M0IITU14 - Differentiation & application qns

M0IITU14 - Differentiation & application qns - 1...

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Unformatted text preview: 1 QUEST TUTORIALS Head Office : E-16/289, Sector-8, Rohini, New Delhi, Ph. 65395439 1. d dx cos-1 x x x x- +-- 1 1 = (A) 1 1 2 + x (B) - + 1 1 2 x (C) 2 1 2 + x (D) - + 2 1 2 x 2. d dx ( ) x x + 1 2 = (A) 1 - 1 2 x (B) 1 + 1 2 x (C) 1 - 1 2x (D) None of these 3. d dx tan cos sin- + 1 1 x x = (A) - 1 2 (B) 1 2 (C) - 1 (D) 1 4. If x = a (t - sin t) & y = a (1 - cos t), then d dx = (A) tan ( ) t 2 (B) - tan ( ) t 2 (C) cot ( ) t 2 (D) - cot ( ) t 2 5. If y = x x , then dy dx = (A) x x (1 + log x) (B) x x ( ) 1 1 + x (C) (1 + log x) (D) None of these 6. If y = e x e x e x + + + ∞ ....... , then dy dx = (A) y y 1- (B) 1 1- y (C) y y 1 + (D) y y- 1 7. If x y = e x - y , then dy dx = (A) log x . [log (ex)]-2 (B) log x [og (ex)] 2 (C) log x . (log x) 2 (D) None of these 8. If y = sin-1 x x x x 1 1 2- +- , then dy dx = (A) -- +- 2 1 1 2 2 2 x x x x (B) ---- 1 1 1 2 2 2 x x x (C) 1 1 1 2 2 2- +- x x x (D) None of these 9. If y = A cos nx + B sin nx, then d y dx 2 2 is equal to : (A) n 2 y (B) - y (C) - n 2 y (D) None of these 10. The volume of a spherical balloon is increasing at the rate of 40 cubic centimetres per minute . The rate of change of the surface of the balloon at the instant when its radius is 8 cm is : (A) 5 2 sq cm/min. (B) 5 sq cm/min. (C) 10 sq cm/min. (D) 20 sq cm/min. Differentiation & Application of Derivative 2 QUEST TUTORIALS Head Office : E-16/289, Sector-8, Rohini, New Delhi, Ph. 65395439 11. If y = 1 4 u 4 , u = 2 3 x 3 + 5, then dy dx = (A) 1 27 x 2 (2x 3 + 15) 3 (B) 2 27 x (2x 3 + 5) (C) 2 27 x (2x 3 + 15) 3 (D) None of these 12. A stone thrown vertically upwards from the surface of the moon at a velocity of 24 m/sec. reaches a height of s = 24 t - 0.8 t 2 metres after t sec. The acceleration due to gravity in m/sec 2 at the surface of the moon is : (A) 0.8 (B) 1.6 (C) 2.4 (D) 4.9 13. If y = f 2 1 1 2 x x- + & f ′ (x) = sin x 2 , then dy dx = (A) ( ) 6 2 2 1 2 2 2 x x x- + + sin 2 1 1 2 2 x x- + (B) ( ) 6 2 2 1 2 2 2 x x x- + + sin 2 2 1 1 2 x x- + (C) ( )- + + + 2 2 2 1 2 2 2 x x x sin 2 2 1 1 2 x x- + (D) ( )- + + + 2 2 2 1 2 2 2 x x x sin 2 1 1 2 2 x x- + 14. Differential co-efficient of, sec-1 1 2 1 2 x- w.r.t. 1 2- x at x = 1 2 is : (A) 2 (B) 4 (C) 6 (D) 1 15. A body moves according to the formula v = 1 + t 2 , where v is the velocity at time t . The acceleration after 3 sec. will be (v in cm/sec.) : (A) 24 cm/sec 2 (B) 12 cm/sec 2 (C) 6 cm/sec 2 (D) None of these 16. If 1 1 2 2- +- x y = a (x - y), then dy dx = (A) 1 1 2 2-- x y (B) 1 1 2 2-- y x (C) x y 2 2 1 1-- (D) y x 2 2 1 1-- 17. If y = (x log x) log log x , then dy dx = (A) (x log x) log log x { 1 x x x x log (log loglog ) + + (loglog ) log x x x 1 (B) (x log x) x log x log log x 2 1 logx x + (C) (x log x) x log x log logx x 1 1 logx +...
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This note was uploaded on 10/05/2011 for the course MATH 1201 taught by Professor Friesner during the Spring '11 term at St. Mary NE.

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M0IITU14 - Differentiation & application qns - 1...

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