List of top Mathematics Questions

$\lim_{x \to 0} \left( \frac{1}{x} \ln \left( \frac{\sqrt{1 + x}}{\sqrt{1 - x}} \right) \right)$ is
$\lim_{x \to \infty} \left[ \frac{x^2 + 1}{x + 1} - ax - b \right], \, (a, b \in \mathbb{R}) = 0$. Then
The value of $\int_0^{\pi/2} \frac{(\cos x)\sin x}{(\cos x)\sin x + (\sin x)\cos x} \, dx$ is
Let $f$ be a non-negative function defined in $[0, \pi/2]$, $f'$ exists and is continuous for all $x$, and $\int_0^x \sqrt{1 - (f'(t))^2} dt = \int_0^x f(t) dt$ and $f(0) = 0$. Then
If $I$ is the greatest of $I_1 = \int_0^1 e^{-x} \cos^2 x \, dx$, $I_2 = \int_0^1 e^{-x^2} \cos^2 x \, dx$, $I_3 = \int_0^1 e^{-x^2} \, dx$, $I_4 = \int_0^1 e^{-\frac{x^2}{2}} \, dx$, then
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 \( \dfrac{3}{__} \).
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 ____.
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
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 ______.
Evaluate: \[ \int_{0}^{\pi} \frac{x\sin x}{1+\cos^2 x}\,dx \]
If \[ \int \frac{1}{(x+100)\sqrt{x+99}}\,dx = f(x)+c \] then $f(x)=$
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:
The minimum distance of a point on the curve $y=x^2-4$ from the origin is
Evaluate: \[ \int \frac{dx}{\cos x+\sqrt{3}\sin x} \]
$1^3 - 2^3 + 3^3 - 4^3 + \cdots + 9^3 =$
A square matrix (non-singular) satisfies $A^2 - A + 2I = 0$. Then $A^{-1}=$
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
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: