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

The solution of the differential equation `dy/dx = (2logx - y)/(xlogx)` is ______

The edge of a cube is increasing at the rate of 20 cm/sec. How fast is the volume of the cube increasing when the edge is 6 cm long?

Let S be a non-empty subset of R. Consider the following statement:

p: There is a rational number x ∈ S such that x > 0. Which of the following statements is the negation of the statement p? 

The negation of the statement: "Getting above 95% marks is a necessary condition for Hema to get admission in good college'' is ______

If the line `x/(-3) = "y"/2 = "z"/5` is perpendicular to the line `(x - 2)/2 = ("y - 1")/"k" = ("z - 3")/("k + 11")`, then the value of k is ______.

`sin^2(sin^-1  1/2) + tan^2 (sec^-1  2) + cot^2(cosec^-1  4)` = ______.

The area of tbe region bounded by the curve y = x³ and the lines y = 8 and x = 0 is ______.

If the lines `(x + 1)/"k" = ("y + 3")/(- 1) = ("z" - 4)/1` and `(x + 10)/(-1) = ("y + 1")/(-3) = ("z - 1")/4` intersect each other, then the value of k is ______.

`int "e"^(sin^-1 x) ((x + sqrt(1 - x^2))/(sqrt1 - x^2)) "dx" = ?`

If x² + (2h - 1)xy + y² - 24x - 8y + k = 0 is the equation of the circle and 12 is the radius of the circle, then ______.

If 2tan^-1 (cos x) = tan^-1 (cosec² x), then x = ______.

`int ((x + 1)(x + log x))^4/(3x) "dx" =`______.

The principal value of `sin^-1 (sin  (3pi)/4)` is ______.

The shortest distance between the skew lines `overliner= (6hati + 2hatj + 2hatk) + t(hati - 2hatj + 2hatk)` and `overliner = (-4hati - hatk) + s(3hati - 2hatj - 2hatk)` is ______.

If the value of `lim_(x -> 1) (1 - (1 - x))^"m"/x` is 99, then n = ______.

Which of the following pair of straight lines intersect at right angles?

The equation of the circle with centre (4, 5) which passes through (7, 3) is ______.

The equation of circle whose diameter is the line joining the points (–5, 3) and (13, –3) is ______.

If sin `(sin^-1  1/3 + cos^-1 x) = 1`, then the value of x is ______.

`tan[2tan^-1 (1/3) - pi/4]` = ______.