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

Let f be the function defined by

f(x) = `{{:((x^2 - 1)/(x^2 - 2|x - 1| - 1)",", x ≠ 1),(1/2",", x = 1):}`

In a triangle ABC, ∠C = 90°, then `(a^2 - b^2)/(a^2 + b^2)` is ______.

The differential equation representing the family of curves y² = `2c(x + sqrt(c))`, where c is a positive parameter, is of ______.

If f(x) = `1/(1 - x)`, the number of points of discontinuity of f{f[f(x)]} is ______.

A coin is tossed three times. If X denotes the absolute difference between the number of heads and the number of tails then P(X = 1) = ______.

In ΔABC, with usual notations, if a, b, c are in A.P. Then `a cos^2 (C/2) + c cos^2(A/2)` = ______.

If X = {4ⁿ – 3n – 1 :n ∈ N} and Y = {9n – 1}:n ∈ N}, then X ∩ Y = ______.

The order of the differential equation of all parabolas, whose latus rectum is 4a and axis parallel to the x-axis, is ______.

If the function f(x) = `[tan(π/4 + x)]^(1/x)` for x ≠ 0 is = K for x = 0 continuous at x = 0, then K = ?

At random variable X – B(n, p), if values of mean and variance of X are 18 and 12 respectively, then total number of possible values of X are ______.

If the volume of spherical ball is increasing at the rate of 4π cm³/s, then the rate of change of its surface area when the volume is 288π cm³, is ______.

If f(x) = `{{:(log(sec^2 x)^(cot^2x)",", "for"  x ≠ 0),(K",", "for"  x = 0):}`

is continuous at x = 0, then K is ______.

If f(x) = `{{:(x, "for"  x ≤ 0),(0,
"for"  x > 0):}`, then f(x) at x = 0 is ______.

For the following distribution function F(x) of a rv.x.

P(3 < x < 5) =

In ΔABC, `(a - b)^2 cos^2  C/2 + (a + b)^2 sin^2  C/2` is equal to ______.

The point on the curve 6y = x³ + 2 at which y-coordinate is changing 8 times as fast as x-coordinate is ______.

If the function f(x) defined by

f(x) = `{{:(x sin  1/x",", "for"  x = 0),(k",", "for"  x = 0):}`

is continuous at x = 0, then k is equal to ______.

For what value of k, the function defined by

f(x) = `{{:((log(1 + 2x)sin^0)/x^2",", "for"  x ≠ 0),(k",", "for"  x = 0):}`

is continuous at x = 0 ?

The degree and order of the differential equation `[1 + (dy/dx)^3]^(7/3) = 7((d^2y)/(dx^2))` respectively are ______.

Which of the following equation does not represent a pair of lines?