List of top Mathematics Questions asked in MHT CET

A, B, C are three events, one of which must and only one can happen. The odds in favor of A are $4:6$, the odds against B are $7:3$. Thus, odds against C are

The area (in sq. units) of the region bounded by the parabola $x = \frac{y^2}{2}$ and the line $x = y + 4$ is

The value of the integral $\int\frac{x+1}{x(1+xe^{x})^{2dx$ is

Let two non-collinear vectors $\hat{a}$ and $\hat{b}$ form an acute angle. A point P moves, so that at any time t the position vector $\overline{OP}$, where O is origin, is given by $\hat{a}\sin t+\hat{b}\cos t.$ when P is farthest from origin O, let M be the length of OP and $\hat{u}$ be the unit vector along $\overline{OP,}$ then

The number of solutions in $[0,2\pi]$ of the equation $16^{\sin^{2}x}+16^{\cos^{2}x}=10$ is

The differential equation of all parabolas, whose axes are parallel to Y-axis, is

If $Z_{1}=4i^{40}-5i^{35}+6i^{17}+2$, $Z_{2}=-1+i$ where $i=\sqrt{-1}$, then $|Z_{1}+Z_{2}|=$

In a Binomial distribution with $n=4$ if $2P(X=3)=3P(X=2)$, then the variance is

If two vertices of a triangle are $A(3,1,4)$ and $B(-4,5,-3)$ and the centroid of the triangle is $G(-1,2,1),$ then the third vertex C of the triangle is

Let $P(x)$ be a polynomial of degree 2, with $P(2) = -1$, $P'(2) = 0$, $P''(2) = 2$, then $P(1.001)$ is

Given a polynomial $P(x) = ax^2 + bx + c$ such that $P''(2)=2$, $P'(2)=0$, and $P(2)=-1$. Find the approximate value of $P(1.001)$ using linear approximation.

If $I = \int \frac{dx}{\sin(x-a) \sin(x-b)}$, then $I$ is given by}

The length of the perpendicular drawn from the point $(1, 2, 3)$ to the line $\frac{x-6}{3} = \frac{y-7}{2} = \frac{z-7}{-2}$ is

Let $f(x) = 5 - |x-2|$ and $g(x) = |x + 1|$, $x \in \mathbb{R}$. If $f(x)$ attains maximum value at $\alpha$ and $g(x)$ attains minimum value at $\beta$, then $\lim_{x \to \alpha\beta} \frac{(x-1)(x^2-5x+6)}{x^2-6x+8}$ is equal to}

If $a \cos 2\theta + b \sin 2\theta = c$ has $\alpha$ and $\beta$ as its roots, then the value of $\tan \alpha + \tan \beta$ is

A vector parallel to the line of intersection of the planes $\vec{r} \cdot (3\hat{i} - \hat{j} + \hat{k}) = 1$ and $\vec{r} \cdot (\hat{i} + 4\hat{j} - 2\hat{k}) = 2$ is

A lot of 100 bulbs contains 10 defective bulbs. Five bulbs are selected at random from the lot and are sent to retail store. Then the probability that the store will receive at most one defective bulb is

$\int \frac{dx}{\cot^2 x - 1} = \frac{1}{A} \log |\sec 2x + \tan 2x| - \frac{x}{B} + c$, (where $c$ is constant of integration), then $A + B =$}

There are 6 positive and 8 negative numbers. From these four numbers are chosen at random and multiplied. Then the probability, that the product is a negative number, is

The area bounded by the curve $y = |x - 2|$, $x = 1$, $x = 3$ and X-axis is

If $f'(x) = \sin(\log x)$ and $y = f\left(\frac{2x+3}{3-2x}\right)$, then $\frac{dy}{dx}$ at $x=1$ is

If $f(x) = \frac{2x-3}{3x-4}, x \neq \frac{4}{3}$, then the value of $f^{-1}(x)$ is

The statement $[p \land (q \lor r)] \lor [\sim r \land \sim q \land p]$ is equivalent to}

If the lines $\frac{x-k}{2} = \frac{y+1}{3} = \frac{z-1}{4}$ and $\frac{x-3}{1} = \frac{y-\frac{9}{2{2} = \frac{z}{1}$ intersect, then the value of k is

If $|\vec{a}| = \sqrt{3}$; $|\vec{b}| = 5$; $\vec{b} \cdot \vec{c} = 10$, angle between $\vec{b}$ and $\vec{c}$ is $\frac{\pi}{3}$, $\vec{a}$ is perpendicular to $\vec{b} \times \vec{c}$. Then the value of $|\vec{a} \times (\vec{b} \times \vec{c})|$ is