List of top Mathematics Questions asked in MHT CET

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

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

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

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

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.

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)

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

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

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 \( P[ |x|<1 ] = \)

If the p.m.f. of a random variable \( X \) is \[ \begin{array}{|c|c|c|c|c|} X & 1 & 2 & 3 & 4 & 5
P(X = x) & k & \frac{k}{3} & \frac{k}{4} & \frac{k}{2} & \end{array} \] then \( k = \)

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

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

If \( | \vec{a} \, \vec{b} \, \vec{c} | = 3 \), then the volume of the parallelepiped with \( 2\vec{a} + \vec{b} \), \( 2\vec{b} + \vec{c} \), \( 2\vec{c} + \vec{a} \) as coterminous edges is:

The minimum value of \( Z = 5x + 8y \) subject to \[ x + y \geq 5, \quad 0 \leq x \leq 4, \quad y \geq 2, \quad x \geq 0, \quad y \geq 0 \] is

In a triangle \(ABC\) with usual notations, if \(\tan A,\tan B,\tan C\) are in H.P., then \(a^2,b^2,c^2\) are in

If \( \sec\theta = \dfrac{13}{12} \) and \( \theta \) lies in the fourth quadrant, then find \[ \tan\theta \times \csc\theta \times \sin\theta \times \cos\theta \]

The joint equation of the pair of lines passing through the point of intersection of the lines \[ 2x^2 - xy - 15y^2 - 7x + 32y - 9 = 0 \] and parallel to the coordinate axes is

The locus of the point of intersection of the two lines \[ x\sqrt{3} - y = k\sqrt{3} \quad \text{and} \quad \sqrt{3}x + ky = \sqrt{3}, \; k \in \mathbb{R}, \] describes

If L.M.V.T. is applicable for the function $f(x) = x + \dfrac{1}{x}$ on $[1,3]$, then $c =$

The equation of the curve which passes through the point \( (1,0) \) and has tangent with slope \[ 1+\frac{y}{x}+\left(\frac{y}{x}\right)^2 \] is

Evaluate \[ \int \frac{dx}{(x+2)\sqrt{x+1}} \]