d) 7⁴/6⁸
34) (1000)¹²÷ +10)³⁰=?
a) 1000² b) 10 c) 100 d) 100²
35) 8⁷ x 2⁶ ÷ 8²·⁴ = 8^?
a) 6.6 b) 8.6 c) 9.6 d) 10.6
36) (0.04)² ÷ (0.008) x (0.2)⁶= (0.2)^?
a) 5 b) 6 c) 8 d) 7
37) (25)⁷·⁵ x (5)²·⁵ ÷ (125)¹·⁵ = 5^?
a) 8.5 b) 13 c) 16 d) 17.5
38) If 2⁰·² x 64 x 8¹·³ x 4⁰·² = 8ˣ then the value of x is
a) 2.5 b) 2.7 c) 3.5 d) 3.7
39) If 2ˣ⁺¹ = 8ˣ then x has the value
a) -1/3 b) 1/2 c) 1 d) 3
40) Which of the following is equal to (3)⁻³ - √81/√25 + (√64)⁻²⁾³/(16)⁻¹⁾⁴ ?
a) -1/541/54-341/270341/270
41) Match the Following
Column - I. Column II
a) If 2³⁴÷ 2¹⁶= 2ᵏ then k is i) 32
b) [(-8/13)⁻¹ ÷(16/5)⁻¹]÷ (-5/2)⁻¹=. ii) 9
c) If {25(a⁴)²}/{(5a)³ a⁵ 2⁵}= 1/(5n) then n is iii) 18
d) If +2/7)⁻⁶(14/9)⁻⁶ = (4/m)⁻⁶ then m is. iv) 13
Choose the correct combination:
a) a- iv, b- iii, c- i, d- ii
b) a- ii, b- i, c- iv, d- iii
c) a- iii, b- ii, c- iv, d- i
d) a- iii, b- iv, c- i, d- ii
42) If 3³·⁵ x 21² x 42²·⁵ ÷ 2²·⁵ x 7³·⁵ = 21ˣ then x is
a) 6.5 b) 8 c) 10 d) 12.5
43) What is the value of x if pˣ/pʸ = p¹⁰ and (pʸ)³ = pˣ for p> 1 ?
a) 5 b) 14 c) 20 d) 25
44) Find the value of 2³⁰ + 20³⁰ + 2³⁰+ 2³⁰.
a) 2³² b) 2³⁶ c) 8³⁰ d) 8¹²⁰
45) If 4ˣ + 4ˣ + 4ˣ + 4ˣ + 4ˣ + 4ˣ + 4ˣ + 4ˣ = 1/512 then what is the value of -3/x ?
a) -0.75 b) -4.25 c) 0.50 d) 0.75
46) Given that 9ⁿ + 9ⁿ + 9ⁿ = 3²⁰¹³, what is the value of n ?
a) 1005 b) 1006 c) 2011 d) 6019
47) If 3ˣ⁻¹ + 3ˣ⁺¹ =90 then x is
a) 0 b) 1 c) 2 d) 3
48) If 2ⁿ⁻¹ + 2ⁿ⁺¹ = 320 then n is
a) 5 b) 6 c) 7 d) 8
49) Income of a company doubles after every 1 year. If the initial income was Rs2 lakhs, what would be the income after n years (in lakh of rupees)?
a) 2ⁿ⁻¹ b) 2ⁿ c) 2ⁿ⁺¹ d) 2 + 2ⁿ
50) Breeding of a certain Species of insects occurs at such a rate that everyday the total number of such insects in a closed glass jar is double the number on the previous day. There was just one insect in the jar on 1st of a certain month and the jar was full to the brim with these insects in 28th of the same month. On which day of the month was the jar quarter full?
a) 7th b) 14th c) 26th d) none
51) the microbes in a petri dish double every minute and the petri dish becomes full in 1 hour. In how much time was the dish 1/32 full ?
a) 12 minutes b) 32 minutes c) 45 minutes d) 55 minutes
52) If (x/y)ⁿ⁻¹ = (y/x)ⁿ⁻³ then the value of n is
a) 1/2 b) 1 c) 2 d) 7/2
53) If 2²ⁿ⁻¹ = 1/8ⁿ⁻³ then the value of n is
a) -2 b) 0 c) 2 d) 3
54) If (25)ˣ = (125)ʸ then x: y equal to
a) 1:1 b) 1:3 c) 2:3 d) 3:2
55) If 3ˣ = √3/9 then the value of x is
a) -3/2 b) -2 c) 2/3 d) 3
56) If (9/4)ˣ(8/27)ˣ⁻¹= 2/3 then the value of x is
a) 1 b) 2 c) 3 d) 4
57) If 5²ˣ⁺¹ ÷ 25= 125 then the value of x is
a) 1 b) 2 c) 4 d) 5
58) The cells of a bacteria double in every 30 minutes. Beginning with a single cell, how many cells will be there after 8 hours ?
a) 2⁴ b) 2⁸ c) 2¹⁶ d) 2¹⁷
59) The solution of 3³ˣ⁺⁵ x 2³ˣ⁺³ = 9 is
a) -1 b) 0 c) 1 d) 2
60) If ((25)²ˣ⁺¹x (125)⁵)/(625)²= (3125)³ˣ then the value of x is
a) 0 b) 9/11 c) 1 d) 11/9
61) What number will replace the question mark in the following equation ?
(√8 x √8)¹⁾² + 9¹⁾² = (?)³ + √8 - 340
a) 7 b) 9 c) 18 d) ³√337
62) The simplified value of (2x 3ⁿ⁺¹+ 7 x 3ⁿ⁻¹)/(3ⁿ⁺² - w(1/3)¹⁻ ⁿ is
a) -1 b) 0 c) 1 d) 3
63) If m= (2⁻² - 2⁻³), n= (2⁻³ - 2⁻⁴) and p= (2⁻⁴ - 2⁻²) then the value of m³ + n³ + p³ is
a) -3/1024 b) -9/2048 c) 3/1024 d) 9/2048
64) The value of (125/64)²⁾³ ÷ 1/(625/256)⁻¹⁾⁴ + [{√36/³√64}⁰]¹⁾² is
a) 4/9 b) 6/5 c) 9/8 d) 9/4
65) If 2⁹⁹⁸ - 2⁹⁹⁷ - 2⁹⁹⁶ + 2⁹⁹⁵ = m . 2⁹⁹⁵ then the value of m is
a) 1 b) 2 c) 3 d) 4
66) The value of {(p + 1/p)ᵐ(p - 1/q)ᵐ}/{(q + 1/p)ᵐ(q - 1/p)ᵐ} is
a) p/q b) (p/q)ᵐ c) (p/q)²ᵐ d) (q/p²ᵐ
67) The value of [⁶√2{(625)³⁾⁵x (1024)⁻⁶⁾⁵÷ (25)³⁾⁵}¹⁾²/{(³√128)⁻⁵⁾². (125)¹⁾⁵} is
a) -1 b) 1 c) -1/2 d) 1/2
68) For what value of x is the given statement false ?
a) 3x² < (3x)².
a) -3 b) 0 c) 1/3 d) 1
69) Number of prime factors in (216)³⁾⁵ . (2500)²⁾⁵. (300)¹⁾⁵ is
a) 6 b) 7 c) 8 d) none
70) (xᵃ/xᵇ)ᵃ⁺ᵇ. (xᵇ/xᶜ)ᵇ⁺ᶜ . (xᶜ/xᵃ)ᶜ⁺ᵃ =?
a) 0 b) xᵃᵇᶜ c) xᵃ⁺ᵇ⁺ᶜ d) 1
71) (xᵇ/xᶜ)ᵇ⁺ᶜ⁻ᵃ . (xᶜ/xᵃ)ᶜ⁺ᵃ⁻ᵇ . (xᵃ/xᵇ)ᵃ⁺ᵇ⁻ᶜ =?
a) xᵃᵇᶜ b) 1 c) xᵃᵇ⁺ᵇᶜ⁺ᶜᵃ d) x ᵃ⁺ᵇ⁺ᶜ
72) (xᵃ/xᵇ)¹⁾ᵃᵇ.(xᵇ/xᶜ)¹⁾ᵇᶜ . (xᶜ/xᵃ)¹⁾ᶜᵃ =?
a) 1 b) x¹⁾ᵃᵇᶜ c) x¹/⁽ᵃᵇ⁺ᵇᶜ⁺ᶜᵃ⁾ d) none
73) If aˣ = b, bʸ = c and cᶻ= a then the value of xyz is
a) 0 b) 1 c) 1/abc d) abc
74) The expression (x⁻²ᵖ y³ᑫ)⁶ ÷ (x³ y⁻¹)⁻⁴ᵖ after simplification becomes
a) dependent on both x and y b) independent both x and y c) dependent on x alone d) dependent on y alone
75)
76)
77)
78)
79)
80)
81) (10 + 10³) equal to
a)!1 x 10⁴ b) 1.1 x 10² c) 1.01 x 10³ d) none
82) The value of (8⁻²⁵ - 8⁻²⁶) is
a) 7 x 8⁻²⁵ b) 7x 8⁻²⁶ c) 8 x 8⁻²⁶ d) none
83) Which is greater 2¹² or 3⁸ ?
a) 2¹² b) 3⁸ c) both are equal d) cannot be compared
84) Which of the following is the greatest?
a) 2¹⁾² b) 3¹⁾³ c) 4¹⁾⁴ d) 6¹⁾⁶
85) Which of the following is the greatest?
a) 18⁶ b) 21¹² c) 45⁶ d) 54⁴
86) The ones digit in 5¹⁰⁰ is
a) 0 b) 5 c) cannot be determined d) none
87) The ones digit in 81¹⁰ is
a) 0 b) 1 c) 9 d) none
88) The ones digit in 17²¹ is
a) 7 b) 9 c) 3 d) 1
89) The ones digit in 29¹⁰ is
a) 1 b) 9 c) 7 d) 6
90) The ones digit in 3¹⁷ is
a) 3 b) 9 c) 7 d) 1
EXERCISE - 2(B)
1) In aᵇ, a is called the ____and b is called the____.
2) The value of (-3⁻⁴) is____
3) a⁷ x a⁻¹⁴= ____
4) (2⁰+ 3⁰)= ____
5) The expression for 5⁴ with a negative exponent is____
6) The multiplicative inverse of 10¹⁰ is _____
7) (-2)⁴ ÷ ⁴2 is equals to_____
8) The value of (-8)⁵÷ 8⁵ is ____
9) 3³ x 3⁻³=____
10) The expression for 8⁻³ as a power with the base 2 is _____
11) 1/343 Expressed as a power with base 7 is____
12) On dividing 9⁵ by _____, we get 9.
13) The one digit is 10¹⁰⁰ is____
14) (a/b)ⁿ ÷ (c/b)ⁿ when simplified is equals to____
15) If p= 10, q= 1 then the value of (p + 1)ᑫ⁻¹ is equal to___
16) The value of (1/2)⁻²+ (1/3)⁻² +(1/4)⁻² is____
17) On multiplying____ by 3⁻⁵, we get 3⁵.
18) On multiplying (7/3)⁴ by ____, we get 7⁴.
19) The value of x for which (3/7)⁴ x (3/7)⁻⁷= (3/7)²ˣ⁻¹ is ____
20) If 3. 3ⁿ= 3 then the value of n is ____.
21) Very small numbers can be expressed in standard form by using___ exponents.
22) Very large numbers can be expressed in standard form by using___ exponents.
23) To add the numbers given in standard form, we first convert them into ___ form or into numbers with___ exponents .
24)
25)
26)
27)
28)
29)
30)
TRUE OR FALSE
1) a⁰ - b⁰= 0.
2) aᵖ x bᑫ = (ab)ᵖᑫ.
3) (10)⁻¹⁰⁰ = (100)⁻¹⁰.
4) (-1)⁻¹= -1.
5) (2⁰ + 3⁰ - 4⁰)=1.
6) The reciprocal of (4/5)⁻² is (5/4)².
7) 1⁰ is equivalent to 0¹.
8) Both 7² and 2⁷ are two digit numbers.
9) 10⁵ x 10⁵= 10¹⁰.
10) (3³ + 3⁵) is the same as (³ x 3⁵).
11) 2¹⁰⁰ is the same as (100)².
12) 2ᵐ x 2ⁿ= 2ᵐⁿ.
13) n⁻¹⁾³ x n¹⁾³= 1.
14)
15)
16) (-6)⁻² x (-6)⁻³= (-6)⁻⁶.
17) aᵐ x bᵐ = (a + b)ᵐ.
18) (16)² > 2¹⁶.
19)5¹⁾⁴ x 5⁰·⁷⁵= 5.
20) [(2)⁻²]⁻³ is the same as 2⁶.
21) The one digit of (106)¹⁰⁶ is 6.
22) (81/256)² is equivalent to (3/4)⁸.
23) (-A)⁻ᵐ= 1/aᵐ.
24) The exponential form for (-2)⁴ x (7/2)⁴ is 7⁴.
25) (aᵖ/bᑫ)= (a/b)ᵖ⁻ᑫ .
26) 5. (2ⁿ⁺¹)+ 10(2ⁿ⁻¹) is the same as 15(2)ⁿ
Test paper - Cube and cuboid
1) The total surface area of a cube is 96 cm². The volume of the cube is
a) 27 b) 64 c) 8 d) 512
2) The number cubes whose edge measures 3cm, that can be formed by melting a cubic block of metal of edge 15 cm is
a) 125 b) 45 c) 75 d) 135
3) The difference between the total surface area of a cube of side 4cm and its lateral surface area is
a) 16 cm² b) 20cm² c) 32cm² d) 24cm²
4) The volume of a cube whose diagonal is 2√3cm is
a) 8cm² b) 4 c) 8√3 d) 4√3
5) The number of plancks of dimensions (5m x 25cm x 10 cm) that can be placed in a pit which is 20m long, 6m wide and 80cm deep is
a) 764 b) 840 c) 768 d) 960
6) The number of 6m cubes that can be formed from another cuboid measuring 18m x 12m x 9m is
a) 9 b) 10 c) 12: d) 15
7) The length of the longest rod that can be placed in a room 12m long, 9m broad and 8m high is
a) 15m b) 20m c) 18m d) 17m
8) The edge of a cube whose volume is equal to the volume of a cuboid of dimensions 36cm x 75cm x 80cm is
a) 48 b) 60 c) 36 d) 42
9) A rectangular pit of dimensions 30m x 15m x 12m is dug and the earth taken out is disposed of in a corner which can carry a maximum load of 540m³ of earth . The least number of rounds the carrier had to make to dispose of the earth dug out is
a) 20 b) 10 c) 15 d) 12
10) A ggranery is in the shape of a cuboid of size 16m x 12m x 9m. If a bag of grain occupies a space of 0.48m³, then the maximum number of bags that can be stored in the granery is
a) 1800 b) 3600 c) 2400 d) 3000
11) When a cuboid dimensions 30 cm x 30 cm x 42.6cm is melted and converted into cubes of edge 3cm, then the number of cubes formed is
a) 2840 b) 2130 c) 1420 d) 710
1) In each of the figures given below, an altitude is drawn to the hypotenuse by a right- angled triangle. The length of different line segments are marked in each figure. Determine x,y,z in each case.
a)
6,2√5,3√5
b) 
5,2√5,3√5
2) There is a staircase as shown in figure, connecting points A and B.
3) In the figure calculate
4) In the figure AB|| DC. M is the midpoint of AB. N is the midpoint of DC
Right angles and measurement of sides are indicated in the figure
5) From the diagram, Find
b) Find AD from the right angled triangle ADF. 23.09
6) Given AB= a, BC= √2 a and AC=√3 a
a) 30 b) 45 c) 60 d) 90
7) Calculate
b) Area of quadrilateral WXZY. 234
8) The diagonal of rhombus are 6cm and 8cm. Calculate the perimeter of the rhombus. 20cm
9) PQRS is a trapezium, PQ|| RS, PR meets PQ at 90°. Given PQ=9cm, PR=12cm, RS=5 cm. Calculate QR, PS, Area of PQRS. 15,13, 84
10) AB= AC= BC= 4cm, BC is produced to D such that CD=3 cm.
11) In the figure: angle PSR=90°, PQ=10cm, QS=6 cm, RQ= 9cm.
12) ∆ ABC is right angled triangle at B, AC=10cm. M is midpoint of BC.
13) Triangle ABC is a right angled at B; and BC= 6cm. PQBR is a rectangle. PQ= 2cm, PR= 8cm.
Calculate
a) value of angle PCR. 63°26'
b) length of AC, correct to 1 dp. 13.4
CIRCLE (MENSURATION)
1) The perimeter of the figure,
a semicircle described on AB as a diameter 7.2cm. Find r the radius of the semi circle. (π=22/7)
2) A. rectangular metal plate of the length 35 cm and of width 23cm has a circular hole of radius 7cm cut out. Find the area of the remaining portion of the plate. (π=22/7).
3) In the adjoining figure,
the area enclosed between the concentric circles is 770 cm². Given that the radius of the outer circle is 21cm, calculate the radius of the inner circle.
4) In the adjoining figure,
ABCD is a square inscribed in a circle of radius 7cm. Calculate
a) the area of the circle.
b) the area of the shaded portion. (π= 22/7)
5) ABCD is a square of side 4cm.
Find the area of the shaded portion . Use π=3.14 and give your answer correct to one places of decimal.
6) Find the perimeter of the quarter of the circle whose radius is 3.5cm, correct to one decimal place.
7) A copper wire when bent in the form of a square encloses an area of 121 cm². if the same wire is bent into the form of circle, find the area of the circle.
8) A road 3.5m wide surrounds a circular plot whose circumference is 44m. Find the cost of paving the road at Rs 10 per m².
9) The diameter represents the wiper of a car. With the dimensions given in the diagram,
calculate the shaded area swept by the wiper. (π=22/7).
10) Find the area of the adjoining figure
in sq.cm.correct to one place of decimal. (π=22/7).
11) Find a) the perimeter b) the area of a circle of radius 6.3cm. (π=22/7).
12) Find the perimeter and area of the shaded portion of the figure,
give your answer correct to 3 significant figures. (π=22/7).
PYTHAGORAS THEOREM
1) A right triangle has hypotenuse length p cm and one side of the length q cm. if p - q = 1, find the length of the third side of the triangle.
2) The side of certain triangles are given below. Determine which of them are right angle triangles:
a) a=6cm, b= 8cm and c= 10 cm.
b) a= 5cm, b= 8cm, c= 11cm.
3) A man goes 10m due east and then 20m due north. Find the distance from the starting point.
4) A ladder is placed in such a way that its foot is at a distance of 5m from a wall and its tip reachers a window 12m above the ground. Determine the length of the ladder .
5) A ladder 25m long reaches a window of a building 20m above the ground. Determine the distance of the foot of the ladder from the building.
6) A ladder 15m long reaches a window which is 9m above the ground on one side of a street. Keeping its foot at the same point , the ladder is turned to other side of the street to reach a window 12m high. Find the width of the street.
7) The hypotenuse of a right angle triangle is 6m more than the twice of the shortest side. if the third side is 2 m less than the hypotenuse, find the side of the triangle.
8) In figure ABC is a right angled at B. AD and CE are the two medians drawn from A and C respectively.
If AC= 5cm and AD= 3√5/2 cm, find the length of CE.
9) In an equilateral triangle with side a, prove that
a) altitude =a√3/2
b) area= √3a²/4.
CUBE CUBOID
1) Find the volume, the surface area and the diagonal of a cuboid 12cm long, 4 cm wide and 3cm high . 144,192,13
2) The volume of a cuboid is 440cm³ and the area of its base is 88cm². Find its height. 5cm
3) The volume of a cube is 1000cm. Find the total surface area. 600cm²
4) How many 3 metres cubes can be cut from a cuboard measuring 18m x 12m x 9m? 72
5) A cube of 9cm edge is immersed completely in a rectangular vessel containing water. If the dimension of the base 15cm and 12cm, find the rise in water level in the vessel. 4.05cm
6) The length of a cold storage is double its breadth . Its height is 3 meters. The area of its four walls (including doors) is 108 m². Find its volume. 216m³.
7) Two cubes each of 10 cm edge are joined end to end. Find the surface area of the resulting cuboid. 1000cm²
8) Three cubes edges measure 3cm, 4cm and 5cm respectively to form a single cube. Find its edge. Also find a surface area of the new cube . 6m, 216cm²
9) The sum of length, breath and depth of a cuboid is 19cm and the length of its diagonal is 11cm. Find the surface area of the cuboid. 240cm²
10) A plot of land in the form of a rectangle has a dimension 240m x 180m. A drainlet 10m wide is dug all around it (on the outside) and the earth dug out is evenly spread over the plot, increasing its surface level by 25 cm. Find the depth of the drainlet. 1.227
11) Three cubes each of side 5cm are joined end to end. Find the surface area of the resulting cuboid . 350cm².
12) Find the number of bricks, each measuring 25cm x 12.5 cm x 7.5 cm required to construct a wall 6m long, 5m high and 0.5m thick, while the cement and sand mixture occupies 1/20 of the volume of the wall. 6080
CIRCLE
1) Find the diameter circle whose circumference is 176m. 56m
2) A bicycle wheel makes 5000 revolutions in moving 11km. Find the diameter of the wheel. 70cm
3) A road which is 7m wide surrounds a circular park whose circumference is 352m. Find the area of the road. 2618 m²
4) Find the circumference of a circle of radius is 4.2cm. 26.4cm
5) Find the area of a circle of radius is 7.7cm. 186.34cm²
6) Find the length of the diameter of a circle whose circumference is 3.3m. 1.05m
7) Find the diameter of a circle whose area is 616m². 28m
8) Assuming that earth's equatorial diameter is 12530 km, find the circumference of the equator . 39380 km
9) Find the radius of a circle whose area is equal to the sum of the areas of three circles whose radii are 3cm, 4cm and 12cm. 13cm
10) The radius of a circle is 3m. What is the circumference of another circle, whose area is 49 times of the first ? 132m
11) A circular track has an inside circumference of 440m. if the which of the track is 7m, what is the outside circumference ? 484m
12) Find the area of a circular ring whose external and internal diameters of 20cm and 6cm respectively ? 286cm²
13) The wheel of a cart is making 2 revolutions per second. if the diameter of the wheel is 126cm, find its speed in km/hr. Give your answer, correct to the nearest km. 29 km/hr
14) How many times will the wheel of a car rotate in a journey of 1925m, if it is known that the radius of the wheel is 49cm ? 626 times
15) A garden roller has a circumference of 3 metres . How many revolutions does it make in moving 21 m ? 7 times
Continue......
CUBOID AND PRODUCTS CUBE
1) Find surface area of a cube whose edge is 6m.
2) Find the edge of a cube whose surface area is 432m².
3) The perimeter of each face of a cube is 32cm. Find lateral surface area.
4) Find the lateral surface area and total surface area of a cuboid whose length, breadth and height are 20cm, 10cm and 40 cm respectively.
5) The length, breadth and height of a cuboid are in the ratio 4: 2:1 and its total surface area is 1372m². Find the dimension of the cuboid.
6) A small indoor greenhouse (herbarium) is made entirely of glass panes (including base) held together with tape. It is 30cm long, 25cm wide and 25cm high.
a) What is the area of the glass ?
b) How much tape is needed for all the 12 edges?
7) How many bricks of dimensions 22.5cm x 10cm x 7.5cm can be painted, if the paint is sufficient for the surface area 2812.50 m²?
8) Three cubes of each side 4cm are joined end to end. Find the attached surface area of the day resulting cuboid.
9) An open box is made of wood 3cm thick. Its external length, breadth and height are 1.48m, 1.16m, and 8.3 dm. Find the cost of painting the inner surface at the rate of Rs 50 per square metre.
10) A room is 8m long, 5m broad and 4m high . There are 2 doors each 3m x 1.2 m and two windows each 1.5m x 1.2m. Find the cost of
a) distempering the walls at Rs 12.50 per square m
b) carpenting the floor at Rs 50 per m.
Part -2
1) Rationalize the denominator :
a) 1/(√5+ 1)
b) 1/(√5-1)
c) 1/{√3+ √5)
d) 1/(√3- √5).
e) 2/√5
f) 1/√18
g) (√3+ √5)/√2
h) √7/(√5+1)
Part- 3
1) Express each one of the following with a rational denominator:
a) √7/(√5 +1).
b) 7√3/(√10+ √3).
c) 10/(7- 2√3)
d) 5/(4√3 - 3√2)
Part- 4
1) Rationalize the denominator and simplify:
a) (6- 4√2)/(6+ 4√2).
b) (√7- √6)/(√7+ √6).
c) (7√3 - 5√2)/(√48 + √18).
d) 1/(√5+ √6 - √11).
e) 3/(√3 - √2 + √5)
Part- 5
1) If a and b are rational numbers, find the values of a and b in each of the following equalities:
a) (5+ 2√3)/(7+ 4√3)= a + b √3
b) (√2+ √3)/(3√2- 2√3)= a - b √6.
c) (7 +√5)/(7 - √5) - (7 - √5)/(7 + √5)= a + 7√5 b.
2) Simplify:
a) 2/(2√5 - √3) + 3/(2√5 + √3)
Part- 6
1) Simplify:
a) 2√6/(√2 + √3) + 6√2/(√6 + √3).
b) (4 +√5)/(4 - √5) + (4 - √5)/(4 + √5).
c) 3√2/(√3+ √6) + 4√3/(√2+ √6) + √6/(√2+ √3).
d) 7√3/(√10+ √3) - 2√5/(√6 + √5) - 3√2/(√15 + 3√2).
Part- 7
1) Find the values of each of the following correct to three places of decimals, it being given that
(√2= 1.414, √3= 1.732, √5 = 2.236, √6= 2.449)
a) √78 + (1/2) √48 - √192.
b) 3/√2.
c) 2/(√3 -1)
2) If a= 9- 4√5, find the value of √a - 1/√a.
3) If x= 3+ 2√2, find the value of x²+ 1/x².
Part- 8
1) If x= 1/(2- √3), find the value of x³- 2x²- 7x +5.
2) If x= (√3+1)/(√3 -1) and y= (√3-1)/(√3 +1), find the value of x²- xy+ y².
3) If x= [{√(p+ 2q) + √(p - 2q)}/{√(p+ 2q) - √(p - 2q)}]. Then show that qx²- px + q=0.
QUADRILATERAL
1) In the given figure,
ABCD is a parallelogram in which angle A=74°. Calculate angle B, C, D.
2) in the given figure
ABCD is a parallelogram in which angle DAB=70°, angle DBC=50°. Compute ang CDB, ADB.
ABCD is a parallelogram in which angle DAB=70°, angle DBC=50°. Compute ang CDB, ADB.
3) In the given figure,
ABCD is a parallelogram in which Angle DAP= 20°, angle BAP= 40° and angle ABP= 80°. Find angle APD, BPC.
4) ABCD is a parallelogram. If AB= 2AD and P is the midpoint of AB, then find angle CPD.
5) if an angle of a parallelogram is two-thirds its adjacent angle, find the angles of the parallelogram.
6) Find each of a parallelogram if two consecutive angles are in the ratio 1:5.
7) Find the measures of an angle of a parallelogram if one angle is 30° less than twice the smallest angle.
8) In the given figure,
ABCD is a parallelogram with perimeter 40cm. Find the value of x and y.
9) In the following figures , find the value of x, y and z.
10) In the given figure,
ABCD is a parallelogram. P and Q are the made points of BC and AD respectively. Prove that APCQ is a parallelogram.
11) ABCD is a parallelogram and points P and Q are the points on the sides AD and BC respectively, such that AP= 1/4 AD and CQ= 1/4 BC. Prove that BPDQ is a parallelogram.
12) ABCD is a parallelogram.
BM bisects angle ABC and DN bisects angle ADC. Prove that BNDM is a parallelogram and BM= DN
21/9/25
1) Evaluate:
a) (sin27°/cos63°)² - (cos63°/sin27°)².
b) cos40°/sin50° - (1/2)(cos35°/sin55°).
c) tan18°/cot72° - sec7°/cosec83°.
d) (cos²20 + cos²70)/(sin²59 + sin²31°).
e) cos80°/sin10° + cos59° cosec31°.
f) sin63° cos27° + cos63° sin27°
g) sin48° sec42 + cos48° cosec42°.
h) sec37°/cosec53° + sin42°/cos48°.
i) tan5° tan10° tan15° tan75° tan80° tan85.
j) (sin10° sin20° sin30°)/(cos80° cos70° cos60°).
k) cos80°/sin10° + cos59°/sin31°.
l) sin²35 + sin²55.
m) sec50° sin40° + cos40° cosec50°.
n) cosec²74° - tan²16.
o) sec²12° - cot²78.
p) cot54/tan36° + tan20°/cot70° - 2.
20/9/25
1) The Simple interest on a certain sum of money for 3 years at 5% p.a is Rs1200. Find the amount due and the compound interest on this sum of money at the same rate after 3 years, intrest is reckoned annually. Rs9261
2) A sum of Rs9600 is invested for 3 years at 10% p.a for compound interest:
a) What is the sum due at the end of the first year ? Rs 10560
b) What is the sum due at the end of the second year ? 11616
c) Find the compound interest earned in 2 years. Rs2016
d) Find the difference between the answer in (b) and (a) and find the interest on this sum for 1 year. Rs105.60
e) Hence , write down the compound interest for the third year . Rs1161.60
3) The compound interest on a certain sum of money at 5% per annum for 2 years is Rs246. Calculate the simple interest on the sum for 3 years at 6% p.a. Rs432
4) What sum of money will amount to Rs3630 in two years at 10%p.a. compound interest ? Rs3600
5) On a certain sum of money, the difference between the compound interest for a year, payable half-yearly, and the simple interest for a yeris Rs180. Find the sum lent out, if the rate of interest in both the cases is 10% p.a. Rs72000
6) A man borrows Rs5000 at 12% compound interest p.a., intrest payable every 6 months . He pays back Rs1800 at the end of every 6 months . Calculate the third payment he had 18 months in order to clear the entire loan . Rs2024.60
7) Calculate the compound intrest for the second year on Rs8000 invested for 3 years at 10% p.a. Rs880
8) A man invests Rs5000 for 3 years at a certain rate of interest compound annually. At the end of 1 year it amounts Rs5600. Calculate :
a) The rate of interest per annum. 12%p.a
b) The interest accrued in the second year. Rs672
c) The amount at the end of the third year. Rs7924.64
9) A man invests Rs46875 at 4% per annum compound interest for 3 years. Calculate :
a) The interest for the first year. Rs1875
b) The amount standing to his credit at the end of the second year. Rs50700
c) The interest for the 3rd year. Rs2028
10) A person invests Rs5600 at 14% p.a compound interest for 2 years. Calculate :
a) The interest for the first year. Rs784
b) The amount at the end of the first year. Rs6384
c) The interest for the second year, correct to nearest Rs. Rs894
11) The compound interest , calculated yearly, on a certain sum of money for the second year is Rs880 and for the third year it is Rs968. Calculate the rate of interest and the sum of the money. 10%, Rs8000
12) A certain sum money amounts to Rs5292 in two years and to Rs556.60 in three years, intrest being compounded annually. Find the rate percent. 5%
13) At what rate percent, per annum compound interest, would Rs80000 amount to Rs88200 in two years; interest being compounded yearly ? 5%
14) A sum of money is lent out at compound interest for 2 years at 20% p.a. compounded being reckoned yearly. If the same sum of money was lent out at compound interest at the same rate per annum, CI being reckoned half-yearly, it would have fetched Rs482 more by the way of intrest. Calculate the sum of money lent out. Rs20000
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