ARITHMETIC PROGRESSION
1) if 7th and 13th terms of an AP be 34 and 64 respectively, then its 18th term is
a) 87 b) 88 c) 89 d) 90
2) If the sum of p terms of an AP is q and the sum of q terms is p, then the sum of p+ q terms will be
a) 0 b) p- q c) p+ q d) -(p+ q)
3) If the sum of n terms of an AP be 3n²- n and its common difference is 6, then its first term is
a) 2 b) 3 c) 1 d) 4
4) Sum of all two digit numbers which when divided by 4 yield unity as remainder is
a) 1200 b) 1210 c) 1250 d) none
5)
6)
7) The first and last terms of an AP are 1 and 11. If the sum of its terms is 36, then the number of terms will be
a) 5 b) 6 c) 7 d) 8
8) If the sum of n terms of an AP is 3n² + 5n then which of its terms is 164 ?
a) 26th b) 27th c) 28th d) none
9) If the sum of n terms of an AP is 2n² + 5n, then its nth term is
a) 4n -3 b) 3n -4 c) 4n + 3 d) 3n +4
10)
11)
12)
13) If four numbers in AP are such that their sum is 50 and the greatest number is 4 times the least, then the numbers are
a) 5,10,15,20 b) 4,10,16,22 c) 3,7,11,15 d) none
14)
15)
16) The first and last term of an AP are a and l respectively. If S is the sum of all the terms of the AP and the common difference is given by (l² - a²)/{k - (l+ a)}, then k=
a) S b) 2S c) 3S d) none
17)
18) If the first, second and last term of an AP are a, b and 2a respectively, then its sum is
a) ab/2(b - a)
b) ab/(b - a)
c) 3ab/2(b - a) d) none
19)
20)
21)
22)
23) If the first term of an AP is 2 and common difference is 4, then the sum of its 40 terms is
a) 3200 b) 1600 c) 200 d) 2800
24) The number of terms of the AP 3,7,11,15,.....to be taken so that the sum is 406 is
a) 5 b) 10 c) 12 d) 14 e) 20
25)
PAPER - 4
1) a)
b) Solve: 21x²- 8x -4=0. (2)
c)
d) Find the coordinates of the image of (5, -4) after reflection in
i) x= 0
ii) y= 2. (2)
e) list the solution set of the following inequation and graph the solution set :
1/2+ 8x > 5x - 3/2, x belongs to Z. (2)
2) a) Calculate the ratio in which the line joining A(6,5) and B(4,-3) is divided by the line y= 2. (2)
b) In the figure, BC is parallel to DE.
Area of the triangle ABC= 25cm²,
Area of trapezium BCED= 24cm² and DE= 21 cm. Calculate the length of BC. (3)
c)
3) a) Calculate the mean, median and mode of the following numbers :
13, 11, 15, 13, 14, 15, 13, 17, 12, 16. (2)
b) Given A= 1 1
8 3
Evaluate A²- 3A. (3)
c)
4) a) Construct a triangle ABC with AB= 7cm, BC= 8cm and angle ABC=60°. Locate by constuction of the point P such that
i) P is equidistant from B and C.
ii) P is equidistant from AB and BC.
iii) measure and record the length of PB. (3)
b)
c) In the figure, I is the incentre of the circle. AI produced to meet the circle in D. Calculate
i) Angle DCB
ii) Angle IBC.
iii) angle BID
iv) angle BIC
Give angle BAC=50° and angle ABC=64°. (3)
5) a) Show that: √{(1- cosA)/(1+ cosA)}= sinA/(1+ cosA). (3)
b) In the figure, AB is a common tangent to two circles intersecting at C and D. Write down the measure of (angle ACB+ angle ADB). (2)
c)
6) a)
b) The surface area of a solid metallic sphere is 1256cm². It is melted and recast into solid right circular cones of radius 2.5cm and height 8cm. Calculate
i) the radius of the solid sphere.
ii) the number of cones recast (π=3.14). (3)
7)a) A dividend of 9% was declared on Rs 100 shares selling at a certain price. If the rate of return is 15/2%, find
i) the market value of the share.
ii) the amount to be invested to obtain an annual dividend of Rs 630. (3)
b) In the figure, AB and CD are the lines 2x - y+ 6=0 and x - 2y= 4 respectively.
i) write down the coordinates of A,B,C,D.
ii) prove that triangles OAB and ODC are similar.
iii) is figure ABCD cyclic ? (3)
8) a)
b)
c)
9) a)
b)
10)a) The following table shows the distribution of the heights of a group of factory workers:
Ht(cm) no of workers
140-145 6
145-150 12
150-155 18
155-160 20
160-165 13
165-170 8
170-175 6
i) Determine the cumulative frequencies
ii) write down the median height in cm. (3)
b) The hotel bill for a number of people for overnight stay is Rs 4800. If there were 4 more, the bill each person had to pay would have reduced by Rs 200. Find the number of people staying overnight. (3)
11) a) ABCD is a rhombus. The coordinates of A and C are (5,8) and (-1,2) respectively. Write down the equation of BD. (3)
b)
TEST PAPER - 24
1)a) The lines given by ax+ 4y= 8 and 2x+ 3y +2=0 are mutually perpendicular. Find the value of a. (2)
b) AB and CD are two chords of a circle intersecting at a point P outside the circle. Find if PC= 30cm, CD= 14cm and PA= 24cm. Determine AB. (2)
c)
d) Find the total surface area of an open pipe of length 50 cm, external diameter 20cm and internal diameter 6cm. (2)
e)
2)a)
b) Find the equation of the lines which passes through the point (-2,3) and are equally inclined to the co-ordinate axes. (3)
c) If P= 2 6 & Q= 3 x
3 9 y 2
Find x and y such that PQ= null matrix. (3)
3) a) Using remainder theorem, factorise the expression 3x³+ 10x²+ x - 6. (3)
b)
c) If (a²+ b²)+x²+ y²)= (ax + by)², show that a/x = b/y. (3)
4) a) If a= 4√6/(√2+ √3), find the value of
(a+ 2√2)/(a- 2√2) + (a+ 2√3)/(a- 2√3). (3)
b)
c) Mr. Ahuja invests equal sums of money in two companies offering 8% shares of Rs 100 at a premium of Rs 25 at 6% shares of Rs 100 at a discount of Rs 25. He finds that if with his total investment he has bought equal number of shares of each company, his income would have been Rs142 less. Find his total investment . (3)
5) a)
b)
6) a)
b) A recurring deposit account of Rs 1200 per month has a maturity value of Rs 12440.00. if the rate of interest is 8% and the interest is calculated at the end of every month, find the time of the recurring deposit account. (3)
7) a) i(plot the point A(3,5) and B(-2,4).
ii) A' is the image of A when reflected in the x-axis . Write down the coordinates of A'b and plot it.
iii) B' is the image of B when reflected in the y-axis, followed by reflection in the origin, Write down the coordinates of B'.
iv) write down the geometrical name of the figure AA'BB'.
v) Name two invariant points under the reflection in the x-axis . (3)
b) The point P(5,-4) divides the line segment AB as shown in the figure in the ratio 2:5. Find the coordinates of points A and B. 3
8) a) The vertices of a ∆ ABC are (0,5), B(-1,-2) and C(11,7). Write down the equation of BC . Find
a) i) the equation of line through A and perpendicular to BC.
ii) the coordinates of the point P, where the perpendicular through A as obtained in (i) meets BC. (3)
b)
9) a) Find the mean of the given data:
C. I frequency
63-70 9
70-77 13
77-84 27
84-91 38
91-98 32
98-105 16
105-112 15 (3)
b)
10a)
b) A, B are the points (9,6) and (10,0). O is the origin, OM is a median and OP is an altitude of ∆ OAB. Find the equations of OM and OP. (3)
11) a) prove: (SinA + cosecA)² + (cosA + secA)²= 7+ tan²A + cot²A. (3)
b)
c) If A= -1 1
a b and A²= I, find a, b.
FACTOR THEOREM
Sap-2
1) Find the value of p if the polynomial f(x)= x³- 3x² - px + 24 is divisible by g(x)= x + 3. Hence find all the factors.
2) Find the value of q if the polynomial f(x)= 2x³ + qx² - 7x -12 is divisible by g(x)= x + 4. Hence find all the factors.
3) Find the value of q if the polynomial f(x)= x³ + 2x² - 13x + q is divisible by g(x)= x -2. Hence find all the factors.
4) Find the value of p if the polynomial f(x)= x³ - px² - x +3 is divisible by g(x)= x² -1. Hence find all the factors.
5) Find the value of p and q if the polynomial f(x)= px³ + qx² - 8x -12 is divisible by g(x)= x² - 4. Hence find all the factors.
6) Find the value of p and q if the polynomial f(x)= px³ + 6x² + qx + 6 is divisible by g(x)= x²+ 4x + 3. Hence find all the factors.
7) Find the value of p if the polynomial f(x)= x³ + px² - 16x +8 has g(x)= x -2 as one of the factors. Hence find the remaining two factors.
8) Find the value of q if the polynomial f(x)= 2x³ + qx² - x -15 has g(x)= 2x + 3 as one of the factors. Hence find all the factors.
9) Factorise 6x³ - 11x² - 3x +2. Completely.
Sap-1
1) Using factor theorem, find out whether polynomial g(x) is a factor of f(x) or not:
a) f(x)= 3x²- 2x - 8, g(x)= 3x +4.
b) f(x)= 9x²- 4a²+ 4ay - y² - 8, g(x)= 3x + 2a - y.
c) f(x)= x³- 3x² + 4x - 2, g(x)= x -1.
d) f(x)= x²(x - 14)+ 37x - 60, g(x)= x -2.
e) f(x)= x³+ x² - 2x - 30, g(x)= x -3.
2) Find the value of k when f(x)= x³- 3x² - x +k, g(x)= x +1 is a factor of f(x).
3) Find the values of p and q if g(x)= x +2 is a factor of f(x)= x³- px² + x + q and f(2)= 4.
4) Find the values of p and q if g(x)= x -4 is a factor of f(x)= 4x³- px² + qx -216 and f(-1)= -225.
5) Find the values of a and b if p(x)= x +2 is a factor of q(x)= ax³- bx² + 2(x -2) and q(2)= 20.
6) Find the value of a if x+ a is a factor of f(x)= x³ + a(x² +1) - 2x + 4.
7) Find the remainder, if f(x)= x³- 2x² + x - 3 is divided by g(x)= x +2.
8) Find the remainder, if f(x)= 2x³- 3x² -4x - 5 is divided by g(x)= 2x + 1.
9) If g(x)= 2x -3 is a factor of f(x)= 2x³- 9x² + x + p, find the value of p. Hence find all the factors.
10) If g(x)= 2x - 2 is a factor of f(x)= 3x³ + x² + px + 12, find the value of p. Hence find all the factors of f(x)
Sap-2 LINEAR INEQUATION- TEST
1) Solve the following inequations:
a) -5<-1-2x ≤ 3, x ∈N
b) -8< x - 7 ≤ 2 - 2x; x ∈ N
c) - 8/3 < - x/3 -1 ≤ -4/3; x ∈ R
d) - 17/5≤ x - 8/3 < 1/3 ; x ∈ R
e) -1≤ 2x -3 < 17 - 3x; x ∈N
f) -10≤ 2x -12 < 8 - 3x ; x∈ W
g) 2≤ x + 3 ≤ 14 - 2x ; x ∈ I
h) -20< x - 19 ≤ -2x - 8; x ∈ W
2) List one of the solution set of 1/8< m/n < 1/7, where m,n ∈ Z.
3) Given P={x: 8< 2x +2 ≤ 14, x ∈ R}
Q={ x: -5≤ -1+ 4x < 19, x ∈ I}
Represent P and Q on number lines. Write down the elements of P∩Q.
4) State for each of the following statements whether it is true or false:
a) If (x - a)(x - b)< 0, then x< a and x < b.
b) If a< 0 and b< 0, then (a+ b)²> 0.
c) If a and b are any two integers such that a> b, then a²> b².
d) If p= q+2, then p> q.
e) If a and b are two negative integers such that a< b, then 1/a < 1/b.
5) The diagram represents two inequations A and B on real number lines
i) Write down A and B in Rooster form.
ii) Represent A ∩B and A - B on two different number lines.
LINEAR INEQUATIONS
SAP-1
1) Solve and hence illustrate on the number line
a) 2x - 3< 5x -3≤ 12, x∈N. Hence .
b) 3(x -2)≥ 2x -3, x ∈R.
c) (x -2)/(2x +5) < 1/3, x ∈ R.
d) Given A={x: -8<5x +2≤ 17, x ∈ I}
B={x: -2≤7+3x < 17, x ∈ R}
Represent A and B on two different number lines. Write down the elements of A∩B.
e) 2x +5< 9; x ∈N.
f) 5x -20÷ 4; x ∈N
g) 5x ≤ 20, x ∈ W
h) 2p/3 + 1 > 3p -2, p∈ R.
2) The diagram represents two inequation A and B on real number lines
i) Write down A and B in set builder notation.
ii) Represent A ∩B and A ∩B' on two different number lines.
3) If the replacement set is {-2,-1,+1,+2,+4,+5,+9}, what is the solution set of each of the following mathematical sentences?
i) x+ 3/2> 5/2.
ii) x -4< -3.
iii) 2x -5≥ 10.
iv) 3y -2≤ 5/2.
4) Translate the following sentences into open sentences:
i) 5 more than 4 times a number.
ii) 2 less than half a number.
iii) Mother's age is 10 years greater than 3 times her daughter's age.
iv) Sum of a number and its reciprocal equals to 2.
v) The length of a rectangle of perimeter 8 is 3 times its width.
5) In the following graphs match each group of column A with one of the sets given in column B.
6) Write open mathematical sentences using, x for variable, whose graphs are the following:
7) Write open mathematical sentences using, x for variable, whose graphs would be
8) Figure shows the graph of the following lines:
Explain the meanings of the following ring, the solid rings and the arrowheads in the diagrams.
9) If the replacement set={-8,-7,....-1,0,1,2,....+8}.
List the solution set of the following:
i) {x: x> 6}
ii) {x: -2≤x≤0}
iii) {x: x< 8}
iv) {x: 0≤2x -3≤ 6}
v) {x: x²< 24< x³}
10) If x∈ {x: -5< x < +5 and x ∈ I} , find the truth sets of the following:
a) 7x > -10
b) 2(3x -5)< 6
c) 7x²÷3x > 4/3
d) x + 1/x = 2
e) 7x²+ 2 ≥ x(7x +2)
11) P is the solution set of 1/x > 3/4 and Q is the solution set of:
x(1- 1/x)≥ 5(x -1), where x ∈ W. Find the set P∩Q.
12) P is the solution set of 8x -1> 5x +2 and Q is the solution set of 7x -2≥ 3(x +6), where x ∈N. Find the set P∩Q
PAPER- 2
1) The price of a TV set inclusive GST of 9% is 40221. Find the marked price.
2) If x: y= 4:3, find (5x +8y): (6x - 7y).
3) Using the reminder theorem, find the remainder when y³- 7y²+ 15y - 19 is divided by y- 3.
4) State and draw the locus of a point eqidistance from two parallel lines.
5) The given figure, the medians QS and RT of a ∆ PQR meet at G. prove that:
a) ∆ TGS~ ∆ RGQ
b) QG= 2 GS from (a) above.
6) Solve the following inequation and graph the solution on the number line:
2x -5≤ 5x +4 < 11, x belongs to R.
7) The marks of 20 students in a test were as follows : 5, 6, 8, 9, 10, 11, 11, 12, 13,13, 14, 14, 15,15, 16,16 18, 19 20. Calculate:
a) the mean
b) the median
c) the mode
8) If the matrix
A= 1 -4 & B= -3 2 & C= 4 0
4 1 4 0 0 -3 find
a) A² b) BC c) A²+ BC .
8) The point A(3,4) is reflected to A' in the x-axis, and O' is the image of O(the origin) when reflected in the AA'. Using graph paper, give
a) the coordinates of A' and O'.
b) the lengths of the segments AA' and OO'.
c) the perimeter of the quadrilateral AOA'O'.
d) the geometrical name of the figure AOA'O'.
9) Prove the following identity:
1/(sinA + cosA) + 1/(sinA - cosA)= 2sinA/(2 sin²A -1).
10) In the given figure, AB is the diameter of a circle with centre O. Angle BCD is 130°. Find
a) angle DBA
b) angle BAD.
11) Find the equation of a line passing through the point (-4,6) and having the x-intercept of 8 units.
12) A man wants to buy 72 shares available at Rs 150 (per value of Rs 100).
a) How much should he invest ?
b) if the dividend is 7.5%, what will be his annual income ?
c) if he wants to increase his annual income by Rs 300, how many extra shares should be buy ?
13) The following table gives the weekly wages of workers in a factory:
weekly wages (Rs). No. of workers
150-150 5
155-160 20
160-165 10
165-170 10
170- 175 9
175-180 6
180-185 12
185- 190 8 Calculate
a) the mean
b) the model class
c) the numbers workers getting weekly wages, below Rs 180.
d) the number of workers getting Rs 165 or more, but less than Rs 185 as weekly wages.
14) A hollow sphere of internal and external diameters 8 cm and 16 cm respectively , is melted into a cone of base diameter 16 cm. Find the height of the cone.
15) The shadow of a vertical tower AD on level ground is increased by 30m, when the altitude of the sun changes from 45° to 30° as shown in the given figure.
Find the height of the tower and give your answer correct to 1/10 of a metre.
16) The marks obtained by 240 students in a mathematics test is given below:
Marks No. if students
00-10 10
10-20 18
20-30 32
30-40 44
40-50 52
50-60 26
60-70 22
70-80 12
80-90 16
90-100 8
Draw an ogive for the given distribution on a graph sheet. Use a suitable scale for your ogive and using ogive, estimate:
a) the median
b) the lower quartile
c) the number of student who obtained more than 75% in the test :
d) the number students who did not passing inthe test if the pass percentage was 40.
17) P(2,4), Q(3,3) and R(7,5) are the vertices of a ∆ PQR. Find
a) the coordinates of the centroid G of ∆ PQR.
b) the equation of a line, through G and parallel to PQ.
18) An aeroplane travelled a distance of 800 km at an average speed of x kmph. On the return journey, the speed was increased by 40 kmph. Write down an expression for the time taken for:
a) the onward journey .
b) the return journey .
If the return journey took 40 minutes less then the onward journey, write down an equation in x and find its value.
Paper - 1
1) The point P(a,b) is reflected in the x-axis to obtain the point Q(3,-4). Find a and b. (1)
2) If A= a 3a & B= 2 & C= 5
b 4b 1 12 find a and b when the relation AB= C. (1)
3) The mean of the number 6, y, 7, x and 14 is 8. Express y terms of x. (1)
4) Solve using the quadratic formula, x²- 5x -2=0. Give your answer correct to 3 significant figures. (2)
5) If (8a + 5b)/(8c + 5d)= (8a - 5b)/(8c - 5d), prove that a/b = c/d. (1)
6) Find the value of k, if x - k is a factor of x³- kx²+ x + 4. (1)
7) Solve 1< 3x -3≤ 11, x ∈ R and mark it on a number line. (1)
8) Calculate the mean, median and mode of the following numbers : 12, 11, 10, 11, 12, 13, 14, 13, 15, 13. (2)
9) In the diagram,
chords AB and CD of the circle are produced to meet at O. Given that CD= 4cm, DO= 12cm and BO= 6cm, calculate AB . (2)
10) If cosA= 4/5 and cosB= 24/25; evaluate
a) cosec²A
b) cotA + cotB. (2)
11) on a map drawn to a scale 1:125000, a triangular plot of land has the following measurements :
PQ=10cm, QR= 8cm, angle PRQ= 90°. Calculate
a) the actual length of PQ in km.
b) the area of the plot in square kilometres. (2)
12) The work done by (2x -3) men in (3x +1) days and work done by (3x +1) men in (x +8) days are in the ratio of 11:15. Find the value of x. (2)
13) Find the mean of the following frequency distribution:
Class interval frequency
00-30 3
30-60 7
60-90 15
90-120 14
120-150 7
150-180 4 (3)
14) A man invests Rs 30800 in buying shares of nominal value Rs 56 at 10% premium . The dividend on the shares is 18% per annum. Calculate
a) The number of shares he buys.
b) The dividend he receives annually.
c) The rate of interest he gets on his money. (3)
15) prove that: sinx/(1- cotx) + cosx/(1- tanx)= sinx + cosx. (2)
16) A straight line passes through the points A(-2,8) and B(10,-4). It intersects the coordinate axes at points E and F. P if the midpoint of the segment EF. 
Find
a) the equation of the line.
b) the coordinate of E and F.
c) the coordinates of the point P. (3)
17) In an auditorium, seats were arranged in rows and columns . The number of rows was equal to the number of seats in each row. When the number of rows was doubled and the number of seats in each row was reduced by 15, the total number of seats increased by 400. Find
a) The number of rows in the original arrangement.
b) the number of seats in the auditorium after rearrangement. (3)
18) Draw a histogram and hence estimate the mode for the following frequency distribution:
Class frequency
00-20 3
20-40 8
40-60 10
60-80 6
80-100 4
100-120 3 (3
19) A man standing on the bank of a river observes that the angle of elevation of a tree on the opposite bank is 60°. When he moves 40m away from the bank, he finds the angle of elevation to be 30°. Calculate:
a) the width of the river and
b) the height of the tree. (3)
20) Find a and b, if
a= 3 -2 & B= 2a & C= 4 & D= 2
-1 4 1 5 b with the relation AB + 4C = 3D. (2)
21) A vessel is in the form of an inverted cone. Its height is 15cm and the diameter of its top which is open, is 5cm. It is filled with water up to the rim. When lead shots, each of which is a sphere of diameter 5mm are dropped into the vessel, 1/3 of the water flows out. Find the number of lead shots dropped into the vessel. (3)
22) In the given circle
with diameter AB, find the value of x. (2)
23) Find the value of k for which the lines kx - 7y + 5=0 and 6x - 2y +9=0 are perpendicular to each other. (3)
1)a) Find the rate of GST levied on a car that was sold at a price 3 times its marked price. (1)
b) If the sum of the series 2+5+8+11......is 60100, then the number of terms are
a) 100 b) 200 c) 150 d) 250
2) When 7x²- 3x + 8 is divided by (x -4), find the remainder (using remainder theorem). (1)
3) If 2 cosx x = 2/5, find sinx. (1)
4) Calculate the length of the tangent drawn to a circle of diameter 8cm from a point 5cm away from the centre of the circle. (1)
4) If x²,4 and 9 are in continued proportion , find the value of x. (1)
5) If x ∈Z, find the solution set for the inequation 5< 2x -3≤ 14 and graph the solution on a number line. (1)
6) Find p and q if g(x)= x +2 is a factor of f(x)= x³- px + x + q and f(2)= 4. (2)
7) 1 -2 0
If X= -3 4 & Y= 1
a) Find the matrix Z such X + Z is a zero matrix.
b) Find the matrix M such that X + M = X.
c) Find XY. (3)
8) a) If 7 is the mean of 5, 3, 0.5, 4.5, b, 8.5, 9.5, find b.
b) If each observation is decreased in value by 1 unit, what would the new mean be ? (2)
9) In the figure below,
AB is a chord of the circle with centre O and BT is tangent to the circle at B, if angle OAB= 32°, Find the value of x and y. (2)
10) Construct a regular pentagon of side 3cm. Draw the lines of symmetry. (2)
11) The volume of a cylinder 14cm long is equal to that of a cube having an edge 11cm. Calculate the radius of the cylinder. (3)
12) A piece of butter 3cm by 5cm by 12cm is placed on a hemispherical bowl of radius 3.25cm. Will the butter overflow when it melts completely. (3)
13) A company with 10000 shares of Rs 50 each declares an annual dividend of 5%.
a) What is the total amount of dividend paid by the company ?
b) What would be the annual income of a man who has 72 shares in the company?
c) if he receives only 4% on his investment, find the price he paid for each share. (3)
14)a) State the equation of the mirror line, if point A(5,0) on reflection is mapped as A'(-5, 0).
b) State the equation of the the mirror line, if point B(4,-3) on reflection is mapped as B'(4,3).
c) Point C(-3,5) on reflection in y=2 is mapped as C'. Find the coordinates of C. (3)
15) Tanya standing on a vertical cliff in a jungle observes two rest-horses in a line with her on opposite sides deep in the Jungle below. If their angles of depression are 30° and 45° and the distance between them is 200mp, find the height of the cliff. (3)
16) Find the equation of a line that passes through (1,3) and is parallel to the line y= -3x +2. (2)
17) In the given figure,
calculate
a) angle APB
b) angle AOB. (2)
18) The midpoint of the line joining A(2,p) and B(q,4) is (3,5). Find the numerical values of p and q. (2)
19) From the following table, find:
a) average wage of a worker. Give your answer, to the nearest paise
b) Modal class.
Wages in Rs No of workers
Less than 10 15
Less than 20 35
Less than 30 60
Less than 40 80
Less than 50 96
Less than 60 127
Less than 70 190
Less than 80 200 (3)
20) Examine the ogive given below
which shows the marks obtained out of 100 by a set of students in an examination and answer the following questions:
a) How many students are there in the set ?
b) How many students obtained 40% marks ?
c) How many students obtained 90% and above ?
d) What is the median marks? (4)
21) Show that: √{(1+ cosx)/(1- cosx)}= cosecx + cot x. (2)
22) if the sum of the first four terms of an AP is 4 and the second term is -5 then find the common difference
LINEAR INEQUATIONS
1) If 2x - 7 < 4, where x is a natural number less than 8, than the solution set is:
a) {0,1,2,3,4} b) {1,2,3,4,5} c) {1,2,3,4,5,6} d) {0,1, 2,3,4,5,6}
2) If - x ≥ -3 then:
a) x≤ -3 b) x ≥ 3 c) x = 3 d) x ≤ 3
3) if 2 + 4 x< 2 x - 5 ≤ 3x ∈Z, then the solution set is :
a) {5,4} b) {- 5,-4} c) {- 5, -4, -3} d) {- 4,-3,-2,-1}
4) if 2≤2x - 3 ≤ 5, x∈ R, then the solution set is:
a) {2.5≤ x ≤ 4, x∈ R} b) {2≤ x ≤ 5, x∈ R} c) {3≤ x ≤ 5, x∈ R} d) {2< x < 4, x∈ R}
5) If a> b, then:
a) a - c ≤ b - c b) a - c≥ b - c c) a - c = b - c d) a - c > b - c
6) If x≥ 5 and- ax ≥ 5a, then :
a) a > 0 b) a < 0 c) both a and b d) neither a nor b
7) If x+1≥ 13 - 5x, x ∈{1,2,3,4.....10}, then the solution set is:
a) {1,2,3,4,5,6} b) {6,7,8,9,10} c) {7,8,9,10} d) {6,7,8.....}
8) If 7 - 5x ≥ 3x -1, then the solution set, when x ∈ W is:
a) {0,1} b) {0} c) {1} d) {0,1,2}
9) Given a >0, b >0, c >0 and d <0, then a < b implies :
a) a+ d> b + d b) a - d < b - d c) a - d > b - d d) a + d = b + d
10) Given 2x - 5≤ 5x +4 < 11. If x ∈ I, the solution set is:
a) {-2,-1,0,1} b) {-3,-2,-1,0,1} c) {-3,-2,-1,0} d) {-2,-1,0,1}
11) For the inequation -12< 3 - 4x ≤ 11, x ∈ N, the solution set on the number line can be shown as:
a) 5 b) 4 c) 3 d) 2
13) If 2x - 5≤ 5x + 4 < 11, x ∈ I, then the solution set can be represented as:
a) -2 b) -1 c) 0 d) 1
15) If -9(x -7)≥ 45 - 21x > x +1, x ∈ R, then the solution set is:
a) {-3/2≤ x < 2, x ∈R}
b) {-3/2 < x < 2, x ∈R}
c) {-2/3 ≤ x ≤ 1, x ∈R}
d) {-1/3 ≤ x ≤ 2, x ∈R}
16) If 2x - 5 ≤ 5x + 4 < 11, x ∈ I, then the smallest whole number for x is:
a) 0 b) 1 c) -3 d) 2
17) If 5 - 3x < 11, x ∈ R, then the solution set is:
a) {x> -2, x∈R} b) {x≥ -2, x∈R} c) {x< 2, x∈R} d) {x< -2, x∈R}
18) Given 3x -1 ≤ x +5, x ∈N, then the solution set is:
a) {1,2,3} b) {1,2,3,4} c) {1,2} d) {0,1,2,3}
19) If 8 < 5(x +1) -2 ≤ 18, x ∈R, then the smallest integer value of x is:
a) 1 b) 0 c) -1 d) 2
20) Given a >0, b >0, c >0 and d <0. Then a > b implies:
a) ad >bd b) ad = bd c) ad < bd d) none
SHORT ANSWER TYPE QUESTIONS
1) Find the value of x, which satisfies the inquation -2≤ 1/2 - 2x/3 ≤ 11/6, x ∈N.
Graph the solution set on the number line.
2) Solve the following inequation, write the solution set and represent it on the number line.
-3(x -7)≥ 15 - 7x > (x +1)/3, x ∈R
3) Solve the following inequation, write down the solution set and represent it on the real number line:
-2+ 10x ≤ 13x +10 < 24+ 10x, x ∈ Z
4) Solve the following inequation and write down the solution set:
11x - 4 < 15x +4 ≤ 13x + 14, x ∈ W
Represent the solution on a real number line.
5) Solve the given inequation and graph the solution set on the number line:
2y - 3 < y +1 ≤ 4y +7, y ∈ R
6) Solve the following inequation and represent the solution set on the number line:
2x -5 ≤ 5x +4 < 11, x ∈I
7) Solve the following inequation and write the solution set:
13x -5 < 15x +4 < 7x +12, x∈R
1) Find the mean of the following distribution:
x: 4 6 9 10 15
f: 5 10 10 7 8
2) Following table shows the weights of 12 students:
Weight (in kgs): 67 70 72 73 75
No of students: 4 3 2 2 1
Find the mean weight.
3) Find the mean of the following distribution:
X: 10 30 50 70 89
F: 7 8 10 15 10.
4) If the mean of the following distribution is 6, find the value of p.
X: 2 4 6 10 p+5
F: 3 2 3 1 2
5) Find the value of p, if the mean of the following distribution is 7.5.
X: 3 5 7 9 11 13
F: 6 8 15 p 8 4
6) Find the missing frequencies in the following frequency distribution if it is known that the mean of the distribution is 1.46.
No of accidents(x): 0 1 2 3 4 5 total
Frequency (f): 46 ? ? 25 10 5 200
BOOSTER - C
1) The following table shows the weight of 12 students:
Weight (in kg): 67 70 72 73 75
No of students: 4 3 2 2 1
Find the mean weight. 70.25 kg
2) Find the mean wage from the data given below:
Wages: 800 820 860 900 920 980 1000
F: 7 14 19 25 20 10 5 891.2
3) Apply step-deviation method to find the AM of the distribution:
Variate (x) Frequency(f)
5 20
10 43
15 75
20 67
25 72
30 45
35 39
40 9
45 8
50 6 22.214
3) The weight in kilograms of 60 workers in a factory are given in the following frequency table. Find the mean weight of a worker.
Weight (in kg): 60. 61 62 63. 64 65
No of workers: 5 8 14 16 10 7 62.65
4) The table given the distribution of villages under different heights from sea level in a certain region. Compute the mean height of the region:
Height: 200 600 1000 1400 1800 2200
F: 142 265 560 271 89 16 984.51
CENTRAL TENDENCY
1) The weight of 6 persons in a firm are 64, 66,63,69,75,68 kg respectively. What is their mean weight?
a) 56.7 b) 67.5 c) 76.5 d) 65.7
2) The profit (in Rs) of a small shopkeeper of a week is 207,205,210,221,230,204,218. What is his mean profit per day?
a) 115 b) 225 c) 215 d) 125
3) The AM of 1,3,5,.......,29 is
a) 13 b) 15 c) 14 d) 16
4) The word length in each of the 40 words are as follows:
X: 2 3 4 5 7
F: 6 8 12 10 4
What is the mean of the above distribution?
a) 4.35 b) 4.05 c) 4.25 d) 4.15
5) The AM of a variable x is 40. What will be the mean of the variable y, when y= 4x - 10.
a) 160 b) 165 c) 155 d) 150
6) The mean age of a group of 30 girls is 20 years, and that of a group of 20 boys is 30 years. If the two groups are taken together to form a new group, what is the mean of this group?
a) 22 b) 24 c) 23 d) 25
7) The mean marks of 170 students in a certain class is 75. The mean mark of boys in the class is 85, and of the girls is 65. Find the number of boys and girls in the class.
a) 85,85 b) 65,105 c) 75,95 d) 80,90
8) The mean marks obtained in an examination by two gr of students were found to be 75, 85 respectively. What will be the ratio of students in the two groups, if the mean marks for all students was 100.
9) Suppose x takes the value 2,4,6,8,10,12. Then what will be the value of ∑(xᵢ - mean x)?
a) 0 b) 1 c) 2 d) 3
10) Sum of the deviation from mean is
a) 0 b) 1 c) mean of the number d) can't determine
11) For a set of 10 observations, what will be the mean for the values of x: 10,10,10,.....10.
a) 8 b) 9 c) 10 d) 11
12) The AM of 7 items is 10. If one more item is added to the series, then the AM becomes 12. Find the value of 8th item.
a) 24 b) 26 c) 28 d) none
13) What will be the weighted AM of the first n natural numbers when the numbers are weighted by the corresponding numbers?
a) (n+1)/3 b) (2n+1)/2 c) (2n+1)/3 d) (2n+3)/2
14) The AM of a set of values is 15. If 5 is added to each value, the new AM will be
a) 10 b) 15 c) 20 d) none
15) The AM of 1, 2,2²,......2⁹ is
a) 18.341 b) 18.431 c) 18.143 d) 18.413
16) The weighted AM of first 11 natural numbers whose weights are equal to the corresponding numbers, is
a) 6.77 b) 8.55 c) 7.66 d) none
17) The marks of 7 students in a test in statistics are 0,100,12,18,17,10,32. A suitable average of these marks is
a) Mean b) median c) mode d) none
18) If 3,9,6,7,10,8,4,1,5,2 are the observations, then find the median
a) 5 b) 5.5 c) 6.5 d) 6
19) Which quartile is the median
a) 1st quartile b) 3rd quartile c) 2nd quartile d) none
20) If the relation between two variables x and y be 3x + 7y=50, and median of y is 5. Then median of x is
a) 4 b) 5 c) 6 d) 7
21) If the mean and median are 24 and 26 respectively. Find mode
a) 27 b) 28 c) 29 d) 30
22) In usual symbols, mode= 3 median - a x mean, where a is
a) 1 b) 2 c) 3 d) none
23) How many quartiles are there
a) 1 b) 2 c) 3 d) 4
Matrix - Test
) If A= 2 0 & B= 1 2
1 2 2 1 find A+ B
2) If A= 1 2 3 & B= 1 2
4 5 6 3 4
find A+ B
3) If A= 0 2 & B= 7 8
2 1 1 4 find
a) 2A + 3B
b) 3A - B
c) AB
4) If A= 1 3
3 4 and A²- kA - 5=0, then find k.
5) If A= 1 0 & B= 0 1
0 1 -1 0
Then show that (aA+ bB)(cA+ dB)= (ac - bd)A+ (ad + bc)B.
BANKING
Sap-1
1) Amit deposited Rs 150 per month in a bank for 8 months under the recurring deposits. If the rate of interest is 8% p.a. and intrest is calculated at end of every month?
2) Laxmi took a cumulative time deposit account of Rs 240 per month at 10% p.a. she received Rs 3840 on maturity. Find the period for this account.
3) Manoj opened Recurring Deposit Account in a bank and deposited Rs 500 per month for 3 years. The bank on Rs 20220 on maturity. Find the rate of interest paid by the bank.
4) Raju opened a Recurring Deposit Account with the Bank of Rajasthan and deposits Rs 600 per month for 20 months. Calculate the maturity value of this account, if the bank pays interest at the rate of 10% per annum.
5) Miss Anshu Gupta deposited Rs 350 per month for 20 months under Recurring Deposit Scheme. Find the total amount payable by the bank on maturity of the account if the rate of interest is 11% per annum.
6) Mrs. Mathew opened Recurring Deposit Account in a bank with Rs 500 per month for 5/2 years. Find the amount she will get on the maturity. If the interest is paid on monthly balance at 12.5% per annum .
7) Calculate the amount received on maturity of a recurring deposit of Rs 150 per month for 1 year 6 months. if the rate of interest is 11% per annum .
8) Amar deposits Rs 1600 per month in a Recurring Deposit for 3 years at the rate of 9% p.a simple interest. Find the amount Amar will get at the time of maturity.
9) A Recurring Deposit Account of Rs 1200 per month has a maturity value of Rs 12440. If the rate of interest is 8% and the interest is calculated at the end of every month, find the time (in months) of this Recurring Deposit Account .
10) Sujata deposited , a certain sum of money, every months, for 5/2 years in a cumulative Time Deposit Account. At the time of maturity she collected Rs 4965. if the rate of interest was 8% p.a., find the monthly deposit.
Sap-2
1) Sunita paid Rs 300 per month for 2 years. He received Rs 7875 as the maturity amount. Find the rate of interest.
2) Meena has a cumulative Time Deposit Account of Rs 340 per month at 6% per annum. If she get Rs 7157 at the time of maturity, find the time for which the account was held.
3) On depositing Rs200, every month paying 9% p.a interest, a person collected Rs 2517 at maturity. Find the period.
4) Mamta has a cumulative Time Deposit Account in a bank. She deposits Rs 800 per month and gets Rs 15198 as maturity value. If the rate of interest be 7% p.a., find the total time for which the account was held.
5) Karim has a recurring deposit account for 2 years at 10%. If he receives Rs 1900 as interest, find the value of monthly installment paid by him.
6) Saloni has a cumulative time deposit account of Rs 340 per month at 6% p.a., if she get 7157 at the time of maturity, find the total time for which the account was held.
7) A man deposited Rs 150, every month in a bank for 8 months under the recurring deposit scheme. Find the maturity value of his deposits, if the interest is calculated every month and the rate of interest is 8% p.a.
8) Calculate the amount receivable on maturity of
a) recurring deposit of Rs 1200, deposited every month for 24 months at 10% p.a.
b) recurring deposit of Rs 100, every month for 5 years at 11% p.a.
c) recurring deposit of Rs 500, every month for 27 months at 10.5% p.a.
