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List of top Mathematics Questions

Angles of elevation of the top of a tower from three points (collinear) A, B and C on a road leading to the foot of the tower are 30$^{\circ}$, 45$^{\circ}$ and 60$^{\circ}$ respectively. The ratio of AB and BC is

Domain of $cos^{-1} [x]$, where $[. ]$ denotes a greatest integer function

The product of all positive real values of $x$ satisfying the equation $x^{\left(16\left(\log _5 x\right)^3-68 \log _5 x\right)}=5^{-16}$ is _____.

If n arithmetic means are inserted between a and 100 such that the ratio of the first mean to the last mean is 1 : 7 and a + n = 33, then the value of n is:

Let
A = $\begin{bmatrix} 1 \\ 1 \\ 1 \\ \end{bmatrix}$ and B = $\begin{bmatrix} 9^2 & -10^2 & 11^2 \\ 12^2 & 13^2 & 14^2 \\ -15^2 & 16^2 & 17^2 \\ \end{bmatrix}$
then the value of A'BA is

The equations of the sides AB, BC and CA of a triangle ABC are 2x + y = 0, x + py = 39 and x – y = 3, respectively and P(2, 3) is its circumcentre. Then which of the following is NOT true?

In the given figure, the diameter of the circle is 3 cm. AB and MN are two diameters such that MN is perpendicular to AB. In addition, CG is perpendicular to AB such that $ AE : EB = 1 : 2 $, and DF is perpendicular to MN such that $ NL : LM = 1 : 2 $. The length of DH in cm is:

The degree measure of $\frac{\pi}{32}$ is equal to

Let the coefficients of the middle terms in the expansion of$\begin{array}{l} \left(\dfrac{1}{\sqrt 6}+ \beta x\right)^4, \left(1 – 3\beta x\right)^2 \text{and}\left(1 – \dfrac{\beta}{2}x\right )^6, \beta > 0,\end{array}$respectively form the first three terms of an A.P. If d is the common difference of this A.P., then $\begin{array}{l} 50-\frac{2d}{\beta^2} \end{array}$is equal to _______.

Let $PQRS$ be a quadrilateral in a plane, where $QR =1, \angle PQR =\angle QRS =70^{\circ}, \angle PQS =15^{\circ}$ and $\angle PRS =40^{\circ}$. If $\angle RPS =\theta^{\circ}, PQ =\alpha$ and $PS =\beta$, then the interval(s) that contain(s) the value of $4 \alpha \beta \sin \theta^{\circ}$ is/are

If a quadratic equation $2x^2 + kx+3=0$ have two equal roots then $k=$

Let ⊙ be a binary operation on Q - {0} defined by a⊙b=$\frac{a}{b}$. Then 1⊙(2⊙(3⊙4)) is equal to

Let P and Q be any points on the curves (x – 1)² + (y + 1)² = 1 and y = x², respectively. The distance between P and Q is minimum for some value of the abscissa of P in the interval

Let the relation R is defined in N by $a \mathbb{R} b$, if $3a+2b = 27$ , then R is

Which of the following is not an irrational number?

The number of matrices
$A=\begin{pmatrix} a & b \\ c & d \\ \end{pmatrix}$, where a,b,c,d ∈−1,0,1,2,3,…..,10
such that A = A^-1, is ______.

If the sum of solutions of the system of equations 2sin²θ – cos2θ = 0 and 2cos²θ + 3sinθ = 0 in the interval [0, 2π] is kπ, then k is equal to _______.

The sum of all the solutions of the equation $ \cos \theta \cos \left( \frac{\pi}{3} + \theta \right) \cos \left( \frac{\pi}{3} - \theta \right) = \frac{1}{4} $, for $ \theta \in [0, 6\pi] $ is:

$\int\limits_{0}^1\frac{xe^x}{(2+x)^3}\ dx$ is equal to

Let the abscissae of the two points P and Q on a circle be the roots of x² – 4x – 6 = 0 and the ordinates of P and Q be the roots of y² + 2y – 7 = 0. If PQ is a diameter of the circle x² + y² + 2ax + 2by + c = 0, then the value of (a + b – c) is

Let A = {x∈Z: -1 ≤ x < 4} and let B = {x ∈ Z:0 < $\frac{x}{2}$ ≤ 3}. Then A∩B is equal to

If the standard deviation of first n natural numbers is 2, then the value of n is

The principal solutions of tan 3θ = –1 are

Let S = {1, 2, 3, 4}.Then the number of elements in the set {f : S × S → S : f is onto and f(a,b)=f(b,a) ≥ a ∀ (a, b)∈ S × S is _____.

If $M=\begin{pmatrix}\frac{5}{2} & \frac{3}{2} \\ -\frac{3}{2} & -\frac{1}{2}\end{pmatrix}$, then which of the following matrices is equal to $M^{2022}$ ?