List of top Questions asked in MHT CET

In a triangle ABC, with usual notations $a = 2$, $b = 3$, $c = 5$, then $\frac{\cos A}{a} + \frac{\cos B}{b} + \frac{\cos C}{c} =$

Given that the total of 16 values is 528 and the sum of the squares of deviation from 33 is 9158. The variance is

Evaluate the limit: $\lim_{x \to 1} \left[ \frac{\sqrt{x} - 1}{\log x} \right] =$

Negation of the statement : $3 + 6 > 8$ and $2 + 3 < 6$ is

If the surrounding air is kept at 25$^\circ$C and a body cools from 80$^\circ$C to 50$^\circ$C in 30 minutes, then temperature of the body after one hour will be

Rooms in a hotel are numbered from 1 to 19. Rooms are allocated at random as guests arrive. The first guest to arrive is given a room which is a prime number. The probability that the second guest to arrive is given a room which is a prime number is

If $f(x) = \frac{1 - \sin x + \cos x}{1 + \sin x + \cos x}$, for $x \neq \pi$ is continuous at $x = \pi$, then the value of $f(\pi)$ is

The combined equation of a pair of lines passing through the origin and inclined at $60^\circ$ and $30^\circ$ respectively with X-axis is

Range of the function $f(x) = 3 + 2^x + 4^x$ is

If $3\hat{j}$, $4\hat{k}$ and $3\hat{j} + 4\hat{k}$ are the position vectors of the vertices $A, B, C$ respectively of $\Delta ABC$, then the position vector of the point in which the bisector of $\angle A$ meets $BC$ is

If $z = x + iy$ satisfies the condition $|z + 1| = 1$, then $z$ lies on the

10 is divided into two parts such that the sum of double of the first and square of the other is minimum, then the numbers are respectively

Evaluate the integral: $\int e^{(e^x + x)} dx$

If $A=\left[\begin{array}{ccc}1 & -1 & 1 \\ 2 & -1 & 0 \\ 3 & 3 & -4\end{array}\right]$, $B=\left[\begin{array}{l}1 \\ 1 \\ 2\end{array}\right]$ and $X=\left[\begin{array}{l}x_1 \\ x_2 \\ x_3\end{array}\right]$ such that $AX = B$, then the value of $x_1 + x_2 + x_3 =$

If $\vec{a} = \hat{i} + 2\hat{j} + 3\hat{k}$, $\vec{b} = -\hat{i} + 2\hat{j} + \hat{k}$, $\vec{c} = 3\hat{i} + \hat{j}$ and $\vec{a} + \lambda \vec{b}$ is perpendicular to $\vec{c}$, then the value of $\lambda =$

The general solution of the differential equation $\frac{dy}{dx} = 2^{y - x}$ is

If two lines represented by $ax^2 + 2hxy + by^2 = 0$ make angles $\alpha$ and $\beta$ with the positive direction of X-axis, then $\tan(\alpha + \beta) =$

If $\tan^{-1} \left[ \frac{\sqrt{1+x^2} - \sqrt{1-x^2}}{\sqrt{1+x^2} + \sqrt{1-x^2}} \right] = \alpha$, then the value of $\sin 2\alpha$ is

The vector equation of the line passing through $\text{P}(1,2,3)$ and $\text{Q}(2,3,4)$ is

If $A=\left[\begin{array}{rr}2 & 3 \\ 5 & -2\end{array}\right]$ and $A^{-1}=K A$, then $K$ is

The coordinates of the foot of the perpendicular drawn from the origin to the plane $2x + y - 2z = 18$ are

If $\mathrm{A}=\left[\begin{array}{ccc}1 & 2 & 3 \\ -1 & 1 & 2 \\ 1 & 2 & 4\end{array}\right]$, then $\mathrm{A}(\text{adj }\mathrm{A}) =$

If a circle passes through the points $(0,0)$, $(x, 0)$ and $(0, y)$, then the coordinates of its centre are

If $x = -2$ and $x = 4$ are the extreme points of the function $y = x^3 - \alpha x^2 - \beta x + 5$, then the values of $\alpha$ and $\beta$ are respectively

A random variable X has the following probability distribution

Then P ( 3 < x $\le$ 6 ) =