Title Essential Mathematics (MCQ).pdf ✅

PHYSICS Q.1 If x = 3t2 + 4t + 3, then (A) dt dx = 6t + 4 (B) 2 2 dt d x = 6 (C) 2 2 dt d x = 0 (D) dt dx . 2 2 dt d x =36 t +24 [A,B,D] Q.2 If y = sin u2 , u = x 2 + 1, then (A) du dy = 2u cos u2 (B) dx du = 2x (C) dx dy = 2 (x2 + 1) sin (x2 + 1) (D) dx dy = 4x (x2 + 1) cos (x2 + 1)2 [A,B,D] Q.3 If y = tan x, then (A) dx dy = sec2 x (B) 2 2 dx d y = 2 sec2 x tan x (C) dx dy = sec x tan x (D) 2 2 dx d y = 2 sec x tan2 x [A,B] Q.4 If y = log sec x, then (A) y = tan2 x (B) y = tan x (C) y = sec2 x (D) y = 2 sec2 x tan x [B,C,D] Q.5 If S = 3 t 3 – 2 t2 + 3t + 4, then (A) at t = 1, S is minimum (B) at t = 1, S is maximum (C) at t = 3, S is maximum (D) at t = 3, S is minimum [B,D] Q.6 Select the correct - (A)  x dx 2 = 3 x 3 + C (B)  x dx –1 = loge |x| + C (C)  x dx –3 = – 2 1 x –2 + C (D)   dx d sin x = 2 1   –1/ 2 sin x . cos x [A,B,C,D] Q.7 Which of the following straight lines have positive slope ? (A) 2y – 3x = – 5 (B) y + 5x = 3 (C) y = 4x + 3 (D) 3y – 5x = 4 Sol.[A,C,D] 2 5 x – 2 3 y  y = 4x + 3 3 4 x 3 5 y   Q.8 If a = 2 1 , then - (A) a = sin 30° (B) a = cos 60° (C) a = tan 30° (D) a = cosec 30° Sol.[A,B] sin 30° = cos 60° = 2 1 Q.9 Which of the following relations is/are correct ? (A) sin (90 + ) = cos (– ) (B) sin (180 – ) = cos (90 – ) (C) sin (360 – ) = cos (360 – ) (D) sin (180 + ) = cos (90 – ) Sol.[A,B] Q.10 For which functions dx dy = 2 2 dx d y ? (A) sin x = y (B) ex = y (C) cos x = y (D) x2 = y Sol.[B] x x (e ) e dx d  Q.11 If y = kx2 where k is positive non-zero constant, then which of the following graphs is/are correct ? (A) y O x (B) y O x 2 (C) y O x (D) y O x