List of top Mathematics Questions

Write \( \int \cot{x} \, dx \).

Write the degree of the differential equation \( \frac{d^2y}{dx^2} + \frac{dy}{dx} = x \).

i. Write the joint equation of coordinate axes.

The solution of the differential equation \( \frac{dx}{dt} = x \log \frac{x}{t} \) is

ii. Find the values of \( c \) which satisfy \( |c\vec{u}| = 3 \) where \( \vec{u} = \hat{i} + 2\hat{j} + 3\hat{k} \).

If the corner points of the feasible solution are \( (0, 10), (2, 2) \), and \( (4, 0) \), then the point of minimum \( z = 3x + 2y \) is

The integral of \( \cos^2x \) is

If \( y \) is a function of \( x \) and \( \log(x + y) = 2xy \), then the value of \( y'(0) \) is

The area of the triangle with vertices \( (1, 2, 0), (1, 0, 2) \), and \( (0, 3, 1) \) in square units is

digit number

denote the (r + 2) digit number where the first and the last digits are 7 and the remaining r digits are 5. Consider the sum S = 77 + 757 + 7557 + …+

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, where m and n are natural numbers less than 3000, then the value of m + n is ______.

The line integral \(\overrightarrow V = x^2\hat{î}-2y\hat{j} + z^2\hat{k}\) over the straight line path from the point (-1, 2, 3) to (2, 3, 5) is

The heights of two right circular cones are in the ratio \(1 : 2\) and the circumferences of their bases are in the ratio \(3: 4.\) Find the ratio of their volumes.

Let $f$ be a twice differentiable function on $R$.
If $f ^{\prime}(0)=4$ and $f(x)+\int\limits_0^x(x-t) f^{\prime}(t) d t=\left(e^{2 x}+e^{-2 x}\right) \cos 2 x+\frac{2}{a} x,$
then $(2 a+1)^5 a^2$ is equal to ______.

A particle moves along the curve \(\frac{x^2}{16}+\frac{y^2}{4}=1\). When the rate of change of abscissa is 4 times that of its ordinate, then the quadrant in which the particle lies is

Let a₁, a₂, a₃, …. be a G.P. of increasing positive numbers. Let the sum of its 6^th and 8^th terms be 2 and the product of its 3rd and 5th terms be \(\frac{1}{9}\) .Then 6 (a₂ + a₄) (a₄ + a₆) is equal to

Let f(x) = sin 2x + cos 2x and g(x)=x²-1, then g(f(x)) is invertible in the domain

If the center and radius of the circle $\left|\frac{z-2}{z-3}\right|=2$ are respectively $(\alpha, \beta)$ and $\gamma$, then $3(\alpha+\beta+\gamma)$ is equal to

Let $A = \begin{bmatrix} 1 & a & a \\ 0 & 1 & b \\ 0 & 0 & 1\end{bmatrix}, a , b \in R$.
If for some $n \in N , A ^{ n }=\begin{bmatrix}1 & 48 & 2160 \\ 0 & 1 & 96 \\ 0 & 0 & 1\end{bmatrix}$
then $n + a + b$ is equal to _________.

The value of \(\begin{vmatrix} \sin^2 14 \degree & \sin^2 66\degree & \tan 135\degree \\ \sin^2 66\degree & \tan 135\degree & \sin^2 14 \degree \\ \tan 135\degree & \sin^2 14 \degree & \sin^2 66\degree \end{vmatrix}\)

If the points of intersection of the parabola y² = 5x and x²= 5y lie on the line L, then the area of the triangle formed by the directrix of one parabola, latus rectum of another parabola and the line L is

If polynomial \(g(x) = 3x^2 - 7x + 2\), then the value of \(g(-1)\) is

If \(\alpha\) and \(\beta\) are zeroes of the polynomial \(p(x) = x^2 - 3x + 5\), then the value of \(4(\alpha + \beta)\) is

In the following distribution, what is the modal class?

Class	Frequency
0-10	15
10-20	20
20-30	45
30-40	15
40-50	25

If \( p(x) = 3x^{3} + x^{2} + 2x + 5 \) is divided by \( q(x) = x^{2} + 2x + 1 \), then the degree of the quotient will be:

Evaluate \( \dfrac{\sin^{2}(90^\circ-\theta)+\sin^{2}\theta}{\csc^{2}(90^\circ-\theta)-\tan^{2}\theta} \).