List of top Mathematics Questions asked in MHT CET

If the p.m.f. of a random variable \( X \) is given by \[ P(X = x) = \frac{5}{25} \quad \text{if} \quad x = 0, 1, 2, 3, 4, 5 \] then which of the following is not true?

Two cards are drawn from a pack of well shuffled 52 playing cards one by one without replacement. Then the probability that both cards are queens is

If \(\displaystyle \sin\!\left(\frac{x+y}{x-y}\right) = \tan \frac{\pi}{5}\), then find \(\displaystyle \frac{dy}{dx}\).

If \[ \int_{0}^{\frac{\pi}{4}} \frac{\sin x + \cos x}{9 + 16 \sin 2x} \, dx = k \log 3, \text{ then } k = \]

If the equation \( ax^2 + hy^2 + cx + cy = 0, c \neq 0 \) represents a pair of lines, then

The angle between the lines \[ \frac{x - 1}{4} = \frac{y - 3}{8} = \frac{z - 2}{2} \quad \text{and} \quad \frac{x - 2}{3} = \frac{y + 1}{4} = \frac{z - 4}{2} \] is

Evaluate the integral \[ \int \frac{\sec x}{\sqrt{\log(\sec x + \tan x)}}\, dx \]

If $f'(x)=k(\cos x-\sin x)$, $f'(0)=3$, $f\!\left(\dfrac{\pi}{2}\right)=15$, then $f(x)=$

If \( u = \tan^{-1}\!\left(\dfrac{1+x^2-1}{x}\right) \) and \( v = \tan^{-1}\!\left(\dfrac{2x(1-x^2)}{1-2x^2}\right) \), then \( \dfrac{du}{dv} \) at \( x = 0 \) is

If \( f(x) = e^{x}g(x) \), \( g(0) = 4 \), and \( g'(0) = 2 \), then \( f'(0) = \)

Evaluate \( \int \frac{x^2}{(x+1)^2(x+2)^2} \, dx \)

Evaluate the integral \( \displaystyle \int \frac{e^x}{\sqrt{x}}(1+2x)\,dx \)

The equation of a circle passing through the origin and making x-intercept 3 and y-intercept -5 is:

The feasible region of the L.P.P.
\[ \text{Maximize } z = 70x + 50y \] subject to \[ 8x + 5y \le 60,\quad 4x + 5y \le 40,\quad x \ge 0,\; y \ge 0 \] is

The angle between the lines \[ \mathbf{r_1} = (i + 2j + 3k) + \lambda (i + j + 2k) \quad \text{and} \quad \mathbf{r_2} = (3i + k) + \lambda' (2i + j - k), \quad \lambda, \lambda' \in \mathbb{R} \] is

The radius of a circle is increasing at the rate of \( 2 \,\text{cm/sec} \). Find the rate at which its area is increasing when the radius of the circle is \( 5 \) decimeters.

The focal distance of the point \( (4, 4) \) on the parabola with vertex at \( (0, 0) \) and symmetric about the y-axis is

In a triangle ABC, if \[ \frac{\sin A - \sin C}{\cos C - \cos A} = \cot B, \text{ then A, B, C are in} \]

The odds in favour of drawing a king from a pack of 52 playing cards is

A plane \( E_1 \) makes intercepts \( 1, -3, 4 \) on the coordinate axes. The equation of a plane parallel to \( E_1 \) and passing through \( (2,6,-8) \) is

The verbal statement of the same meaning, of the statement 'If the grass is green then it rains in July' is

Evaluate the integral \( \int \frac{4e^x + 6e^{-x}}{9e^x - 4e^{-x}} dx = Ax + B \log |9e^{2x} - 4| + c \), then (where \( c \) is the constant of integration)

If \[ p \rightarrow \left( \sim p \vee q \right) \text{ is false, then the truth values of } p \text{ and } q \text{ are respectively} \]

Evaluate \( \sin^{-1}\left(\frac{1}{2}\right) + \cos^{-1}\left(\frac{\sqrt{3}}{2}\right) + \cot^{-1}\left(-\frac{1}{\sqrt{3}}\right) \)

The p.d.f. of a continuous random variable \( X \) is given by \[ f(x) = \frac{x + 2}{18}, \quad \text{if} \, -2<x<4, \quad f(x) = 0, \, \text{otherwise}. \] Then \( P[ |x|<1 ] = \)