List of top Questions asked in MHT CET

The frequency of a tuning fork is $256 \text{ Hz}$. It will not resonate with the tuning fork of frequency}

A convex lens of focal length $\frac{1}{3} \text{ m}$ forms a real, inverted image twice the size of the object. The distance of the object from the lens is

The resultant of two vectors $\vec{A}$ and $\vec{B}$ is $\vec{C}$. If the magnitude of $\vec{B}$ is doubled, the new resultant vector becomes perpendicular to $\vec{A}$, then the magnitude of $\vec{C}$ is

If two curves $x^2 - 4y^2 = 2$ and $8x^2 = 40 - my^2$ are orthogonal to each other then m =

The value of 'a' so that the sum of squares of the roots of the equation $x^2 - (a - 2)x - a + 1 = 0$ assumes the least value is

If the tangent at $(1, 7)$ to the curve $x^2 = y - 6$ touches the circle $x^2 + y^2 + 16x + 12y + \text{C} = 0$, then C =}

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

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

If $\frac{z-1}{2z+1}$ is an imaginary number and if it represents a circle then its radius 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 domain of the function $f(x) = {^{7-x}\text{P}_{x-1}$ is

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

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

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

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

Which of the following are pairs of equivalent circuits

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? ($e^{0.5} = 1.648$)