Topic: Maths Test – 6 Ch.

1, 2, 3, 4, 5 Standard:
10 th

Total Time: 3 hrs Date: Total

Marks: 80

Section – A
1. If xy = 180 and HCF (x, y) = 3, then the LCM (x, y) is 1
(a) 100 (b) 60 (c) 54 (d) 18
2. The value of K for which the system of linear equations x + 2y = 3, 5x + ky + 7 = 0 is 1
inconsistent is
2 −14
(a) (b) (c) 5 (d) 10
5 3
3. 25 1
If sum of the squares of zeroes of the quadratic polynomial 6x2 + x + k is , then the
36
value of k is:
(a) 4 (b) -4 (c) 2 (d) -2
4. If x = m and y = n is the solution of the equations x – y = 2 and x + y = 4, then the values 1
of ‘m’ and ‘n’ are, respectively.
(a) 3 and 5 (b) 5 and 3 (c) 3 and 1 (d) -1 and -3
5. The HCF of smallest prime number and the smallest composite number is 1
(a) 2 (b) 3 (c) 1 (d) -1
6. The graph of the equation 2x + 3y = 5 is a 1
(a) vertical line (b) straight line (c) horizontal line (d) none of these
7. The pair of linear equations 2kx + 5y = 7, 6x – 5y = 11 has a unique solution, if 1
2 2
(a) k ≠ -3 (b) k ≠ (c) k ≠ 5 (d) k ≠
3 9
8. The roots of the equation √ 2x + 7x + 5√ 2 are
2
1
5 −5 √ 2
(a) √ 2, √ 5 (b) √ 2, (c) -√ 2, (d) -√ 2, 5√ 2
√2 2
9. If ‘a’ is 3 and ‘b’ is 7, then the least prime factor of (a + b) is 1
(a) 2 (b) 5 (c) 3 (d) 11
10. The HCF and LCM of two numbers are 33 and 264 respectively. When the first number 1
is completely divided by 2 the quotient is 33. The other number is:
(a) 66 (b) 130 (c) 132 (d) 196
11. Which of the following is not the graph of a quadratic polynomial? 1

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12. If (x + 1) is a factor of 2x3 + ax2 + 2bx + 1, then find the values of a and b given that 2a – 1
3b = 4.
(a) a = -1, b = -2 (b) a = 2, b = 5 (c) a = 5, b = 2 (d) a = 2, b = 0
13. The pair of equations y = 0 and y = -7 has 1
(a) one solution (b) two solutions (c) infinitely many solutions (d)
no solution

14. If 3 chairs and 1 table costs Rs. 1500 and 6 chairs and 1 table costs Rs. 2400. Which of 1
the following linear pair of equations will represent this situation?
(a) 3x + y = 1500 and 6x + y = 2400 (b) 8x + y = 1800, 6x + y = 2400
(c) x + 3y = 1500 and 6x – 7y = 2400 (d) 3x – y = 1500 and 6x + y = 2400
15. If p1 and p2 are two odd prime numbers such that p1 > p2, then p21 - p22 is 1
(a) an even number (b) an odd number
(c) an odd prime number (d) a prime number
16. If p(x) is a polynomial of at least degree one and p(k) = 0, then K is known as 1
(a) value of p(x) (b) zero of p(x)
(c) constant term of p(x) (d) none of these
17. A polynomial of degree n has 1
(a) only 1 zero (b) at most n zeros (c) exactly n zeroes (d) more than n
zeroes
18. If the zeroes of the quadratic polynomial ax2 + bx + c where a ≠ 0 are equal, then 1
(a) c and a have opposite signs (b) c and b have opposite signs
(c) c and a have same sign (d) c and b have the same sign
19. Graphically, the pair of equations 7x – y = 5; 21x – 3y = 10 represents two lines which 1
are
(a) intersecting at one point (b) parallel
(c) intersecting at two points (d) coincident
2
20. The roots of the equation 7x + x – 1 = 0 are: 1

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IX,X,XI,XII Com CBSE
 (a) real and distinct (b) not real (c) real and equal (d) none of these
21. The number of polynomials having zeroes as 3 and 5 is 1
(a) 1 (b) 2 (c) 3 (d) more than 3
22. If a pair of linear equations is consistent, then the lines will be 1
(a) always coincident (b) parallel (c) always intersecting (d) intersecting or
coincident
23. If two positive integers A and B can be expressed as A = xy3 and B = xy2z; x, y, z being 1
prime numbers, then LCM (A, B) is
(a) xy2 (b) x4y2z (c) x4y3 (d) xy3z
24. Which term of the AP: 21, 42, 63, 84, ….. is 210? 1
(a) 9th (b) 10th (c) 11th (d) 12th
25. The product of a non-zero rational and an irrational number is 1
(a) always rational (b) rational or irrational (c) always irrational
(d) zero
26. Which of the following is a quadratic equation? 1
(a) (x + 1) (x2 + 3) (b) x (x - 2) – 3 = 0 (c) x3 + 2 = -3x (d) x – 7x = 9
27. One equation of a pair of dependent linear equations is 2x + 5y = 3. The second 1
equation will be
(a) a divides p (b) p divides a (c) a2 divides p (d) p2 divides a
28. The value of k, for which the system of equations x + (k + 1)y = 5 and (k + 1)x + 9y = 8k – 1
1 has infinitely many solutions is
(a) 2 (b) 3 (c) 4 (d) 5
29. The zeroes of the quadratic polynomial x2 – 15x + 50 are 1
(a) both negative (b) one positive and one negative (c) both positive (d)
both equal
30. What is the common difference of an AP in which a18 – a14 = 32? 1
(a) 8 (b) -4 (c) -8 (d) 4

31. If p(x) = ax2 + bx + c, and a + b + c = 0, then one zero is: 1

(a) -b/a (b) c/a (c) b/c (d) none of these
32. Zeroes of a polynomial can be expressed graphically. Number of zeroes of polynomial 1
p(x) is equal to number of points where the graph of polynomial is:
(a) Intersects x-axis (b) Intersects y-axis (c) Intersect y-axis or x-axis (d)
None of the above
33. If 3x + 4y : x + 2y = 9 : 4, then 3x + 5y : 3x – y is equal to 1
(a) 4 : 1 (b) 1 : 4 (c) 7 : 1 (d) 1 : 7
34. If k + 9, 2k – 1, 2k + 7 are consecutive terms of an AP, then K = ____________ 1
(a) 18 (b) 15 (c) 11 (d) none of these
Read the following statements: Assertion and Reason. Choose one of the correct alternatives:

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IX,X,XI,XII Com CBSE
(a) Both Assertion and Reason are True and Reason is the correct explanation of Assertion.
(b) Both Assertion and Reason are True and Reason is not the correct explanation of Assertion.
(c) Assertion is True but Reason is False.
(d) Assertion is False but Reason is True.
35. Assertion (A): The HCF of two numbers is 5 and their product is 150, then their LCM is 1
30.
Reason (R): For any two positive integers a and b HCF (a, b) + LCM (a, b) = a x b.
36. Assertion (A): ( 2−√ 3 ) is one zero of the quadratic polynomial then other zero will be (2 1
+ √ 3).
Reason (R): Irrational zeros (roots) always occurs in conjugate pairs.
37. Assertion (A): HCF of 26 and 91 is 31. 1
Reason (R): The prime factorization of 26 = 2 × 13 and 91 = 7 × 13.
38. Assertion (A): If the sum of the zeroes of the quadratic polynomial x2 – 2kx + 8 is 2 then 1
value of k is 1.
Reason (R): Sum of zeroes of a quadratic polynomial ax2 + bx + c is -b/a.
th
39. Assertion (A): If Sn is the sum of the first n terms of an AP., then its n term an is given 1
by an = Sn – Sn-1
Reason (R): The 10th term of the AP 5, 8, 11, 14 ___________ is 35.
Section – B
40. The larger of two supplementary angles exceeds the smaller by 18 degree. Find them. 2

41. If α and β are the zeroes of the polynomial ax2 + bx + c, find the value of α 2 + β 2. 2

42. Find the LCM of 96 and 360 by using Fundamental Theorem of Arithmetic. 2

43. Find the 9th term from the end (towards the first term) of the A.P. 5, 9, 13, …………., 185. 2

OR
44. Check whether 44 in a term of the A.P, -7, -4, -1, ……… or not? 2

45. The angles of a triangle are in A.P., the least being half the greatest. Find the angles. 2

46. A two digit number is seven times the sum of its digits. The number formed by reversing 3
the digits is 18 less than the given number. Find the given number.
47. Find the zeroes the following quadratic polynomial and verify the relationship between 3
the zeroes and their coefficients: 6x2 – 3 – 7x
48. If α and β are the zeroes of the polynomial 6y2 – 7y + 2, find a quadratic polynomial 3
1 1
whose zeroes are and .
α β
OR

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IX,X,XI,XII Com CBSE
49. If the roots of the quadratic equation (a – b)x2 + (b – c)x + (c – a) = 0 are equal, prove 3
that 2a = b + c.
50. Prove that √ 2 is an irrational number. 3

51. Find the sum of all three – digit natural numbers, which are multiples of 9. 3

Section – C
52. While boarding an aeroplane, a passenger got hurt. The pilot, showing promptness and 4
concern, made arrangements to hospitalize the injured and so the plane started late by
30 minutes. To reach the destination, 1500 km away in time, the pilot increased the
speed by 100 km/hour. Find the original speed and duration of the plane.
Section – D
53. For the box to satisfy certain requirements, its length must be three units greater than
the width, and its height must be two units less than the width.

(a) If width is taken as x, then find the polynomial which represents volume of box. 1
(b) Find the polynomial which represents the area of paper sheet used to make box. 1
(c) If box is made of a paper sheet, and paper sheet costs Rs. 100 per square unit, then 2
what is the cost of paper used in making bx of width 3 unit?
54. Your elder brother wants to buy a car and plans to take loan from a bank his car. He
repays his total loan of Rs. 1,18,000 by paying every month starting with the first
installment of Rs. 1000. If he increases the insallment by Rs. 100 every month, answer
the following: 1
(i) What is the amount paid by him in the 30th installment? 1
(ii) What is the amount paid by him in the 30 installments? 2
(iii) What amount does he still have to pay after 30 installments?
OR
In how many installments will he clear his entire loan?
55. Quadratic equations started around 3000 B.C. with the Babylonians. They were one of
the world’s first civilization, and came up with some great ideas like agriculture,
irrigation and writing. There were many reason why Babylonians needed to solve
quadratic equations. For example: To know what amount of crop you can grow on the
square field.
(i) The sum of squares of two consecutive integers is 650. Represent this in the form of 1
quadratic equation.
(ii) Two numbers differ by 3 and their product is 504. Represent this in the form of 1
quadratic equation. 2
(iii) Find the two consecutive integers as mentioned in (i).
OR
Find the two numbers as mentioned in (ii).

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214, Ashirwad villa, Nr St Thomas School | MOB:- 7990255539
IX,X,XI,XII Com CBSE
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214, Ashirwad villa, Nr St Thomas School | MOB:- 7990255539
IX,X,XI,XII Com CBSE