List of top Mathematics Questions asked in MHT CET

If truth values of statements p, q are true, and r, s are false, then the truth values of the following statement patterns are respectively:
$a:\sim(p\wedge\sim r)\vee(\sim q\vee s)$
$b:(\sim q\wedge\sim r)\leftrightarrow(p\vee s)$
$c:(\sim p\vee q)\rightarrow(r\wedge\sim s)$

The maximum value of $xy$ when $x+2y=8$ is

The value of $\alpha$, so that the volume of the parallelopiped formed by $\hat{i}+\alpha\hat{j}+\hat{k}$, $\hat{j}+\alpha\hat{k}$ and $\alpha\hat{i}+\hat{k}$ becomes maximum, is

If $\sin^{-1}x+\cos^{-1}y=\frac{3\pi}{10}$, then the value of $\cos^{-1}x+\sin^{-1}y$ is

The approximate value of $\log_{10} 998$ is (given that $\log_{10}e=0.4343$)

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

Two sides of a triangle are $\sqrt{3}+1$ and $\sqrt{3}-1$ and the included angle is $60^\circ$, then the difference of the remaining angles is

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 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 $|Z_{1}+Z_{2}|=$

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

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

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.

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

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

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

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

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