Techno India Group Public School

1. The product of all real integral solutions of (x ² - 3x+3) ^{x ²-16x+48} = 1 is

(A) 24
(B) 48
(C) 96
(D) 144

2.

(A)12
(B) 17
(C) 25
(D) 32

3.

(A) cosec θ
(B) cosec²θ
(C) sin²θ
(D) sec²θ + 1

4.

(A) Both (A) and (R) are true and (R) is the correct explanation of (A)
(B) Both (A) and (R) are true but (R) is not the correct explanation of (A)
(C) (A) is true but (R) is false
(D) (A) is false but (R) is true

5. If the HCF of 85 and 153 is expressible in the form 85x – 153, then x equals

(A) 1
(B) 2
(C) 0
(D) 4

6.If 5secθ – 2tanθ = 5, then the value of 5tanθ – 2secθ can be

(A) 7
(B) 5
(C) 3
(D) 2

7. KITE is a parallelogram in which P and Q are points on KE and KT respectively such that PQ||ET. If PQ = 4 cm, KQ = (4x – 5) cm, QT = (5x – 4) cm, KP = (x – 1) cm and PE = x cm, then KI equals

(A) 8 cm
(B) 10 cm
(C) 11 cm
(D) 12 cm

8. If a and b are primes less than 10 and x² – ax + b = 0 has distinct positive integral roots, then a^b equals

(A) 16
(B) 27
(C) 9
(D) 64

9. How many different real values of x satisfy the equation (x² – 5)² = 16?

(A) 2
(B) 3
(C) 0
(D) 4

10. The polynomial x³ – ax² + bx – 1830 has three positive integral zeroes. The smallest possible value of a is

(A) 78
(B) 81
(C) 72
(D) 82

11.

(A)

(B)

(C)

(D)

12. The area of the triangle formed by the lines 4x + 3y – 12 = 0, 4x – 3y + 12 = 0 and y = 0, is

(A) 6 sq units
(B) 12 sq units
(C) 18 sq units
(D) 24 sq units

13.

(A) 12 m
(B) 13 m
(C) 14 m
(D) 22 m

14.

(A) 1
(B) 0
(C) -1
(D) 1/2

15.

(A) (3, 1)
(B) (33, 11)
(C)(– 33, – 11)
(D) (22, 11)