List of top Mathematics Questions asked in MHT CET

If $x^2+y^2=t+\dfrac{1}{t}$ and $x^4+y^4=t^2+\dfrac{1}{t^2}$, then $\dfrac{dy}{dx}=$

The coordinates of the point where the line $\dfrac{x-1}{2}=\dfrac{y-2}{-3}=\dfrac{z+3}{4}$ meets the plane $2x+4y-z=1$ are

If \[ \sec x + \tan x = 3, \quad x \in \left( 0, \frac{\pi}{2} \right), \] then \( \sin x = \)

If the equation \[ kxy + 5x + 3y + 2 = 0 \text{ represents a pair of lines, then } k = \]

The general solution of \( \tan 3x = 1 \) is

If the radius of a circular blot of oil is increasing at the rate of $2$ cm/min, then the rate of change of its area when its radius is $3$ cm is

Evaluate $\displaystyle \int_{0}^{1} x(1-x)^5 \, dx$

Evaluate the integral: \[ \int \left[ \frac{1 - \log x}{1 + (\log x)^2} \right]^2 dx \]

If the elements of matrix \( A \) are the reciprocals of the elements of the matrix \( \begin{pmatrix} 1 & \omega & \omega^2 \\ \omega & \omega^2 & 1 \\ \omega^2 & 1 & \omega \end{pmatrix} \), where \( \omega \) is a complex cube root of unity, then

The cumulative distribution function of a continuous random variable \( X \) is given by \( F(X = x) = \dfrac{\sqrt{x}}{2} \). Then \( P(X>1) \) is

Find the value of the following expression:
\[ 5^2 + 6^2 + 7^2 + \cdots + 20^2 = \]

The perimeter of a triangle is \(10\) cm. If one of its sides is \(4\) cm, then the remaining sides of the triangle, when the area of the triangle is maximum, are

The particular solution of the differential equation \[ \left( y + x \frac{dy}{dx} \right) \sin y = \cos x \quad \text{at} \quad x = 0 \, \text{is:} \]

The population \( P(t) \) of a certain mouse species at time \( t \) satisfies the differential equation \[ \frac{dP(t)}{dt} = 0.5P(t) - 450. \quad \text{If} \, P(0) = 850, \, \text{then the time at which the population becomes zero is} \]

The integrating factor of the differential equation \[ \frac{dy}{dx} + \frac{1}{x}y = x^3 - 3 \] is

Degree of the differential equation \[ \frac{dy}{dx} e^x + \left( \frac{dy}{dx} \right)^3 = x \]

A body is heated to $110^\circ$C and placed in air at $10^\circ$C. After $1$ hour its temperature is $60^\circ$C. The additional time required for it to cool to $30^\circ$C is

Evaluate the integral \[ \int \frac{dx}{\cos 2x - \cos^2 x} \]

The logical expression \( [p \wedge (q \vee r)] \vee [\neg r \wedge \neg q \wedge p] \) is equivalent to

The length of the perpendicular from the point \( P(a,b) \) to the line \( \dfrac{x}{a} + \dfrac{y}{b} = 1 \) is

Evaluate \[ \int \frac{\log x - 1}{1 + (\log x)^2} \, dx \]

If the points \( (1, 1, \lambda) \) and \( (-3, 0, 1) \) are equidistant from the plane \( 3x + 4y - 12z + 13 = 0 \), then the integer value of \( \lambda \) is

If \[ O = (0, 0, 0), \quad P = (1, \sqrt{2}, 1), \] then the acute angles made by the line OP with the \( XOY, \, YOZ, \, ZOX \text{ planes are, respectively,} \)

The joint equation of bisectors of the angle between the lines represented by $3x^2+2xy-y^2=0$ is

The derivative of $\sin^{-1}\!\left(\dfrac{\sqrt{1+x}+\sqrt{1-x}}{2}\right)$ with respect to $\cos^{-1}x$ is