List of top Mathematics Questions

If $(\cot \alpha_1)(\cot \alpha_2) \cdots (\cot \alpha_n) = 1$, with $0<\alpha_1, \alpha_2, \ldots, \alpha_n<\frac{\pi}{2}$, then the maximum value of $(\cos \alpha_1)(\cos \alpha_2) \cdots (\cos \alpha_n)$ is
Let $R$ and $S$ be two equivalence relations on a non-void set $A$. Then
A line passes through the point $(-1, 1)$ and makes an angle $\sin^{-1} \left( \frac{3}{5} \right)$ with the positive direction of the $x$-axis. If this line meets the curve $x^2 = 4y - 9$ at $A$ and $B$, then $|AB|$ is equal to
If the 2$^{\text{nd}}$, 5$^{\text{th}}$ and 9$^{\text{th}}$ terms of a non-constant A.P. are in G.P., then the common ratio of this G.P. is
The ratio in which $\hat{i}+2\hat{j}+3\hat{k}$ divides the join of $-2\hat{i}+3\hat{j}+5\hat{k}$ and $7\hat{i}-\hat{k}$ is
The ratio of the coefficient of $x^{15}$ to the term independent of $x$ in the expansion of $\left(x^2+\dfrac{2}{x}\right)^{15}$ is
For the following question, enter the correct numerical value upto TWO decimal places. If the numerical value has more than two decimal places, round-off the value to TWO decimal places. (For example: Numeric value 5 will be written as 5.00 and 2.346 will be written as 2.35) The eccentricity of the ellipse \[ \frac{x^2}{25} + \frac{y^2}{16} = 1 \] is \( \dfrac{3}{__} \).
For the following question, enter the correct numerical value upto TWO decimal places. If the numerical value has more than two decimal places, round-off the value to TWO decimal places. (For example: Numeric value 5 will be written as 5.00 and 2.346 will be written as 2.35) If \( z \), \( iz \) and \( z+iz \) are the vertices of a triangle and if \( |z| = 4 \), then the area (in sq. units) of that triangle is ______.
Two vertices of a triangle are $(5,-1)$ and $(-2,3)$. If the origin is the orthocentre of this triangle, then the coordinates of the third vertex of that triangle are
If the midpoints of the sides $BC$, $CA$ and $AB$ of a triangle $ABC$ are respectively $(2,1)$, $(-1,-2)$ and $(3,3)$, then the equation of the side $BC$ is
For the following question, enter the correct numerical value upto TWO decimal places. If the numerical value has more than two decimal places, round-off the value to TWO decimal places. (For example: Numeric value 5 will be written as 5.00 and 2.346 will be written as 2.35) Minimum number of times a fair coin must be tossed so that the probability of getting at least one head is more than 99% is ____.
For the following question, enter the correct numerical value upto TWO decimal places. If the numerical value has more than two decimal places, round-off the value to TWO decimal places. (For example: Numeric value 5 will be written as 5.00 and 2.346 will be written as 2.35) An envelope is known to have come from either `LONDON` OR `CLIFTON`. On the postal card only two successive letters `ON` are visible. The probability that the envelope comes from LONDON is \( \dfrac{12}{__} \).
For the following question, enter the correct numerical value upto TWO decimal places. If the numerical value has more than two decimal places, round-off the value to TWO decimal places. (For example: Numeric value 5 will be written as 5.00 and 2.346 will be written as 2.35) There are 10 points in a plane out of which 6 are collinear. The number of straight lines formed by joining all these points is ____.
Evaluate: \[ \int_{0}^{\pi} \frac{x\sin x}{1+\cos^2 x}\,dx \]
The minimum distance of a point on the curve $y=x^2-4$ from the origin is
If $y=y(x)$ is the solution of the differential equation \[ x\frac{dy}{dx}+2y=x^2 \] satisfying $y(1)=1$, then $y\!\left(\dfrac{1}{2}\right)$ is equal to:
Let $f$ be a polynomial function such that $f'(x)=f(x)\,f''(x)$ for all $x\in\mathbb{R}$. Then:
Evaluate: \[ \int \frac{dx}{\cos x+\sqrt{3}\sin x} \]
If \[ \int \frac{1}{(x+100)\sqrt{x+99}}\,dx = f(x)+c \] then $f(x)=$
$1^3 - 2^3 + 3^3 - 4^3 + \cdots + 9^3 =$
Consider the following statements \[ P:\ \text{Suman is brilliant} \] \[ Q:\ \text{Suman is rich} \] \[ R:\ \text{Suman is honest} \] The negation of the statement “Suman is brilliant and dishonest if and only if Suman is rich” can be expressed as:
10 men and 6 women are to be seated in a row so that no two women sit together. The number of ways they can be seated is
A square matrix (non-singular) satisfies $A^2 - A + 2I = 0$. Then $A^{-1}=$
If \[ A(\alpha)= \begin{pmatrix} \cos\alpha & \sin\alpha\\ -\sin\alpha & \cos\alpha \end{pmatrix} \] then $A(\alpha)\,A(\beta)=$
Universal set, \[ U = \{x \mid x^5 - 6x^4 + 11x^3 - 6x^2 = 0\} \] \[ A = \{x \mid x^2 - 5x + 6 = 0\} \] \[ B = \{x \mid x^2 - 3x + 2 = 0\} \] What is $(A \cap B)$ equal to?