List of top Mathematics Questions asked in MHT CET

The negation of the statement “If $5<7$ and $7>2$, then $5>2$” is

The order and degree of the differential equation $\sqrt{1+\dfrac{1}{\left(\dfrac{dy}{dx}\right)^2}}=\left(\dfrac{d^2y}{dx^2}\right)^{\tfrac{3}{2}}$ are respectively

If $\displaystyle \int \frac{x^2+1}{(x-3)(x-2)}\,dx = Px + Q\log|x-3| + R\log|x-2| + c$, where $c$ is constant of integration, then the values of $P,Q,R$ are respectively

Evaluate $\displaystyle \int_{-2}^{2} [x]\,dx$, where $[x]$ denotes the greatest integer function

Evaluate $\displaystyle \int \frac{dx}{1+\sqrt{x}}$

If a function $f:\mathbb{R} \to \mathbb{R}$ is defined by $f(x) = \dfrac{4x}{5} + 3$, then $f^{-1}(x) =$

If $f:\mathbb{R}\rightarrow\mathbb{R}$ is given by $f(x)=7x+8$ and $f^{-1}(12)=\dfrac{k}{7}$, then the value of $k$ is

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

The derivative of $\cot^{-1}x$ with respect to $\log(1+x^2)$ is

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

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

The separate equations of the lines represented by $4x^2 - y^2 + 2x + y = 0$ are

The sum of first four terms of a G.P. is $160$ and the common ratio is $3$, then the $4^{\text{th}}$ term is

The bacteria increases at the rate proportional to the number of bacteria present. If the original number $N$ doubles in $4$ hours, then the number of bacteria in $12$ hours will be

The equation of the line passing through the point $(1,2,3)$ and perpendicular to the lines $\dfrac{x-1}{1} = \dfrac{y-2}{2} = \dfrac{z-3}{3}$ and $\vec r = \lambda(-3\hat i + 2\hat j + 5\hat k)$ is

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

The dual of the statement `Mangoes are delicious but expensive' is

The angle between the lines $\vec r = (2\hat i + \hat j - 3\hat k) + \lambda(\hat i - \hat j + \hat k)$ and $\dfrac{x-1}{1} = \dfrac{y+2}{3} = \dfrac{z-3}{2}$ is

If $AX = B$, where $A = \begin{bmatrix} 1 & 3 & 3 \\ 1 & 4 & 4 \\ 1 & 3 & 4 \end{bmatrix}$, $X = \begin{bmatrix} x \\ y \\ z \end{bmatrix}$ and $B = \begin{bmatrix} 12 \\ 15 \\ 13 \end{bmatrix}$, then $x^2 + y^2 + z^2 =$

If the length of perpendicular drawn from the point $(4,1)$ on the line $3x - 4y + k = 0$ is $2$ units, then the values of $k$ are

The principal solutions of $\cos 2x = -\frac{1}{2}$ are

The differential equation of the circles having their centres on the line $y = 8$ and touching the $x$-axis is

The integrating factor of the differential equation $(1 + y + x^2y)\,dx + (x + x^3)\,dy = 0$ is

The function $f(x) = (x + 2)e^{-x}$ is

The value of $\cos^{-1}\left(\cos\left(\frac{7\pi}{6}\right)\right)$ is