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List of top Mathematics Questions

For the binary operation defined on $ \mathbb{R} - \{1\} $ such that: \[ a b = \frac{a}{b + 1} \] which of the following is true?

The locus of points(x,y) in the plane satisfying sin²x + sin²y =1 consists of

If $ i = \sqrt{-1} $ then $\text{Arg}\left[ \frac{(1+i)^{2025}}{1+i^{2022}} \right]=$

The surface area of the sphere x² + y² + z² = 9 lying inside the cylinder x² + y² = 3y is

$\text{The value of } cosec20°tan60°-sec20° \text{is }$

The area of the region in the first quadrant which is above the parabola $y = x^2$ and enclosed by the circle $x^2 +y^2 = 2 $ and the y-axis is

The area of the region in the first quadrant enclosed by the curves$ y=√x,y=-x+6 $and the x-axis is

Which of the following statements are true?

For $i=1,2,3,4$, suppose the points$(\cosθi,\secθi)$ lie on the boundary of a circle,where $θi∈[0,\frac{π}{6})$ are distinct. Then $\cosθ_1\ \cosθ_2\ \cosθ_3\ \cosθ_4$ equals

Let A be a set containing n elements, A subset P of A is chosen and set A is reconstructed by replacing the elements of P. A subset Q of A is chosen again. The number of ways of choosing P and Q such that Q contains just one element more than P is

Let α,β be the roots of the equation, ax²+bx+c=0.a,b,c are real and s_n=αⁿ+βⁿ and $\begin{vmatrix}3 &1+s_1 &1+s_2\\1+s_1&1+s_2 &1+s_3\\1+s_2&1+s_3 &1+s_4\end{vmatrix}=\frac{k(a+b+c)^2}{a^4}$ then k=

The mean and variance of a random variable $ X $ having binomial distribution are 4 and 2, respectively. Find $ P(X = 1) $.

For any $n≥0$ the value of $\sum_{r=0}^n \dfrac{(4r+3).(nC_r)^2}{(2n+3)}$ is

If the system of equations
x + y + az = b
2x + 5y + 2z = 6
x + 2y + 3z = 3
Has infinitely many solutions, then 2a + 3b is equal to

The value of $\int_{0}^{\frac{1}{2}}\frac{dx}{\sqrt{1-x^{2n}}}$ is (n∈N)

Let $ X = \left\{ \begin{bmatrix} a & b \\ c & d \end{bmatrix} \middle| a, b, c, d \in \mathbb{R} \right\} $. If $ f: X \to \mathbb{R} $ is defined by $ f(A) = \det(A) $ for all $ A \in X $, then $ f $ is

For a real number t ,the equation $(1+t)x^2 + (t-1)y^2 + t^2 - 1 = 0$ represents a hyperbola provided

The set of points of the form(t^2+t+1,t^2-t+1),where t is a real number, represents a/an

If the sum of 12th and 22nd terms of an AP is 100, then the sum of the first 33 terms of an AP is

The price of the fifteen shares in rupees are as follows:
46, 25, 11, 73, 73, 59, 28, 25, 73, 30, 25, 8, 25, 80, 25.
What is the Mode of the price?

In a trapezium ABCD with $AB || DC$ and diagonals intersect each other at the point 'O'. If $AB=2CD$, then the ratio of areas of triangles COD and AOB is

If $\sec \theta = \frac{2}{\sqrt{3}}$,then $cosθ=$

The angle of elevation of top of the cliff from a point 300 m from its foot is 600. Then the height of the cliff is

What is the median of 47, 52, 57, 62, 67, 72, 77, 78 ?

Empirical relation between Mean, Median and Mode is