CLASS- X
MATHEMATICS
F.M-80 TIME: 2 hrs.30 mins
Section - A(40 Marks)
Answer all questions.
1) a) If A=3 1 &. B= 1 0
-1 2 0 1 find A²- 5A + 7I. (3)
b) A certain sum of money is invested per month in a recurring deposit account for 2 years at 10% p.a. If the maturity amount is Rs 79500, find the sum invested per month. (4)
c) A boy scored the following marks in various class test each test being marked out 20.
15, 17, 16, 7, 10, 12, 14, 16, 19, 12, 16. (3)
i) What are his medium marks ?
ii) What is his model marks ?
2) a) Using reminder theorem, factorize the following polynomial completely.
3x³+ 2x² -19x +6. (4)
b) For the given progression 90, 81, 72, 63..... Find
i) the 200th term
ii) sum of first first 100 terms. (3)
c) If 3x - 5y= 2x + y, find the value of (3x + 5y)/(3x - 5y). (3)
3)a) Given a line segment PQ joining the points P(-4,6) and Q(8,-3). Find
i) the ratio in which PQ is divided by Y Axis.
ii) the coordinates of point of intersection.
iii) find the co-ordinate of mid point of PQ. (3)
b) Solve the following equation and calculate the answer correct two decimal places.
x²- 5x - 10=0. (3)
c) Solve the inequation, write the solution set and represent on the number line.
-3(x -7) ≥ 15 - 7x > (x +1)/3, x belongs to R. (4)
4)a) A certain number of metallic cones, each of 2cm radius and 3cm height are melted and recent into a solid sphere of 6cm radius. Find number of cones. (4)
b) Prove that: (sinx - 2 sin³x)/(2cos³x - cosx) = tanx. (3)
c) A man invests Rs 4500 in shares of a company which is paying 7.5% dividend. If Rs 100 shares are available at a discount of 10%. Find
i) the number of shares he purchases.
ii) his annual income. (3)
SECTION - B
5) a) use a graph paper for this question. (take 2cm= 1 unit on both x and y axis)
i) plot the following points A(0,4), B(2,3), C(1,1) and D(2,0)
ii) reflect points B, C, D on y-axis and write down, their coordinates. Name the images as B',C',D' a respectively.
iii) join points A, B, C D, D', C', B', A' in order so as to form a closed figure. Draw the line of locus of the figure formed. (4)
b) i) Find the geometric progression of which first term is 3 and common ratio is 4.
ii) Find 10th term. (3)
c) If (x+2) and (x +3) are factors of x³+ ax + b, find the values of a, b. (3)
Or
6) a) Rs 7500 divided equally among a certain number of children. Had there been 20 less children each would have received Rs 100 more. Find the original number of children. (4)
b) Calculate the mean of the following distribution using step deviation method
Marks no of students
00-10 10
10-20 9
20-30 25
30-40 30
40-50 16
50-60 10 (3)
c) Find the sum of 8 terms of AP 5, 10, 15, 20,..... (3)
7) a) in the figure given
diameter AB and chord CD of a circle meet at P. PT is a tangent to the circle at T. CD =7.8cm, PD= 5cm, PB= 4cm. Find
i) AB ii) length of tangent PT. (4)
b) If (x -9): (3x +6) is the duplicate ratio of 4:9. Find the value of x. (3)
c) if the given figure,
AB and DE are perpendicular to BC
AB and DE are perpendicular to BC
i) prove that ∆ ABC ~ ∆ DECA
ii) If AB= 6cm, De= 4cm and AC= 15cm. Calculate CD.
iii) find the ratio of the area ∆ ABC: area ∆ DEC. (3)
8) a) From the top of a building 60m high , the angle of depression of the top and bottom of a vertical lamp-post or observed to be 30° and 60° respectively. Find
i) horizontal distance between building and lamp post.
ii) the height of the lamp post. (4)
b) ifA= -2 0 & B= -1 & C= -2 D= 1
3 1 2x 1 3 with the relation AB + 3C = 2D, then find x and y. (3)
c) If the X intercept of a line is - 5 and y intercept is 16, find the equation of the line. (3)
9) If (x -9) : (3x +6) is the duplicate ratio of 4:9, find the value of x. (3)
b) Show that: √{(1- cosA)/(1+ cosA)}= sinA/(1+ cosA). (3)
c) in the given figure,
angle DBC=58°, BD is the diameter of the circle. Calculate i) angle BDC ii) angle BEC iii) angle BAC. (4)
Or
10) a) If [{√(3x +1)+ √(3x -1)}/{√(3x +1) - √(3x -1)}]= 3, find x. (4)
b) The circumference of the base of cylindrical vessel is 132cm and its height is 25cm. find the i) radius of the cylinder ii) volume of cylinder. (π=22/7). (3)
c) A card is drawn from my pack of 52 cards. Find the probability that the card drawn is
i) a red face card.
ii) neither a club nor a spade.
iii) neither an ace nor a king of red colour. (3)
MATH-2
F. M=80. TIME= 2:30 mins
Section - A (40 Marks )
(Answer all the questions in this section)
1) Choose the correct answer: (15)
i) If the classes of a frequency distribution are 1-10, 11-20,...71-80, then the upper limits of the class 21- 30 is
a) 30 b) 31 c) 30.5 d) 29.5
ii) if 1/2 is a root of the quadratic equation 4x²- 4kx + k +5=0, then the value of k is
a) 6 b) 3 c) - 3 d) -6
iii) A square metrix in which each diagonal element is 1 and other elements and 0 is called
a) null matrix b) square matrix c) rectangular matrix d) identity matrix
iv) If x, 12, 8 and 32 are proportion, then the value of x is
a) 6 b) 4 c) 3 d) 2
v) in an AP if d= -4, n= 7 and aₙ= 4 then a is
a) 6 b) 7 c) 20 d) 28
vi) The first and the last term of a GP are 3 and 96 respectively. if the common ratio is 2, the number of terms of the GP is
a) 4 b) 6 c) 7 d) 9
vii) The coordinates of the point P(-3,5) on reflection in the x-axis are
a) (3,5) b) (- 3,-5) c) ( 3,-5) d) (-3,5)
viii) If one end of the diameter of a circle is (2,3) and the centre is (-2,5), then the other end is
a) (-6,7) b) (6,-7) c) (0,8) d) (0,4).
ix) The reflection of a point P(-2,3) in the x-axis is
a) (2,3) b) (2,-3) c) (-2,-3) d) (-2,0).
x) The slope of a line passing through (3,-2) and (3,-4) is
a) -2 b) 0 c) 1 d) not defined
xi) If the area of 2 similar triangles are in the ratio 4:9, then their corresponding side are in the ratio
a) 9:4 b) 3:2 c) 2:3 d) 16:8
xii) (secx + tanx)(1- sinx) is equal to:
a) secx b) sinx c) cosx d) cosecx
xiii) When a dice is thrown the probability of getting an odd number less than 3 is
a) 1/6 b) 1/3 c) 1/2 d) 0
xiv) when 2x³ - x²- 3x +5 is divided by 2x +1, then the remainder is
a) 6 b) -6 c) -3 d) 0
xv) the mean proportion between 1/2 and 128 is
a) 64 b) 32 c) 16 d) 8
2) a) Rita has a recurring deposit account of Rs 1000 per month at 10% per annum . If she gets Rs 5550 as intrest at the time of maturity, find the total time for which the account was held. (4)
b) If A=2 0 & I= 1 0
-1 7 0 1 and A²= 9A + mI, find m. (3)
c) Solve the equation: 3x²- x -7=0 and give your answer correct to two decimal places. (3)
d) Find the range of values of x, which satisfy the inequation -1/5 ≤ 5x + 4 < 11, x belongs to R. Graph the solution on the number line. (3)
3) a) three numbers whose sum is 21 are in AP if 2, 2, 14 are added to them respectively, the resulting numbers are in GP. Find the numbers. (3)
b) calculate the ratio in which the line joining A(-4,2) and B(3,6) is divided by the point P(x,3). also find i) x and ii) length of AP. (4)
c) Mr Tiwari invested Rs 29040 in 15%, Rs 100 shares at a premium of 20%. Calculate
i) number of shares bought by Mr Tiwari .
ii) Mr tiwari's income from the investment.
iii) percentage return on his investment. (3)
d) State and draw the locus of a point which is equidistance from two fixed points. (2)
Section - B (40 marks)
Answer 4 in this section)
4) a) Ravi deposits Rs 2400 per month in a recurring deposit scheme of a bank for one year. if he gets Rs1248 as interest at the time of maturity, find the rate of interest. also find the maturity value of this deposit. (4)
b) In the given figure DE || BC and AD : DB = 2:5. Find
i) area of the triangle ADE/ area of the triangle ABC.
ii) area of triangle ABC /area of trapezium DBCE. (3)
c) Draw a histogram and find the mode for the following data:
Class frequency
10-20 7
20-30 15
30-40 26
40-50 14
50-60 5
60-70 2 (3)
5) a) a manufacturers buy raw material worth Rs4000, paying GST at the rate of 5%. He sells the finished product to the shopkeeper at a profit of 30%. If the rate of GST for the finished product is 12%, find the tax liability of the manufacturer. (4)
b) prove that: tan²x + cot²x +2= sec²x cosec²x. (3)
c) the equation of the line is 3x - 4y + 12 = 0. It meets the x-axis at the point A and y axis at the point B. Find
u) the coordinates of A and B.
ii) length of AB. (3)
6) a) What must be added to the polynomial 2x³- 3x²- 8x, so that it leaves a reminder 10 when divided by 2x +1? (3)
b) If x, 2x+ 2, 3x +3 are first three terms of a geometric progression, find the fourth term. (3)
c) Use graph paper for this question taking 1cm= 1 unit on both x and y axis.
i) plot the following points on your graph paper: A(-4,0) B(- 3,2) C( 0,4) D(4,1) and E(7,3).
ii) reflect the point B, C, D, E on the axis and name them as B', C' , D', E' respectively.
iii) join the points A,B,C,D, E, E', D', C', B' and A in order
iv) name the closed figure formed. (4)
7)a) 40 students entered for a game of shot put competition. The distance thrown in metres) is given below :
Distance. No of students
12-13 3
13-14 9
14-15 12
15-16 9
16-17 4
17-18 2
18-19 1
use graph paper to draw an ogive for the given distribution.
Use a scale of 2cm= 1m on one axis and 2cm= 5 students in the other axis. Using the graph find:
i) The median ii) upper quartile iii) number of students who cover a distance which is above 16 and 1/2 m. (6)
b) if x, y, z are in continued proportion, prove that: x²- y² : x²+ y²= x - z : x + z. (4)
8) a) a man on the top of a vertical Tower observes a car moving with uniform speed coming directly towards it. if it takes 12 minutes for the angle of depression to change 30° to 45°, how soon after this will the car reach the observation Tower. (3)
b) Find the mean by shortcut method :
C. I frequency
35-40 7
40-45 6
45-50 9
50-55 5
55-60 3. (4)
c) Find the probability of having 53 Sundays in a i) leap year ii) non leap year. (3)
CLASS- X
MATHEMATICS
F.M-80 TIME: 2 hrs.30 mins
Section - A(40 Marks)
Answer all questions.
1) a) If A=3 1 &. B= 1 0
-1 2 0 1 find A²- 5A + 7I. (3)
b) A certain sum of money is invested per month in a recurring deposit account for 2 years at 10% p.a. If the maturity amount is Rs 79500, find the sum invested per month. (4)
c) A boy scored the following marks in various class test each test being marked out 20.
15, 17, 16, 7, 10, 12, 14, 16, 19, 12, 16. (3)
i) What are his medium marks ?
ii) What is his model marks ?
2) a) Using reminder theorem, factorize the following polynomial completely.
3x³+ 2x² -19x +6. (4)
b) For the given progression 90, 81, 72, 63..... Find
i) the 200th term
ii) sum of first first 100 terms. (3)
c) If 3x - 5y= 2x + y, find the value of (3x + 5y)/(3x - 5y). (3)
3)a) Given a line segment PQ joining the points P(-4,6) and Q(8,-3). Find
i) the ratio in which PQ is divided by Y Axis.
ii) the coordinates of point of intersection.
iii) find the co-ordinate of mid point of PQ. (3)
b) Solve the following equation and calculate the answer correct two decimal places.
x²- 5x - 10=0. (3)
c) Solve the inequation, write the solution set and represent on the number line.
-3(x -7) ≥ 15 - 7x > (x +1)/3, x belongs to R. (4)
4)a) A certain number of metallic cones, each of 2cm radius and 3cm height are melted and recent into a solid sphere of 6cm radius. Find number of cones. (4)
b) Prove that: (sinx - 2 sin³x)/(2cos³x - cosx) = tanx. (3)
c) A man invests Rs 4500 in shares of a company which is paying 7.5% dividend. If Rs 100 shares are available at a discount of 10%. Find
i) the number of shares he purchases.
ii) his annual income. (3)
SECTION - B
5) a) use a graph paper for this question. (take 2cm= 1 unit on both x and y axis)
i) plot the following points A(0,4), B(2,3), C(1,1) and D(2,0)
ii) reflect points B, C, D on y-axis and write down, their coordinates. Name the images as B',C',D' a respectively.
iii) join points A, B, C D, D', C', B', A' in order so as to form a closed figure. Draw the line of locus of the figure formed. (4)
b) i) Find the geometric progression of which first term is 3 and common ratio is 4.
ii) Find 10th term. (3)
c) If (x+2) and (x +3) are factors of x³+ ax + b, find the values of a, b. (3)
Or
6) a) Rs 7500 divided equally among a certain number of children. Had there been 20 less children each would have received Rs 100 more. Find the original number of children. (4)
b) Calculate the mean of the following distribution using step deviation method
Marks no of students
00-10 10
10-20 9
20-30 25
30-40 30
40-50 16
50-60 10 (3)
c) Find the sum of 8 terms of AP 5, 10, 15, 20,..... (3)
7) a) in the figure givendiameter AB and chord CD of a circle meet at P. PT is a tangent to the circle at T. CD =7.8cm, PD= 5cm, PB= 4cm. Find
i) AB ii) length of tangent PT. (4)
b) If (x -9): (3x +6) is the duplicate ratio of 4:9. Find the value of x. (3)
c) if the given figure,
AB and DE are perpendicular to BC
AB and DE are perpendicular to BC
i) prove that ∆ ABC ~ ∆ DECA
ii) If AB= 6cm, De= 4cm and AC= 15cm. Calculate CD.
iii) find the ratio of the area ∆ ABC: area ∆ DEC. (3)
8) a) From the top of a building 60m high , the angle of depression of the top and bottom of a vertical lamp-post or observed to be 30° and 60° respectively. Find
i) horizontal distance between building and lamp post.
ii) the height of the lamp post. (4)
b) ifA= -2 0 & B= -1 & C= -2 D= 1
3 1 2x 1 3 with the relation AB + 3C = 2D, then find x and y. (3)
c) If the X intercept of a line is - 5 and y intercept is 16, find the equation of the line. (3)
9) If (x -9) : (3x +6) is the duplicate ratio of 4:9, find the value of x. (3)
b) Show that: √{(1- cosA)/(1+ cosA)}= sinA/(1+ cosA). (3)
c) in the given figure,angle DBC=58°, BD is the diameter of the circle. Calculate i) angle BDC ii) angle BEC iii) angle BAC. (4)
Or
10) a) If [{√(3x +1)+ √(3x -1)}/{√(3x +1) - √(3x -1)}]= 3, find x. (4)
b) The circumference of the base of cylindrical vessel is 132cm and its height is 25cm. find the i) radius of the cylinder ii) volume of cylinder. (π=22/7). (3)
c) A card is drawn from my pack of 52 cards. Find the probability that the card drawn is
i) a red face card.
ii) neither a club nor a spade.
iii) neither an ace nor a king of red colour. (3)
1) Find the value of k if (x -2) is a factor of x³+ 2x²- Kx +10
Hence, determine whether x + 5 is also factor.
2) If A= 3 5 & B= 2
4 -2 4 is the product AB possible ? give reason. If yes find AB
3) From a pack of 52 playing cards all cards whose numbers are multiples of 3 are removed. A card is now drawn at random.
What is the probability that card drawn is:
a) a face card (king, Jack , queen)
b) an even numbered red card.
4) Solve the following equation:
x - 18/x = 6. Give your answer correct to two significant figures.
5) In the figure O is the centre of the circle.
Tangents at A and B meet at C
If angle ACO= 30°, find the angle BCO, AOB, APB
6) Abhi has a recurring deposit account in a bank. He deposits Rs 2500 per month for 2 years. If he gets RS 66250 at the time of maturity, find;
a) The intrest paid by the bank.
b) the rate of interest.
7) ABC is a triangle and G(4,3) is the centroid of the triangle. If A(1,3), B(4,b) and C(a,1l, find a and b.
8) Solve the following inequation and represent the solution set on the number line 2x - 5 ≤ 5x + 4< 11, where x belongs to I, I is a set of integers .
9) A mathematical aptitude test of 50 students was recorded as follows :
Marks no of students
50-60 4
60-70 8
70-80 14
80-90 19
9-100 5
Draw a histogram for the above data using a graph paper and locate the mode.
10) A manufacturer sells a washing machine to a wholesaler for Rs 15000. The wholesaler sells it to a trader at a profit of Rs 1200 and the trader in turn sells it to a consumer at a profit of Rs 1800. If the rate of GST is 8% find,
a) The amount of GST received by the State Government on the sale of this machine from the manufacturer and the wholesaler.
b) The amount that consumer pays for the machine.
11) A solid cone of radius 5cm and height 8cm is melted and made into small spheres of radius 0.5cm. Find the number of spheres is formed.
12) ABCD is a parallelogram where A(x,y), B(5,8), C(4,7) and D(2,-4). Find
a) coordinates of A.
b) equation of diagonals BD.
13) use a graph paper to answer the following questions. (Take 1cm= 1 unit on both axes)
a) plot A(4,4), B(4,-6) and C(8,0), the vertices of a triangle ABC .
b) Reflect ABC on the y-axis and and name it as A'B'C'.
c) Write the co-ordinate of the image A', B' and C'.
d) Give a geometrical name for the figure AA'C'B'BC.
e) identify the line of symmetry of AA'C'B'BC.
14) Solve for x: {√(3x+4) + √(3x -5)}/{√(3x+4) - √(3x -5)} = 9.
15) If A= 2 5 & B= 4 -2
1 3 -1 3 and I is the identity matrix of the same order and A' is the transpose of matrix A, find A'B + BI.
16) In the following figure ABC is a right angled triangle with angle BAC= 90°,
and AD perpendicular BC.
a) prove ∆ ADB ~ ∆ CDA
b) if BD= 18cm, CD = 8cm find AD.
c) find the ratio of the area of ∆ ADB to area of ∆ CDA.
17) a) Using step deviation method, calculate the mean marks of the following distribution.
b) State the model class .
Class interval frequency
50-55 5
55-60 20
60-65 10
65-70 10
70-75 9
75-80 6
80-85 12
85-90 8
18) Marks obtained by 200 students in an examination are given below:
Marks frequency
00-10 5
10-20 11
20-30 10
30-40 20
40-50 37
60-70 40
70-80 29
80-90 14
90-100 6
Draw an ogive for the given distribution taking 2 cm= 10 marks on one axis and 2cm = 20 students in the other axis. Using the graph, determine:
a) The median marks
b) The number of students who failed if minimum marks required to pass is 40.
c) If scoring 85 and more marks is considered as grade one. find the number of students who secured grade one in the examination.
19) Mr parik invested Rs 52000 on Rs 100 shares at a discount of Rs 20 playing 8% dividend . At the end of 1 year he sells the shares at a premium of Rs 20. Find
a) the annual dividend.
b) the profit earned including his dividend.
20) Draw a circle of radius 3.5cm. Mark a point P outside the circle at a distance of 6cm from the centre. Construct two tangents from P to the given circle. Measure and write down the length of tangent.
21) Show: (cosecA - sinA)(secA - cosA) sec²A= tanA.
22) 6 is the mean proportion between two numbers x and y and 48 is a third proportional of x and y. Find the numbers.
23) A man observes the angle of elevation of the top of a building to be 30°. He walks towards it in a horizontal line through its base. On covering 60m the angle of elevation changes to 60°. Find the height of the building correct to the nearest metre.
24) ABC is a triangle with AB= 10cm, BC= 8cm and AC= 6cm (not drawn to scale).
Three circles are drawn touching each other with the vertices as their centres. Find the radii of the three circles .
25) Rs 480 is divided equally among x children. if the number of children were 20 more than each would have Rs 12 less. Find x
26) Given equation of line L₁ is y= 4.
a) Write the slope of line L₂ if L₂ is the bisector of angle O.
b) Write the coordinates of point P.
c) Find the equation of L
Short questions
1) Roots of the equation 3x² - 2√6x +2=0 are
a) ±√(2/3) b) √(2/3), √(2/3) c) - √(2/3), √(2/3) d) √(2/3), √(3/2)
2) If x -2 is a factor of x²- 7x + 2m, then the value of m is
a) 5 b) 6 c) 4 d) 3
3) The transpose of the matrix
1 5 4
-2 1 6 is
a) 1 -2 b) -2 1 6 c) 1 -2 d) 4 5. 1
5 1 1 5. 4 5 1 6 1 -2
-2 6 4. 6
4) Which term of the GP 18, 12, 8,.....is 512/729 ?
a) 9th b) 10th c) 11th d) 12th
5) The sum of the first 16 terms of the AP 10, 6, 2 is :
a) -320 b) 320 c) -350 d) -300
6) The roots of the quadratic equation x²- 5x +5=0 are
a) real and equal
b) real and unequal
c) rational d) imaginary
7) The remainder when x³- 2x²- 5x +6 is divided by x + 2 is:
a) -1 b) 1 c) 2 d) 0
8) For a GP with first term a, common ratio r and last term l, the nth term from the end is:
a) lrⁿ⁻¹ b) rⁿ⁻¹/l c) rⁿ⁻¹/l d) l/rⁿ⁻¹
9) 30th of AP 10, 7, 4,... is :
a) 97 b) 77 c) -77 d) -87
10) If 8- x ≥ 6 - 2x, x belongs to N, then the solution set is:
a) {-2,-1,0,1...} b) {1, 2, 3,...} c) { 0,1, 2,3,...} d) {-1,0,1,2,...}
11) The order of a column matrix is of the form:
a) m x 1 b) 1 x m c) m x 2 d) 2x2
12) On dividing x²- 4x + m by x -2 the remainder is -1. The value of m is:
a) 1 b) 2 c) -2 d) 3
13) An identity matrix is always :
a) a square Matrix
b) a rectangular Matrix
c) a row matrix
d) a null matrix
14) the sum of 1+ 3+ 7+ ....199 is
a) 10000 b) 9000 c) 8000 d) 8500
15) 12th term of the GP 4, 8, 16, 32 is
a) 8000 b) 8050 c) 8120 d) 8192
16) The discriminant of the quadratic equation x²- 2x +1=0:
a) =0 b) > 0 c) < 0 d) none
17) The value of m so that x + 6 is a factor of x³+ 5x²- 4x + m, is:
a) 7 b) - 3 c) 6 d, 12
18) Which term of the AP 72, 68, 64,......is 0.
a) 15 b) 18 c) 19 d) 20
19) the progression a₁, a₂, a₃, ......., aₙ forms of an GP only is
a) aₙ/aₙ₋₁ = constant b) aₙ - aₙ₋₁ = constant
c) aₙ x aₙ₋₁= constant d) aₙ₋₁/aₙ= constant
20) If 4x - 2≥ 8 - x, x belongs to N, then the solution is
a) { 2, 3, 4, 5,...}
b) { 1, 2, 3, 4,....}
c) { 0, 1, 2, 3,...}
d) { 2, 3, 4, 5, 6}
21) Order of Matrix P is 2 x 1 and that of Q is also 2 x 1. The order of the matrix 2P - Q is
a) 2x2 b) 4x1 c) 2x1 d) 3x2
TEST PAPER - 2
SECTION A(40 Marks)
Answer All questions from this Section
Question 1.
a) Solve the following Quadratic Equation: x²- 7x +3=0
Give your answer correct to two decimal places. (3)
b) Given A= x 3
y 3
If A²= 3I , where I is the identity matrix of order 2. Find x and y. (3)
c) Using ruler and compass construct a triangle ABC where AB= 3cm. BC= 4cm and angle ABC= 90°. Hence constructed a circle circumscribing the triangle ABC . Measure and write down the radius of the circle. (4)
Question 2
a) Use factor theorem to factorise 6x³+ 17x²+ 4x - 12 completely. (3)
b) Solve the following inequation and represent the solution set on the number line.
3x/5 + 2< x + 4 ≤ x/2 + 5, x ∈R. (3)
c) Draw a Histogram for given data, using a graph paper:
Weekly wages(Rs) no of people
3000-4000 4
4000-5000 9
5000-6000 17
6000-7000 6
7000-8000 7
8000-9000 2
9000-10000 4
Estimate the mode from the graph. (4)
Question 3
a) In the figure given below,
O is the centre of the circle and AB is a diameter.
If AC= BD and angle AOC= 72, find: angle ABC, BAD, ABD. (3)
b) Prove that: sinA/(1+ cotA) - cosA/(1+ tanA)= sinA - cosA. (3)
c) In what ratio is the line joining P(5,3) and Q(-5,3) divided by the y-axis? Also find the coordinates of the point of intersection. (4)
Question 4
a) A solid spherical ball of radius 6cm is melted and recast into 64 identical spherical marbles.
Find the radius of each marble. (3)
b) Each of the letters of the word AUTHORISE is written on identical circular disc and put in a bag. They are will suffered. If a disc is drawn at random from the bag, what is the probability that the letter is:
(i) a vowel
ii) one of the first 9 letters of the English alphabet which appears in the given word.
iii) one of the last 9 letter of the English alphabet which appears in the given word ? (3)
c) Mr. Bedi visit the market and buys the following articles:
Medicine costing Rs 950, GST @ 5%
A pair of shoes costing Rs 3000, GST @ 18%
A laptop bag costing Rs 1000 with a discount of 30%, GST @ 18%.
i) Calculate the total amount of GST paid
ii) The total bill amount including GST paid by Mr. Bedi. (4)
SECTION B(40 Marks)
Attempt any four questions from this Section.
Question 5
a) A company with 5000 shares of nominal value Rs 120 declares an annual dividend of 15%, calculate
i) the total amount of dividend paid by the company.
ii) annual income of Mr. Sharma who holds 80 shares of the company.
If the return percentage of Mr. Sharma from his shares is 10%, find the market value of each share . (3)
b) The mean of the following data is 16, Calculate the value of f.
Marks : 5 10 15 20 25
No of boys: 3 7 f 9 6. (3)
c) The 4th, 6th and the last term of a geometric progression are 10, 40 and 640 respectively. If the common ratio is positive, find the first terms , common ratio and the number of terms of the series. (4)
Question 6
a) if A= 3 0 & B= -4 2
5 1. 1 0
Find A²- 2AB + B². (3)
b) In the given figure AB= 9cm, PA= 7.5cm and PC= 5cm
Chords AD and BC intersect at P
i) prove that ∆ PAB ~ ∆ PCD
ii) Find the length of CD
iii) Find area of ∆ PAB: area of ∆ PCD. (4)
c) From the top of a cliff, the angle of depression of the top and bottom of a tower are observed to be 45° and 60° respectively. If the height of the tower is 20m. Find
i) the height of the cliff .
ii) the distance between the Cliff and the tower. (4)
Question 7
a) Find the value of p if the lines, 5x - 3y +2=0 and 6x - py+7=0 are perpendicular to each other. Hence find the equation of a line passing through (-2, -1) and parallel to 6x - py+7= 0. (3)
b) Using properties of proportion find x: y. Given (x²+ 2x)/(2x +4)= (y²+ 3y)/(3y +9). (3(
c) In the given figure TP and TQ are two tangents to the circle with centre O,
touching at A and C respectively. If angle BCQ= 55° and angle BAP= 60°, find:
Angle OBA, OBC, AOC, ATC. (3)
Question 8
a) What must be added to the polynomials 2x³- 3x²- 8x, so that it leaves a remainder 10 when divided by 2x +1. (3)
b) Mr. Sonu has a recurring deposit account and deposits Rs 750 per month for 2 years. If he gets Rs19125 at the time of maturity, find the rate of interest. (3)
c) Use graph paper for this question.
Take 1cm= 1 unit on both x and y axes.
i) Plot the following points on your graph sheets:
A(-4,0), B(-3,2), C(0,4), D(4,1) and E(7,3).
ii) Reflect the points B, C, D and E on the x-axis and name them as B',C', D', E' respectively.
iii) join the points A,B, C, D, E, E', D', C', B' and A in order.
iv) Name the closed figure formed. (4)
Question 9
a) 40 students enter for a game of shot-put competition. The distance thrown (in metres) is recorded below:
Distance (in m) no of students
12-13 3
13-14 9
14-15 12
15-16 9
16-17 4
17-18 2
18-19 1
Use graph paper to draw on Ogive for the above distribution.
Use a scale of 2cm = 1m on one axis and 2cm= 5 students on the other axis.
Hence using your graph find:
i) the median
ii) Upper quartile
iii) Number of students who cover a distance which is above 33/2 m. (6)
b) If x= {√(2a +1) + √(2a -1)}/{√(2a +1) - √(2a -1)} , prove that x²- 4ax +1=0. (4)
Question 10
a) if the 6th term of an AP is equals 4 times its first term and the sum of first six terms is 75, find the first term and the common difference. (3)
b) The difference of two natural numbers is 7 and their product is 450. Find the numbers. (3)
c) Use ruler and compass for this question. Construct a circle of radius 4.5cm. (4)
Question 11.
a) A model of a high rise building is made to a scale of 1:50.
i) If the height of the model is 0.8m, find the height of the actual building.
ii) if the floor area of a flat in the building is 20m², find the floor area of that in the model. (3)
b) From a solid wooden cylinder of height 28cm and diameter 6cm, two conical cavities are hollowed out.
The diameter of the cones are also 6cm and height 10.5cm. (3) find the volume of the remaining solid prove The Identity
Section - A (Attempt all questions)
Question 1: Choose the correct answers to the question from the given options: (15)
i) A Dealer in Mumbai sold a washing machine to a consumer in Mumbai for Rs18000. If the rate of GST is 18%, then SGST is
a) Rs1620 b) Rs3240 c) nil d) none
ii) Roots of the equation 3x²- 2√6x + 2=0 are:
a) ±√(2/3) b) √(2/3), √(2/3) c) - √(2/3) , -√(2/3) d) -√(2/3) , -√(3/2)
iii) if x - 2 is a factor of x²- 7x + 2m, then the value of m is
a) 5 b) 6 c) 4 d) 3
iv) The transpose of the matrix
1 5 4
-2 1 6 is
a) 1 -2 b) -2 1 6 c) 1 -2 d) 4 5 1
5 1 1 5 4 5 1 -6 1 -2
-2 6 4 6
v) 21% Rs 100 shares at Rs 140 gives rate of return as:
a) 10% b) 120% c) 15% d) 25%
vi) The Reflection of the point P(0,3) in the y-axis is:
a) (0,-3) b) (3,0) c) (0, 3) d) (0,0)
vii) In the figure,
all dimensions are in cm.
The length of AD is:
a) 12cm b) 14cm c) 16 cm d) 18 cm
viii) Richa attaches a conical attachment to one side of the coin. The radius of coin and conical attachment is same. Which of the following is the surface area of the combined solid ?
a) coin base area + coin CSA
b) coin base area + coin CSA + cone CSA
c) total surface area of coin + total surface area cone.
d) total surface area of cone.
ix) Which term of the GP 18, 12, 8, ...., is 512/729 ?
a) 9th b) 10th c) 11th d) 12th
x) if a coin is tossed 3 times, what is the probability of getting a tail each time ?
a) 1/8 b) 1/4 c) 1/16 d) 1/6
xi) Two similar jugs have heights of 4cm and 6cm respectively. If the capacity of the smaller jug is 48 cm³, then the capacity of the larger jug is:
a) 100 cm⅔ b) 130cm³ c) 152cm³ d) 162cm²
xii) x-axis divides the line segment joining the points (2,-3) and (5,6) in the ratio.
a) 1:2 b) 2:1 c) 3:5 d) 2:3
xiii) In the given figure,
O is the centre of the circle. If Angle OAB=40°, then angle ACB is equal to
a) 50° b) 40° c) 60° d) 70°
xiv) The sum of the first 16 terms of the AP is 10, 6, 2,.... is
a) -320 b) 320 c) -350 d) -300
xv) Assertion (A): The median of the following: 12.5, 12, 13, 15, 11, 12, 14, 16, 10, 12, 13
Reason (R): The value of the middle most observation obtained after arranging the data in an ascending and descending order is called the medium of the data
a) A is true, R is false
b) A is false, R is true
c) both A and R are true
d) both A and R are false
Question 2:
i) A conical tent is to accommodate 77 perso. Each person must have 16 m³ of air to breathe. Given the radius of the tent as 7m, find the height of the tent and also its curved surface area. (4)
ii) Amit Kumar invests Rs 36000 in buying Rs100 shares at Rs20 premium. The dividend is 15% per annum. Find :
a) the number of shares he buys.
b) his yearly dividend.
c) the percentage return on his investment. (4)
iii) The sum of three numbers in GP is 35 and their product is 1000. Find the numbers . (4)
Question 3:
i) Pawan deposituRs 150 every month in a bank for 8 months under the recurring deposit scheme. Find the maturity value of his deposit, if the interest is calculated every month and the rate of the interest is 8% per annum. (4)
ii) Find the equation of a line passing through the point (-2,3) and having the x-intercept of 4 units. (4)
iii) Use graph paper to solve this question.
a) Plot the points P(0,3), Q(3,-2) and O(0,0) .
b) Plot R, the image of Q, when reflected in the y-axis and write its coordinates.
c) What is the geometrical name of the figure PQOR ? (5)
SECTION - B
(Attempt any four questions from this section)
Question 4:
i) A dealer is Patna (Bihar) supplies goods worth Rs 15000 to a dealer in Sonipat (Haryana). The dealer in Sonepat supplies the same goods to a dealer in Rohtak (Haryana) at a profit of Rs3000. If the rate GST is 18%. calculate:
a) The cost of goods to the dealer in Rohtak.
b) Net GST paid by the dealer in Sonepat . (3)
ii) Solve the equation 4x²- 5x -3=0 and give your answer to correct to two decimal places. (3)
iii) On a map drawn to a scale if 1: 250000, a triangular plot of land has the following measurements. AB= 3cm, BC =4 cm and angle ABC=90°. Calculate
a) the actual length of AB in km.
b) the area of the plot in km². (4)
Question 5:
i) If A= 0 -1 B= 1 3 C= 1 0
2 5 6 4 -3 -2
find A(B + C). (3)
ii) Two circles touch externally at P. a tangent touches the circles at A and B. Prove that the tangent at P bisects AB. (3)
iii) The polynomial (px³+ 3x²-3) and (2x³- 5x +p) when divided by (x -4) leave the same reminder. Find the value of p. (4)
Question 6:
i) Find the coordinates of the point of trisection of the line segment joining the points A(5,-3), and B( 2,-9). (3)
ii) Prove that: cotA - tanA = (2cos²A -1)/(sinA cosA). (3)
iii) How many terms of the AP 72, 66, 60,..... must be taken to give the sum 0 ? (4)
Question 7:
i) The daily wages of 80 workers in a project ate given below:
Wages No. Of workers
400-450 2
400-500 6
500-550 12
550-600 18
600-650 24
650-700 13
700-750 5
Use a graph paper to draw an ogive for the above distribution, (use a scale of 2cm = Rs50 on x-axis and 2cm= 10 workers on yaxr). Use your ogive to estimate :
a) the median wagy of the workers .
b) the lower quartile wage of workers.
c) the number of workers who earns more than Rs625 daily. (5)
ii) A bus covers distance of 240 km at a uniform speed. Due to heavy rain its speed gets reduced by 10 km/hr and as such it takes two hours longer to cover the total distance. Assume the uniform speed to be x km/hr, form an equation and solve it to evaluate x. (5)
Question 8:
i) In a lottery there are 5 prizes and 20 blanks. What is the probability getting a prize ? (3)
ii) Construct a quadrilateral ABCD which AB= 5cm, BC= 4cm, angle B= 60°, AD= 5.5cm and D is equidistant from AB and BC. (3)
iii) In the given figure,
PQ is a tangent to the circle at A. AB and AD are bisectors of angle CAQ and angle PAC. If Angle BAQ= 30°, show that
a) BD is a diameter of the circle.
b) ABC is an isosceles triangle. (4)
Question 9:
i) Solve the following inequation and graph the solution set on the number line:
-1/5 ≤ 3x/10 +1 < 2/5, x ∈ R. (3)
ii) Calculate the mean of the following distribution using step deviation method.
Marks no.of students
00-10 10
10-20 9
20-30 25
30-40 30
40-50 16
50-60 10 (3)
iii) In the figure,
ABCD is a parallelogram. P is a point on BC such that BP: PC= 1:2. DP produced meets produced at Q. Given ar(∆CPQ) is 20 m², find
a) ar(∆ DCP)
b) ar(|| gm ABCD). (4)
Question 10:
i) using properties of proportion, solve for x. Given that x is positive:
{2x + √(4x²-1)}/{2x - √(4x²-1)}= 4. (3)
ii) Draw a circle with centre O and radius 3.1cm. Take a point P outside the circle at a distance of 6.2cm from its Centre. Draw two tangents to the circle from the point P. (3)
iii) An aeroplane at an altitude of 1500 metres finds that two ships are selling towards it in the same direction. The angles of depression as observed from the aeroplane are 45° and 30° respectively. Find the distance between the two ships. (4)
