List of top Mathematics Questions asked in MHT CET

If \[ 2 + 4 + 6 + \cdots \text{ up to } n \text{ terms} = \frac{37}{36}, \] then \( n = \)

The eccentricity of the hyperbola \( 16x^2 - 3y^2 - 32x - 12y - 44 = 0 \) is

The derivative of $\cot^{-1}x$ with respect to $\log(1+x^2)$ is

The rate of growth of bacteria is proportional to the bacteria present. If it is found that the number doubles in 3 hours, then the number of times the bacteria are increased in 6 hours is

$\cosec 2\theta-\cot 2\theta=$

In \( \triangle ABC \), if \( \frac{\cos A}{a} = \frac{\cos B}{b} = \frac{\cos C}{c} \) with usual notations, then the triangle is:

Two dice are thrown together. The probability that the sum of the numbers is divisible by 2 or 3 is

Which of the following statement patterns is a tautology?
\[ \begin{aligned} S_1 &: (\sim q \land p) \land q
S_2 &: [p \land (p \rightarrow q)] \rightarrow q
S_3 &: (p \land q) \land (\sim p \lor \sim q)
S_4 &: (p \land q) \rightarrow r \end{aligned} \]

Evaluate the integral \[ \int_{-5}^{5} \log \left( \frac{7 - x}{7 + x} \right) \, dx \]

If \( a, b, c \) are lengths of the sides \( BC, CA, AB \) respectively of \( \triangle ABC \) and \( a\vec{AH} + b\vec{BH} + c\vec{CH} = \vec{0} \), then point \( H \) is the

The letters of the word 'LOGARITHM' are arranged at random. The probability that the arrangement starts with a vowel and ends with a consonant is

Evaluate the integral \[ \int_{0}^{1} \tan^{-1}\!\left( \frac{2x - 1}{1 + x - x^2} \right) dx \]

The coordinates of the foci of the ellipse \( 16x^2 + 9y^2 = 144 \) are

If the angle between the lines whose direction ratios are \( 4, -3, 5 \) and \( 3, 4, k \) is \( \frac{\pi}{3} \), then \( k = \)

If rectangles are inscribed in a circle of radius \( r \) units, then the dimensions of the rectangle which has maximum area are

If \( f(x) = \frac{x^2 + 2{18} \), for \( -2<x<4 \), and 0 otherwise, is the p.d.f. of a random variable \( X \), then the value of \( P(|X|<2) \) is}

If \( \tan \theta = \dfrac{1}{3} \), then find \( \cos 2\theta \).

If \( \int x^x (1 + \log x) \, dx = k x^x + c \), then \( k = \)

Evaluate $\displaystyle \int \frac{dx}{1+\sqrt{x}}$

The derivative of \( f(\tan x) \) w.r.t. \( g(\sec x) \) at \( x = \frac{\pi}{4} \), where \( f'(1) = 2 \) and \( g'( \sqrt{2} ) = 4 \), is

If \(\sqrt{x} + \sqrt{y} = \sqrt{xy}\), then find \(\dfrac{dy}{dx}\).

If the displacement of a particle at time \(t\) is given by \[ s = 3t^2 - 12t + 14, \] then the displacement of the particle when its velocity becomes zero is

If \(f'(x) = k(\cos x + \sin x)\) and \(f(0) = 9,\ f\!\left(\dfrac{\pi}{2}\right) = 15\), then \(f(x)=\)

The area bounded by the parabola \( y^2 = 16x \) and its latus-rectum in the first quadrant is

The differential equation of the family of curves \( y = e^{x} (A \cos x + B \sin x) \), where \( A \) and \( B \) are arbitrary constants, is