List of top Questions asked in MHT CET

The eccentricity of the ellipse $9x^2 + 5y^2 - 30y = 0$ is

The lines $\frac{x-3}{1} = \frac{y-2}{1} = \frac{z-5}{-k}$ and $\frac{x-4}{k} = \frac{y-3}{1} = \frac{z-3}{2}$ are coplanar, hence $k =$}

If $\int \tan^4 x dx = a \tan^3 x + b \tan x + cx + k$ (where k is the constant of integration) then the value of $a - b + c =$

Let $A$ and $B$ are independent events with $\text{P(B)} = \frac{2}{5}, \text{P(A} \cup \text{B)} = \frac{11}{20}$, then $\text{P(A}' | \text{B)}$ is root of the equation}

$\int \frac{x dx}{(x-1)(x-2)} =$}

If $\frac{z-1}{2z+1}$ is an imaginary number and if it represents a circle then its radius is

The equation of tangent to the curve $y = \cos(x + y)$ where $-2\pi \le x \le 2\pi$ and which is parallel to the line $x + 2y = 0$, is

Total number of 3-digit numbers, whose g.c.d with 36 is 2, is

If $\bar{a}, \bar{b}, \bar{c}$ are three vectors such that $|\bar{a}| = 3, |\bar{b}| = 5, |\bar{c}| = 7$ then $|\bar{a} - \bar{b}|^2 + |\bar{b} - \bar{c}|^2 + |\bar{c} - \bar{a}|^2$ does not exceed}

$\int \frac{x + \sin x}{1 + \cos x} dx =$}

The coordinates of the foot of the perpendicular drawn from a point $P(-1, 1, 2)$ to the plane $2x - 3y + z - 11 = 0$ are

The domain of the function $f(x) = {^{7-x}\text{P}_{x-1}$ is

The value of $\int_{-3}^{3} \sin^7 x \cos^{16} x \, dx$ is

$\lim_{x \to 0} \frac{|x|}{|x| + x^2} =$}

The equation of the plane passing through the line of intersection of the planes $x + y + z = 1$ and $3x + 4y + 5z = 2$ and perpendicular to the XY- plane is

The solution of $\frac{dy}{dx} = (x + y)^2$ is

If $f(x) = \frac{(27-2x)^{\frac{1}{3}} - 3}{9 - 3(243+5x)^{\frac{1}{5}}}, x \ne 0$ is continuous at $x = 0$, then the value of $f(0)$ is

A normal is drawn at a point $P(x, y)$ of a curve $y = f(x)$. The normal meets the $X$ axis at $Q$. $l(PQ) = k \cdot$ (k is a constant) Then equation of the curve through $(0, k)$ is

In a game, 3 coins are tossed. A person is paid Rs \( 150 \) if he gets all heads or all tails and he is supposed to pay ₹\( 50 \) if he gets one head or two heads. The amount he can expect to win lose on an average per game in ₹ is

If $A = \begin{bmatrix} 1 & 2 \\ -1 & 4 \end{bmatrix}$ and $A^{-1} = \alpha I + \beta A$, $\beta \in R$ where I is the identity matrix of order 2, then $4(\alpha + \beta) =$}

If \( \sin \left(\sin^{-1} \frac{1}{5} + \cos^{-1} x\right) = 1 \), then the value of \( x \) is

The principal increases continuously in a newly opened bank at the rate of $10%$ per year. An amount of Rs. 2000 is deposited with this bank. How much will it become after 5 years? ($e^{0.5} = 1.648$)

If two sides of a triangle are \( \sqrt{3} - 1 \) and \( \sqrt{3} + 1 \) units and their included angle is \( 60^\circ \), then the third side of the triangle is

Which of the following are pairs of equivalent circuits

The value of \( \int_{1/3}^{1} \frac{(x - x^3)^{\frac{1{3}}}{x^4} dx \) is