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PQS-01

A Compilation By

O.P. GUPTA Math Mentor & Author, INDIRA Award Winner SACHIN PANDEY HOD Maths, St Mary’s School, Rudrapur 01. 02. 03.

13 terminates after 1250 (a) 2 places (b) 3 places (c) 4 places (d) 5 places The value of k for which the lines 3x  y  3 and 6x  ky  8 do not have solution, is (b) 4 (c) 3 (d) 2 (a) 5 A tree of height 20 m breaks at a point 5m high from the foot of the tree touching the ground at

The decimal expansion of

a point, then the distance between the foot of the tree and top of the tree is 04.

(b) 10 2 m (c) 200 m (d) 2 100 m (a) 2 10 m The lengths of the two diagonals of a rhombus are 16 cm and 14 cm, then the length of each side of the rhombus is (a) 15 cm

05.

06. 07. 08.

09. 10.

(b) 28 cm (c) 113 cm (d) 115 cm A die is drawn once. What is the probability of getting a prime number? 1 2 4 5 (a) (b) (c) (d) 2 3 5 6 If ABC  PQR , BC  4 cm and QR  7 cm , then area of ABC : area of PQR  (b) 16 : 49 (c) 44 : 77 (d) 8:14 (a) 4 : 7 If sec sin  0 , then the value of  is (a) 30 (b) 45 (c) 90 (d) 0 The smallest natural number by which 300 should be multiplied so that the square root of the product is rational number is (a) 3 (b) 5 (c) 7 (d) 11 The lines represented by 4x  5y  3 and 16x + 20y  6 are (a) intersecting (b) coincident (c) parallel (d) None of these The coordinates of the point which divides the line segment joining the points ( 3, 3) and (3,  3) in the ratio 2 : 1 is (a) (3,  3) (b) (2,  2) (c) (1,  1) (d) (0, 1)

12.

The LCM of the smallest composite number and smallest 2-digit number is (a) 4 (b) 40 (c) 20 (d) 14 The LCM of two numbers p and q is 200 and their HCF is 5. Then Pq=

13.

(b) 2000 (c) 1000 (a) 5 If 5cot A=8, then the value of sin A sec A is

11.

(d) 40

MATHEMATICIA By O.P. GUPTA : A New Approach in Mathematics

1

CBSE Practice Questions Sheet Term I (2021-22)

(a)

25 64

(b)

64 25

(c)

By O.P. GUPTA (INDIRA Award Winner)

5 8

(d)

5 8

15.

If α  30°, then 3sinα  4sin3α = (a) 0 (b) 1 (c) 2 (d) 3 The circumference of a circle that can be inscribed in a square of side 14cm is

16.

(b) 77 cm (c) 80cm (d) 44cm (a) 154cm Which of the following represents area of a quadrant, with radius r?

17.

 r2 r 2  r2 (b) (c) (d)  r 2 4 2 8 The altitude of an equilateral triangle when each of its side is ‘a’ cm, is

14.

(a)

2 2 a cm 3 1 The value of sin2 60   is 2 cosec 30 (a)

18.

2 a cm 3

(b)

(c)

3 2 a cm 4

(d)

3 a cm 2

1 31 (b) (c) 1 (d) 0 2 2 The pair of linear equations 22x  3y  9 and 4x  6y  18 is (a) Consistent and dependent (b) Consistent but not dependent (c) Inconsistent (d) Coincident on each other All the kings are removed from a well-shuffled deck of 52 cards. A card is drawn from the remaining cards. Then probability of getting a red card is 11 1 6 5 (a) (b) (c) (d) 25 2 13 12

(a)

19.

20.

21. 22. 23. 24.

25. 26.

27.

28. 29. 2

Mid-point of a line segment joining (0, 8) and (–6, 4), is (a) (0, 0) (b) (–3, –6) (c) (–3, 6) (d) (6, –3) Solve : x  y  2, 2x  y   8 . (a) x   2, y  4 (b) x  2, y  4 (c) x  2, y   4 (d) x  2, y  4 sin 4 A  cos 4 A = (a) 2 sin 2 A  1 (b) 2 cos2 A  1 (c) 1 2 sin A (d) 1 2 cos A For which value of k will the pair of linear equations 3x  y  1 and 3k x  5y  2 have no solution? (b) 3 (c) 5 (d) 7 (a) 2 LCM of two prime numbers x and y is 187 (x  y). Find the value of 2(x y). (a) 10 (b) 12 (c) 11 (d) 13 A die is thrown once. What is the probability of getting a number greater than or equal to 3? 2 1 4 5 (a) (b) (c) (d) 3 2 5 6 Two coins are tossed simultaneously. Then the probability of getting both the heads or tails is 1 1 3 (b) (c) (d) 1 (a) 4 2 4 The value of 5 tan2 x  5sec 2 x is (b) 0 (c) 5 (d) 5 (a) 10 ( 4 , 3)   The distance of the point from the origin is MATHEMATICIA By O.P. GUPTA : A New Approach in Mathematics

 Mathematics for X

For all the Math-Gyan, visit at THEOPGUPTA.COM

(a) 7 units (b) 7 units (c) 5 units (d) 6 units Diagonals of a trapezium ABCD with AB  DC intersect each other at O. If AB  2CD, then (area AOB) : (area COD)  (a) 4:1 (b) 3:4 (c) 2 : 3 (d) 5:1 What is the solution of the pair of equations 2x  y  6 and x  y  9 ? (a) x = 4 , y = 5 (b) x = 5, y = 4 (c) x = 1, y = 2 (d) x =  2 , y = 3

30.

31.

2 1  tan 45 is 2 1  tan 45 (b) 1 (c) 2 (d) 3 (a) 0 Prime factorization of 11  13  13 is (a) 22  3 13 (b) 2  32  13 (c) 2  3 13 (d) 2  3 132 A man goes 10 m due east and then 24 m due north. Find the distance from the starting point.

The value of

32. 33.

34.

(b) 576 m (c) 676 m (d) 26 m (a) 476 m The coordinates of a point A which divides the line segment joining the point P(4, –3) and Q(8, 5) are (7, 3). In what ratio the point A divides the line PQ internally? (b) 1: 3 (c) 3 :1 (d) 2 : 1 (a) 1: 2 The area of a quadrant of a circle with radius 7 cm is 77 2 74 22 2 35 cm cm 2 cm cm 2 (a) (b) (c) (d) 2 4 7 2 Which of the following will satisfy the pair of equations kx  y  2, x  y  4 with unique solution? (a) k   1 (b) k   1 (c) k  1 d) None of these 2 If 1 is a zero of the polynomial p(x) = x  7x  8 , then the other zero is (b) 8 (c) 1 (d) 0 (a) 7 The perimeter and area of a circle are numerically equal. What is the radius of the circle? (a) 1units (b) 2 units (c) 3units (d) 4 units The number of solutions of the pair of linear equations 3x  5y =  1 and 6x  y = 7 (b) infinite (c) 1 (d) 2 (a) 0

35.

36.

37.

38. 39. 40.

If you’ve any doubt or want help, please post the image (screenshot) of your question in the Telegram Group https://t.me/Mathematicia4Tenth

 ANSWER KEY 01. 07. 13. 19. 25. 31. 37.

(c) (d) (c) (b) (b) (b) (b)

02. 08. 14. 20. 26. 32. 38.

(d) (a) (b) (b) (a) (a) (b)

03. 09. 15. 21. 27. 33. 39.

(b) (c) (d) (c) (b) (a) (b)

04. 10. 16. 22. 28. 34. 40.

(c) (c) (a) (a) (d) (d) (c)

05. 11. 17. 23. 29. 35.

(a) (c) (d) (a) (c) (c)

MATHEMATICIA By O.P. GUPTA : A New Approach in Mathematics

06. 12. 18. 24. 30. 36.

(b) (c) (b) (c) (a) (a)

3

CBSE Practice Questions Sheet Term I (2021-22)

By O.P. GUPTA (INDIRA Award Winner)

PQS-02

A Compilation By

O.P. GUPTA Math Mentor & Author, INDIRA Award Winner SACHIN PANDEY HOD Maths, St Mary’s School, Rudrapur 01.

02.

If two positive integers a and b are written as a  x3 y2 and b  xy3 , where x , y are prime numbers, then HCF (a , b) is (b) xy2 (c) x3 y (d) x 2y 2 (a) xy One equation of a pair of dependent lines is 5x  7y  2, the second equation can be (a) 10x  14y 4 0

(b)  10x  14y  4  0

(c) 10x  14y  4  0 03.

(d) 10x  14y   4

If the zeroes of the quadratic polynomial ax  bx  c; c  0 are equal, then (b) c and b have opposite signs (a) c and a have opposite signs 2

(c) c and a have the same sign 04.

05. 06.

07.

08.

09.

10.

The zeroes of the quadratic polynomial x 2  99x  127 are (a) both positive (b) both negative (c) one positive one negative (d) both equal The number of polynomials having zeroes and 2 and 5 is (b) 2 (c) 3 (d) more than 3 (a) 1 The product of the HCF and LCM of the smallest prime number and smallest composite number is (a) 2 (b) 4 (c) 6 (d) 8

 2  5 2  5  is

(a) a rational number (b) a whole number (c) a positive integer (d) All of the above If x  3sec2   1, y  tan    2 then x  3y is (a) 3 (b) 4 (c) 8 1 If cosec   cot   , the value of cosec   cot  3 (b) 2 (c) 3 (a) 1 In  PQR is right angled at R , then the value of cos (P  Q) is (a) 1

4

(d) c and b have the same sign

(b) 0

(c)

1 2

(d) 5

(d) 4

(d)

3 2

MATHEMATICIA By O.P. GUPTA : A New Approach in Mathematics

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 Mathematics for X

11.

The lengths of the diagonals of a rhombus are 24 cm and 32 cm. The perimeter of the rhombus is (b) 128cm (c) 80cm (d) 156cm (a) 9 cm

12.

The areas of two similar triangles ABC & PQR are 25cm2 , 49 cm2 . If QR  9.8cm , then BC is (a) 9.8cm (b) 7cm (c) 49cm (d) 25cm

13.

If P(not E)  1, then P(E)  (a) 1 (b) 0 (c) 1 (d) Can not be obtained 4 If sin A  , then tan A  5 4 3 3 4 (b) (c) (d) (a) 3 4 5 5 Three unbiased coins are tossed. What is the probability of getting at most two heads. 3 1 7 (a) (b) (c) (d) 1 8 2 8 A bag contains card numbered from 1 to 25 . One card is drawn at random from the bag. What is the probability of getting a card has a number which is divisible by both 2 & 3

14.

15.

16.

3 6 4 1 (b) (c) (d) 25 25 25 5 If the point P(2 , 1) lies on the line segment joining points A(4 , 2) and B(8, 4) , then

(a)

17.

1 1 1 (d) AP  AB (c) PB  AB AB (b) AP  PB 3 3 2 The perpendicular bisector of the line segment joining the points A(2 , 5) and B(4 ,  5) meets AB at P. Then coordinates of P is (a) (0, 13) (b) (0 ,  13) (c) (0, 12) (d) (3, 0) If the perimeter of a circle is equal to that of a square, then the ratio of their areas is 22 14 7 11 (b) (c) (d) (a) 7 11 22 14 The radius of a circle whose circumference is equal to the sum of the circumference of the two circles of diameter 36cm and 20 cm (a) 56cm (b) 42cm (c) 28cm (d) 16cm

(a) AP 

18.

19.

20.

21.

22.

23.

Two dice are thrown at the same time. Determine the probability that the difference of the numbers on the two dice is 2 . 1 2 1 4 (a) (b) (c) (d) 9 9 3 5 A school has five houses A , B, C , D and E. A class has 23 students, 4 from house A, 8 from house B, 5 from house C, 2 from D and rest from E. A single student is selected at random for head boy. The probability that the selected student is not from A, B, C is 4 6 8 17 (a) (b) (c) (d) 23 23 23 23 Area of a semi-circle (with radius of 1 unit) is

MATHEMATICIA By O.P. GUPTA : A New Approach in Mathematics

5

CBSE Practice Questions Sheet Term I (2021-22)

By O.P. GUPTA (INDIRA Award Winner)

11 22 (b) sq.units sq.units (c) 3.14 sq. units (d) 6.28 sq.units 7 7 A piece of wire 20 cm long is bent into the form an arc of a circle, subtending an angle of 60 at the centre. The radius of the circle is equal to 60 50 (b) (a) cm cm (c) 30 cm (d)  cm   The difference of the areas of a sector of an angle 120 and its corresponding major sector of a circle of radius 21cm is

(a)

24.

25.

2

26.

(b) (c) 462 cm (a) 382 cm From the figure, the value of sin A  cot A is

29 19 9 (b) (c) 15 15 15 If cos ec2 (1 cos )(1 cos )   , then the value of  is (a) 0 (b) cos2 θ (c) 1 If 2 sin 60     1, then the value of  is

(a)

27. 28. 29. 30. 31.

32.

33. 34.

35.

36. 6

2

2

(d) 924 cm

(d)

29 51

(d) 1

(a) 45 (b) 15 (c) 60 (d) 130 If n is any natural number, then which of the following expression ends with 0? (a) (3 2)n (b) (4  3) n (c) (2  5) n (d) (6  2)n n 2  1 is divisible by 8 if n is (a) an integer (b) a natural number (c) an odd number (d) an even integer The points (  4, 0), (4, 0) and (0, 3) are the vertices of a/an (a) right triangle (b) isosceles triangle (c) equilateral triangle (d) scalene triangle The fourth vertex D of a parallelogram ABCD whose three vertices are A(  2, 3), B(6 , 7) and C(8, 3) is (a) (0, 1) (b) (0 ,  1) (c) ( 1, 0) (d) (1, 0) The distance between the points P(6 , 8) from the origin is (b) 2 7 (c) 10 (d) 6 (a) 8 A line intersects the y-axis and x-axis at the points P and Q, respectively. If (2,  5) is the midpoint of PQ, then the coordinates of P and Q, are respectively (a) (0 ,  5) and (2 , 0) (b) (0 , 10) and ( 4 , 0) (c) (0 , 4) and ( 10 , 0) (d) (0 ,  10) and (4 , 0) The point which divides the line segment joining the points (7 ,  6) and (3, 4) in the ratio 1: 2 internally lies in the (a) I quadrant (b) II quadrant (c) III quadrant (d) IV quadrant x y xy The number of solutions of 3  243 and 243  3 is (a) 0 (b) 1 (c) 2 (d) Infinite MATHEMATICIA By O.P. GUPTA : A New Approach in Mathematics

 Mathematics for X

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37.

If  is the angle (in degrees) of a sector of a circle of radius r , then area of sector is 2 r  2 r  r  r  (b) (c) (d) 180 360  180 360 The ratio in which the line segment joining ( 3, 10) and (6 ,  8) is divided by ( 1, 6) (a) 7 : 2 (b) 2 : 7 (c) 1: 1 (d) 3 : 7 2

2

2

(a)

38.

39.

40.

If one root of the polynomial P(y)  5 y2  13y  m is reciprocal of the other, then the value of m is (a) 6 (b) 0 (c) 5 (d) –5 2 2 tan 60  sin 30 The value of is 2 2 tan 45   cos 30  7 11 13 11 (b) (c) (d) (a) 11 13 11 7

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 ANSWER KEY 01. 07. 13. 19. 25. 31. 37.

(b) (d) (b) (b) (c) (b) (a)

02. 08. 14. 20. 26. 32. 38.

(d) (c) (a) (c) (a) (b) (b)

03. 09. 15. 21. 27. 33. 39.

(c) (c) (c) (b) (c) (c) (c)

04. 10. 16. 22. 28. 34. 40.

(b) (b) (c) (b) (b) (d) (d)

05. 11. 17. 23. 29. 35.

(d) (c) (d) (b) (c) (d)

MATHEMATICIA By O.P. GUPTA : A New Approach in Mathematics

06. 12. 18. 24. 30. 36.

(d) (b) (d) (b) (c) (b)

7

CBSE Practice Questions Sheet Term I (2021-22)

By O.P. GUPTA (INDIRA Award Winner)

PQS-03

A Compilation By

O.P. GUPTA Math Mentor & Author, INDIRA Award Winner SACHIN PANDEY HOD Maths, St Mary’s School, Rudrapur 01.

02. 03.

04. 05.

06.

5  3  2 is (a) a rational number (b) a natural number (c) equal to zero (d) an irrational number A quadratic polynomial whose zeroes are 3 and  4, is (d) x2  7x  12 (a) x 2  x  12 (b) x2  x  12 (c) x 2  x  12 The pair of linear equations (3k  1) x  3 y  5  0 and 2 x  3 y  5  0 have infinite number of solutions. Then the value of k is (b) 0 (c) 2 (d) 1 (a) 1 The distance between the points A(0 , 7) and B(0,  3) is (b) 10 units (c) 7 units (d) 3units (a) 4 units A bag has 9 black balls and 3 white balls. A ball is drawn at random from the bag. What is the probability of getting a white ball? 3 1 4 5 (a) (b) (c) (d) 4 4 9 9 If ABC is right angled at B, then the value of cos(A  C) is 1 (d) n.d. 2 It is proposed to build a single circular park equal in area to the sum of areas to two circular parks of diameters 16 m and 12 m in a locality. The radius of the new park would be

(a) 0

07.

08.

09.

10.

(c)

(b) 15m (c) 20 m (d) 24 m (a) 10 m The probability of getting a bad egg in a lot of 400 is 0.035. The number of bad eggs in the lot is (b) 14 (c) 21 (d) 28 (a) 7 7 Let x  be a rational number. Then x has decimal expansion, which terminates 20  25 (a) after four places of decimal (b) after three places of decimal (c) after two places of decimal (d) after five places of decimal 2 If p is a prime number and p divides k , then p divides (a) 2k 2

8

(b) 1

(b) k

(c) 3k

(d) None of these

MATHEMATICIA By O.P. GUPTA : A New Approach in Mathematics

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11.

12. 13.

14.

The father’s age is six times his son’s age. Four years hence, the age of the father will be four times his son’s age. The present ages (in years) of the son and the father are, respectively (a) 4 and 24 (b) 5 and 30 (c) 6 and 36 (d) 3 and 24 The points at which the graph lines of the equations ax  by  0 and ax  by  0 intersect is (a) (a , 0) (b) (b, 0) (c) (0, 0) (d) (a , b) The measure of angle included between the lines represented by x  0, y  0 and the coordinates of the point of intersection of these lines are respectively (b) 90 , (0, 0) (a) 180 , (1, 1) (c) 120 , (0, 1) (d) 60 , (1, 0) XY is drawn parallel to the base BC of a ABC cutting AB at X and AC at Y . If AB  4BX and YC  2 cm , then AY is (a) 2 cm

15.

16.

18.

19. 20.

21. 22. 23. 24.

25.

(b) 6cm

(1  tan A  sec A)(1  cot A  cosec A)  (a) 0 (b) 1 a If sin  , then cos is equal to b (a)

17.

 Mathematics for X

b

(b)

b a

(c) 8cm

(d) 4 cm

(c) 2

(d) 1

(c)

b2  a 2 b

(d)

a

b a b a2 The diameters of two circles are 38cm and 18cm. Then, the diameter of the circle having circumference equal to the sum of circumference of the two circles is (b) 52cm (c) 48cm (d) 50cm (a) 56cm The probability that a non leap year selected at random will contain 53 Sundays is 1 2 3 5 (b) (c) (d) (a) 7 7 7 7 If the HCF of 408 and 1032 is expressible in the form 1032 m  408  5, then the value of m is (a) 4 (b) 3 (c) 1 (d) 2 The points (5, 0) , (5, 0), (0, 4) are the vertices of (a) an equilateral triangle (b) an isosceles triangle (c) a right triangle (d) a scalene triangle 2

2

2

A number when divided by 61 gives 27 quotient and 32 as remainder is (a) 1679 (b) 1664 (c) 1449 (d) None of these HCF (2, 11) is (a) 22 (b) 1 (c) 2 (d) 0 The largest number which divides 70 and 125, leaving remainders 5 and 8, respectively is (a) 13 (b) 65 (c) 875 (d) 1750 2 If 2 and 3 are the zeroes of the polynomial 3x  2kx  2m, then the values of k and m are 7 15 (b) 7, 9 (c) 9, (d) None of these (a) 9, 2 2 The x coordinate of the point which lies on the line represented by 2x  y  7  0 and whose y coordinate is 13 is (a) 4 (b) 5 (c) 6 (d) 10

MATHEMATICIA By O.P. GUPTA : A New Approach in Mathematics

9

CBSE Practice Questions Sheet Term I (2021-22)

26. 27. 28. 29. 30.

31.

32.

33.

34. 35. 36.

If bx  ay  a 2  b 2 and ax  by  0, then the value of x  y is (b) b  a (c) a2  b2 (d) b2  a2 (a) a  b Point A is on the y-axis at a distance 4 units from the origin. If B(–3, 0), then the length AB is (b) 5 units (c) 49 units (d) 25units (a) 7 units If the point (x , 4) lies on a circle whose centre...