FA-1 REVISION QUESTIONS MATHEMATICS

1. The HCF of 18and 45is A) 3 B) 9 C) 18 D) 90

2. The LCM of 8 and 12 is 24, then their HCF is A) 4 B) 24 C) 8 D) 12
3. If the HCF of 72 and 120 is 24, then their LCM is A) 36 B) 720 C) 360 D) 72
4. If 𝑎and 𝑏are any two positive integers then HCF ( 𝑎, 𝑏 )× LCM ( 𝑎, 𝑏 ) is equal to
A) 𝑎 + 𝑏 B) 𝑎 − 𝑏 C) 𝑎 × 𝑏 D) 𝑎 ÷ 𝑏
5. If 𝐻and 𝐿are the 𝐻𝐶𝐹 and 𝐿𝐶𝑀 of two numbers 𝐴and𝐵respectively then
A) 𝐴 × 𝐻 = 𝐿 × 𝐵 B) 𝐴 × 𝐵 = 𝐻 × 𝐿 C) 𝐴 + 𝐵 = 𝐻 + 𝐿 D) 𝐴 + 𝐵 = 𝐿 − 𝐻
6. HCF of any two prime numbers is
A) a prime number B) a composite number. C) an odd number D) an even number
7. LCM of 18 and 45 is A) 9 B) 45 C) 90 D) 81
8. ( 7 × 11 × 13 + 13 ) is a / an
A) Composite number B) Prime number C) Irrational number D) Imaginary number
9. The H.C.F. of two co-prime expressions is A) 0 B) ∞ C) 10 D) 1
10. The product of two numbers is 300 and their H.C.F. is 10. The L.C.M. of the numbers is
A) 100 B) 300 C) 3000 D) 30
11. Find the H.C.F of the smallest prime number and the smallest composite number.
12. Write 96 as the product of prime factors.
13. Find the HCF of 14 and 21.
14. The H.C.F. of 12 and 18 is 6. Find their L.C.M.
15. Find the H.C.F. of 12 and 18.
16. Express 210 as the product of prime factors.
17. Prove that 2 + √3is an irrational number.
18. Find the LCM of 12, 15 and 21 by the method of prime factorization.
19. Prove that 2 + √3 is an irrational number.
20. Show that 7 × 11 × 13 + 13 is a composite number.
21. Prove that 5 + √3 is an irrational number.
22. Prove that 5 − √3 is an irrational number.
23. Prove that 2 + √3 is an irrational number.
24. Prove that 2 + √5 is an irrational number.
25. Prove that 3 + √5 is an irrational number.
26. Prove that 5 − √3 is an irrational number.
27. Prove that 2 + √5 is an irrational number.
28. Prove that √3 is an irrational number.
29. Prove that √5 is an irrational number.
30. Prove that √2 + √3 is an irrational number.
31. Prove that 7 + √5 is irrational number
32. Find the two numbers whose sum is 75 and difference is 15.
33. In a two digit number, the ten’s digit number is three times the unit’s
digit. When the number is decreased by 54, the digits are reversed. Find the
number.
34. When the son will be as old as what his father is today their ages will add
upto 126 years. When the father was as old as what his son is today, their ages
added upto 38 years. Find their present ages.
35. 4 chairs and 3 tables cost ₹ 2100 and 5 chairs and 2 tables cost ₹ 1750.
Find the cost of one chair and one table separately.
36. A number consists of two digits. When it is divided by the sum of the
digits, the quotient is 6 with no remainder. When the number is diminished by 9,
the digit are reversed.
37. Seven times a two digit number is equal to four times the number
obtained by reversing the order of the digits. If the difference of the digits is 3,
determine the number.
38. A man travel 370 km partly by train and partly by car. If he covers 250 km
by train and the rest by car, it takes him 4 hours. But, if he travels 130 km by
train and the rest by car, he takes 18 minutes longer. Find the speed of the train
and that of the car.
39. The taxi charges in a city comprise of a fixed charges together with
charge for the distance covered. For a journey of 10 km, the charges paid is ₹75
and for a journey of 15 km, the charges paid is ₹110. What will a person has to
pay for travelling a distance of 25 km?
40. The cost of 2 kg of apples and 1kg of grapes on a day was found to be
Rs.160. After a month, the cost of 4 kg of apples and 2 kg of grapes is Rs.300.
Represent the situation algebraically
41. Aftab explains to his daughter, “Seven years ago, I was seven times as old
as you were then. Moreover, three years from now, I shall be three times as old
as you will be.” Represent the given situation algebraically and graphically.
42. Five years ago, Sagar was twice as old as Tiru. Ten year later Sagar’s age
will be ten years more than Tiru’s age. Find their present ages. What was the
age of Sagar when Tiru was born?
43. SOLVE THE FOLLOWING QUESTIONS IN SUBSTITUTION ,
ELIMINATION AND GRAPHICAL METHOD.

44. If the pair of lines 2x + 3y + 7 = 0 and ax + by + 14 = 0 are coincident

lines , then the values of ‘a’ and ‘b’ are respectively equal to
45. The lines represented by x + 2y – 4 = 0 and 2x + 4y – 12 = 0 are, (A)
intersecting lines (B) parallel lines (C) coincident lines D)perpendicular
lines to each other
46. In the pair of linear equations x + y = 9 and x – y = 1 , the value of x and
y are
47. Find the value of k, if the pair of linear equations 2x – 3y = 8 and 2 ( k –
4 ) x – ky = k + 3 are inconsistent.
48. Number of solutions of pair of linear equations x – y = 8 and 3x – 3y = 16
are
49. Write the general form of a quadratic polynomial.
50. Write the degree of the polynomial 𝑔(𝑥) = 4𝑥 5
− 6𝑥 3
+ 2𝑥 2
+5
51. Write the number of zeroes of the polynomial 𝑝(𝑥) = 4𝑥 3 + 5𝑥 2
− 6𝑥 + 8
52. Find the degree of the polynomial (𝑥) = 𝑥 3
+ 2𝑥 2
− 5𝑥 − 6.
53. Write the degree of the polynomial 𝑝(𝑥) = 2𝑥 2
−𝑥 3
+5
54. Write the number of zeroes of the polynomial 𝑓(𝑥) = 𝑥 2
− 3𝑥 3
+2
55. Find the degree of the polynomial 𝑥 3
+ 2𝑥 2
− 5𝑥 − 6
56. Write the degree of the polynomial (𝑥) = 𝑥² + 2𝑥 3
− 5𝑥 4
+ 6.
57. Write the degree of the polynomial 19𝑥 + √3𝑥 3
+ 14
58. Write the number of zeroes of the polynomial 𝑝(𝑥) = 𝑥 3
+ 2𝑥 2
+𝑥+6
59. If 𝑝(𝑥) = 2𝑥 3
+ 3𝑥 2
− 11𝑥 + 6then find the value of 𝑝(1)
60. If 𝑓(𝑥) = 2𝑥 2
+ 3𝑥 + 2 then find the value of 𝑓 ( 2 )
61. Find the zeroes of the polynomial 𝑝(𝑥) = 𝑥 2
–3
62. Find the zeros of the polynomial 𝑝(𝑥) = 𝑥 2 + 14𝑥 + 48
63. Find the zeros of the polynomial 𝑝(𝑥) = 𝑥 2
− 15𝑥 + 50
64. Find the zeroes of the polynomial 𝑝(𝑥) = 𝑥 2
− 2𝑥 − 15
65. Find the zeroes of the quadratic polynomial 𝑝(𝑥) = 𝑥 2
− 2𝑥 − 8 and verify
the relationship between the zeroes and coefficients
66. Find the zeroes of the quadratic polynomial 𝑝(𝑥) = 𝑥 2
+ 7𝑥 + 10 and
verify the relationship between the zeroes and coefficients
67. Find the zeroes of the quadratic polynomial 𝑝(𝑠) = 4𝑠 2
− 4𝑠 + 1 and
verify the relationship between the zeroes and coefficients
68. Find the zeroes of the quadratic polynomial 𝑝(𝑥) = 6𝑥 2
− 3 − 7𝑥 and
verify the relationship between the zeroes and coefficients
69. Find the zeroes of the quadratic polynomial 𝑝(𝑥) = 3𝑥 2 − 𝑥 − 4 and verify
the relationship between the zeroes and coefficients
70. Find the zeroes of the quadratic polynomial 𝑝(𝑥) = 𝑥 2
− 3 and verify the
relationship between the zeroes and coefficients
71. Find the zeroes of the quadratic polynomial 𝑝(𝑢) = 4𝑢 2
+ 8𝑢 and verify
the relationship between the zeroes and coefficients
72. Find the zeroes of the quadratic polynomial 𝑝(𝑡) = 𝑡 2
− 15 and verify the
relationship between the zeroes and coefficients
73. Find a quadratic polynomial whose sum and product of the zeroes are 3
and 4 respectively.
74. Find a quadratic polynomial whose sum and product of the zeroes are −3
and 2 respectively.
75. Sum and product of the zeroes of a quadratic polynomial P (x) = ax 2 + bx
– 4 are ¼ and – 1 respectively. Then find the values of a and b.