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Bahwan International Institute of Technology

IIT JEE Model Test – X class  Dt: 26/8/2017

1. If p cot  = , then the value of sin  is

(A) (B) (C) (D) none of these.

2. If p = r cos  and q = r sin , then the value of is

(A) 0 (B) 1 (C) r2tan2 (D) none of these.

3. If sec  = , then the value of is

(A) (B) (C) (D) none of these

4. The value of cot2300 – 2 cos2 600 sec2 450 – 4 sin2 300 is

(A) 0(B) 1(C) –1(D) none of these

5. = ……………..

(A) (B) (C) (D) none of these.

6. = ……….

(A) cot2 A – cot2B (B) tan2A = tan2B (C) (D) none of these.

7. If tan  + sin  = m & tan  – sin  = n then m2 – n2 = ………

(A) (B) (C) 4 (D) none of these.

8. If tan A = n tan B and sin A = m sin B then = ………….

(A) sin2A (B) (C) (D) cos2A

9. If 7 sin2  + 3 cos2  = 4 then sec  + cosec  = …………

(A) (B) (C) (D) none of these.

10. If sin (A + B) = ; cos B = value of A is

(A) 450 (B) 600(C) 300 (D) 900

11. =

(A) sin  (B) cos  (C) sec  (D) 1

12. If 3 sin  + 5 cos  = 5 then 5 sin  – 3 cos  =

(A) 3(B) –3(C) both A and B(D) none of these

13. If tan A = n tan B and sin A = m sin B then = ……….

(A) sin2A (B) (C) (D) cos2A

14. The value of sec 700 sin 200 + cos200 cosec 700 = ……….

(A) 1(B) 0(C) 2(D) none of these

15. The value of tan 10 tan 20 tan 30…… tan 890 = ………

(A) 1(B) 0(C) –1(D) none of these

16. If the roots of the equation ax2 + bx + c = 0 are equal, then each root is equal to

(A) c/a      (B) –b/a

(C) –b/2a     (D) –c/a

17.The sum of the roots of a quadratic equation is –7/2 and product is 5/2. The equation is

(A) 2x2 + 7x – 5 = 0 (B) 2x2 – 7x + 5 = 0

(C) x2 + + 5 = 0 (D) 2x2 + 7x + 5 = 0

18. x2 – 5x + 6 < 0

(A) x > 3     (B) x < 2

(C) x lies between 2 and 3   (D) x does not lies between 2 and 3

19. The graph of y = x2 – x – 12 meets the x–axis at

(A) (4, 0), (3, 0)     (B) (4, 0), (–3, 0)

(C) (4, –3)     (D) (0, 4), (0, –3)

20. The solution set of = x + 1 is

(A) {4}      (B) {4, –3}

(C) {2}      (D) {1, –1}

21.If the given system of the equations kx + 3y – (k – 3) = 0

12x + ky – k    = 0

has infinitely many solutions if k =

(A) 3      (B) 2

(C) 6      (D) None of these

22. The system of equation 5x + 2y = 16; (A) has a unique solution   (B) has no solution

(C) has infinitely many solutions   (D) are inconsistent

23. If 10 – 5x < 5(x + 6), x  N the smallest value of x is

(A) x = –1     (B) x = 0

(C) x = 1     (D) None of these

24. If – 3 is one root of the equation x2 + kx – 6 = 0, then the value of k is

(A) 1      (B) 3

(C) 2      (D) – 1

25. The roots of x2/3 + x1/3 – 2 = 0 are

(A) 1, 8     (B) 2, 4

(C) –8, 1     (D) –2, 4

26. If the product of the roots of the equation x2 + bx + 2 + 1 = 0 is – 2 then  equals

(A) –1      (B) 1

(C) 2      (D) – 2

27. If the product of the roots of the equation x2 – 2 kx + 2k2 – 1 = 0 is 31, then the roots of the equation are real for k equal to

(A) –1      (B) 2

(C) 3      (D) 4

28. If  and  are the roots of the equation ax2 + bx + c = 0, then the value of 2 + 2 +  is

(A) c(a – b)/a2 (B) 0

(C) –bc/a2 (D) none of these

29. If (m2 – 3)x2 + 3mx + 3m + 1 = 0 has roots which are reciprocals of each other, then the value of m equals to

(A) 4      (B) –3

(C) 2      (D) none of these

30. If 4  x  9 then

(A) (x – 4)(x – 4)  0 (B) (x – 4)(x – 9)  0

(C) (x – 4)(x – 9)  0 (D) (x – 4)(x – 9) > 0