MAH-MHT CET (PCM/PCB) entrance exam Question Bank Solutions for Mathematics

The principal value of sin^–1 `(- sqrt3/2)` is ______.

If sin^-1 x = `pi/10`, for some x ∈ [-1, 1], then the value of cos^-1 x is _______.

`cos^-1 (cos  (4pi)/3)` = ______.

The value of tan 57°- tan 12°- tan 57° tan 12° is ______.

`int 1/(sin x * cos x)` dx = ?

The equation of circle whose diameter lies on 3x + 5y = -7 and 2x - y = 4 which passes through `(-5, 1/2)` is

If `|bar"a"|` = 10, `|bar"b"| = 2`, then `sqrt(|bar"a" xx bar"b"|^2 + |bar"a"*bar"b"|^2)` = ?

The symbolic form of the statement 'lt is not true that Mathematics is not difficult and interesting' is _______.

If p: Resbama is hardworking, q: Reshama is successful, then the verbal form of ~p ∧ ~q is

The general solution of sec θ = `sqrt2` is

`int (sin (log x))^2/x` log x dx = ?

If tan^-1 x + 2cot^-1 x = `(5pi)/6`, then x is

`[sin (tan^-1  3/4)]^2 + [sin(tan^-1  4/3)]^2 = ?`

The equation of normal to the curve y = sin`((pi)/4 x)` at the point (2, 5) is ______.

If f(x) = sin^-1`(sqrt((1 - x)/2))`, then f'(x) = ?

If x + y = `pi/2`, then the maximum value of sin x. sin y is.

The point P lies on line A, B where A = (2, 4, 5} and B = (1, 2, 3). If z co-ordinate of point P is 3, the its y co-ordinate is ______.

If R = {(a, b) lb = a - 1, a ∈ Z, 5 < a < 9, then the range of R is ______.

If y = sin^-1 `[(sqrt(1 + x) + sqrt(1 - x))/2]`, then `"dy"/"dx"` = ?

The equation of the normal to the curve 2x² + y² = 12 at the point (2, 2) is ______.