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Assertion & ReasonSome questions (AssertionReason type) are given below. Each question contains Statement 1 (Assertion) and Statement 2

(Reason). Each question has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct. So select the correct choice :

(A) Statement 1 is True, Statement 2 is True; Statement 2is a correct explanation for Statement 1.

(B) Statement 1 is True, Statement 2 is True; Statement 2isNOT a correct explanation for Statement 1.(C) Statement 1 is True, Statement 2 is False. (D) Statement 1 is False, Statement 2 is True.

1. Statement-1: sin3 < sin1 < sin2 is true Statement-2: sinx is positive in first and second quadrants.

2. Statement-1: The equation 2sin2x (P + 3) sinx + (2P 2) = 0 possesses a real solution if

P[-1, 3] Statement-2 : -1 sinx 1

3. Statement-1: The maximum value of 3sin + 4cos4

+

is 5 here R.

Statement-2:: -2a b+ 2 asin+bcos 2 2a b+

4. Statement-1: If A + B + C = , cosA + cosB + cosC 3/2

Statement-2:: If A + B + C = , sinA B C

sin sin2 2 2

1

8

5. Statement-1: The maximum & minimum values of the function f(x) =1

6sin x 8cos x 5 + does not exists.

Statement-2: The given function is an unbounded function.

6. Statement-1: If x < 0 tan-1x +tan-11

x

= /2

Statement-2: tan-1x + cot-1x = /2 xR.

7. Statement-1: In any triangle square of the length of the bisector AD is bc

2

2

a1

(b c)

+

Statement-2: In any triangle length of bisector AD =bc A

cosb c 2+

8. Statement-1: If in a triangle ABC, C = 2acosB, then the triangle is isosceles.

Statement-2: Triangle ABC, the two sides are equal i.e. a = b.

9. Statement-1: If the radius of the circumcircle of an isosceles triangle pqR is equal to pq = PR then the angle p = 2 /3.Statement-2: OPQ and oPR will be equilateral i.e., OPq = 60, OPR = 60

10. Statement-1: The minimum value of the expression sin + sin + sin is negative, where , , are real numbers suchthat + + = .

Statement-2: If, , are angle of a triangle then sin + sin + sin = 4cos cos cos2 2 2

.

11. Statement-1: If in a triangle sin2A + sin2B + sin2C = 2 then one of the angles must be 90.

Statement-2: In any triangle sin2A + sin2B + sin2C = 2 + 2cosA cosB cosC.

12. Statement-1: If in a ABC a 2c and b 3c then cosB must tend to 1.

Statement-1: In a ABC cosB =2 2c a b

2ac

+ 2.

13. Statement-1: cos(45 A) cos(45 B) sin(45 A) sin (45 B) = sin(A + B).Statement-2: cos(90 ) = sin .

14. Statement-1: The maximum and minimum values of 7cos + 24sin are 25 and 25 respectively.

Statement-2:2 2 2

a b a cos bsin a b+ + 2 for all .

21

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TEKO CLASSES GROUP, MATHS BY SUHAAG SIR, PH.: (0755)32 00 000, 98930 58881

15. Statement-1: If1 1 1 2 1sin x sin (1 x) sin 1 x then x 0,

2

+ = =

Statement-2:1

sin sin x x x R =

Answer Key1. B 2. A 3. D 4. B 5. A 6. D

7. C 8. A 9. A 10. B 11. A 12. A

13. C 14. A 15. C

IMP QUESTION FROM COMPETETIVE EXAM1. The circular wire of diameter 10cm is cut and placed along the circumference of a circle of diameter 1 metre. The angle subtended by the

wire at the centre of the circle is equal to [MNR 1974]

(a) radian4

(b) radian

3

(c) radian

5

(d) radian

10

2. The value of ++++ ...15sin10sin5sin 222 ooo oo 90sin85sin 22 + is equal to [Karnataka CET 1999]

(a) 7 (b) 8 (c) 9 (d)2

19

3. If ,4

3

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TEKO CLASSES GROUP, MATHS BY SUHAAG SIR, PH.: (0755)32 00 000, 98930 58881

16. If ,1,130cos80sin,80cos130sin xyzyx oooo +===

which one of the following is true [AMU 1999]

(a) (b)0,0,0 >>> zyx 10,0,0

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33. The value of cossin + will be greatest when [MNR 1977, 1983; RPET 1995]

(a) (b) (c) (d)o30= o45= o60= o90=

34. If then [MNR 1986],seccos)( 22 xxxf += (a) (b) 1 (c)1)(