List of top Mathematics Questions asked in MHT CET

If $y = \left[(x+1)(2x+1)(3x+1)\cdots(nx+1)\right]^n$, then $\frac{dy}{dx}$ at $x=0$ is

Let $B\equiv(0,3)$ and $C\equiv(4,0)$. The point A is moving on the line $y=2x$ at the rate of 2 units/second. The area of $\triangle ABC$ is increasing at the rate of

If $p$ is the length of perpendicular from the origin to the line whose intercepts on the axes are $a$ and $b$ respectively, then $\frac{1}{a^2} + \frac{1}{b^2}$ equals

If $\cos^{-1} x + \cos^{-1} y + \cos^{-1} z = 3\pi$, then the value of $x^{2025} + x^{2026} + x^{2027}$ is

$\int \frac{\sin x + \sin^3 x}{\cos 2x} \, dx = A \cos x + B \log f(x) + c$ (where $c$ is a constant of integration). Then values of $A$, $B$ and $f(x)$ are

Equation of the plane passing through $(1,-1,2)$ and perpendicular to the planes $x+2y-2z=4$ and $3x+2y+z=6$ is

The integral $\int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \sec^{\frac{2}{3}} x \, \csc^{\frac{4}{3}} x \, dx$ is equal to

If $\vec{a}$, $\vec{b}$, $\vec{c}$ are unit vectors and $\theta$ is the angle between $\vec{a}$ and $\vec{c}$ and $\vec{a} + 2\vec{b} + 2\vec{c} = \vec{0}$, then $|\vec{a} \times \vec{c}|$ is equal to

If $\vec{a}$, $\vec{b}$, $\vec{c}$ are three vectors with magnitudes $\sqrt{3}$, $1$, $2$ respectively, such that $\vec{a} \times (\vec{a} \times \vec{c}) + 3\vec{b} = \vec{0}$, if $\theta$ is the angle between $\vec{a}$ and $\vec{c}$, then $\sec^2 \theta$ is

Let the curve be represented by $x=2(\cos t+t\sin t)$, $y=2(\sin t-t\cos t)$. Then normal at any point '$t$' of the curve is at a distance of _____ units from the origin.

The principal solutions of the equation $\sec x+\tan x=2\cos x$ are

In $\triangle ABC$, with usual notations, $2ac \sin\left(\frac{A-B+C}{2}\right)$ is equal to

If $f'(x) = \tan^{-1}(\sec x + \tan x)$, $-\frac{\pi}{2}<x<\frac{\pi}{2}$ and $f(0) = 0$, then $f(1)$ is

$\int \frac{\sin 2x \left(1 - \frac{3}{2}\cos x\right)}{e^{\sin^2 x + \cos^3 x}} \, dx =$

If $\int \frac{\cos \theta}{5 + 7\sin \theta - 2\cos^2 \theta} \, d\theta = A \log_e |f(\theta)| + c$ (where $c$ is a constant of integration), then $\frac{f(\theta)}{A}$ can be

If $a>0$ and $z = \frac{(1+i)^2}{a - i}$ ($i = \sqrt{-1}$) has magnitude $\frac{2}{\sqrt{5}}$, then $\overline{z}$ is

If $\triangle ABC$ is right angled at A, where $A\equiv(4,2,x)$, $B\equiv(3,1,8)$ and $C\equiv(2,-1,2)$, then the value of $x$ is

If $\sin(\theta-\alpha)$, $\sin~\theta$ and $\sin(\theta+\alpha)$ are in H.P., then the value of $\cos~2\theta$ is

The angle between the lines, whose direction cosines \( l, m, n \) satisfy the equations \( l + m + n = 0 \) and \( 2l^{2} + 2m^{2} - n^{2} = 0 \), is

Let \( f:\mathbb{R}\rightarrow \mathbb{R} \) be a function such that \( f(x)=x^{3} + x^{2}f^{\prime}(1) + x f^{\prime\prime}(2) + 6 \) for \( x \in \mathbb{R} \), then \( f(2) \) equals

If $y = (\sin^{-1}x)^2 + (\cos^{-1}x)^2$, then $(1 - x^2)\,y'' - x\,y' = $

Let \( A=\begin{bmatrix}2 & -1 \\ 0 & 2\end{bmatrix} \). If \( B=I-{}^{3}C_{1}(\mathrm{adj}\,A)+{}^{3}C_{2}(\mathrm{adj}\,A)^{2}-{}^{3}C_{3}(\mathrm{adj}\,A)^{3} \), then the sum of all elements of the matrix \( B \) is

If \( \vec{a}, \vec{b}, \vec{c} \) are three vectors such that \( |\vec{a}+\vec{b}+\vec{c}|=1 \), \( \vec{c}=\lambda(\vec{a}\times\vec{b}) \) and \( |\vec{a}|=\frac{1}{\sqrt{2}} \), \( |\vec{b}|=\frac{1}{\sqrt{3}} \), \( |\vec{c}|=\frac{1}{\sqrt{6}} \), then the angle between \( \vec{a} \) and \( \vec{b} \) is

Let \( \vec{a}, \vec{b}, \vec{c} \) be three vectors such that \( |\vec{a}|=\sqrt{3} \), \( |\vec{b}|=5 \), \( \vec{b}\cdot\vec{c}=10 \) and the angle between \( \vec{b} \) and \( \vec{c} \) is \( \frac{\pi}{3} \). If \( \vec{a} \) is perpendicular to the vector \( \vec{b}\times\vec{c} \), then \( |\vec{a}\times(\vec{b}\times\vec{c})| \) is equal to

The equation \( x^{3} + x - 1 = 0 \) has