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List of top Mathematics Questions

In the given figure, $ PQ $ and $ PR $ are tangents to the circle such that $ PQ = 7 \, \text{cm} $ and $ \angle RPQ = 60^\circ $.

The length of chord QR is:

From the word ARRANGEMENT, how many distinct 9-letter words can be formed?

Prove that $\int_{\pi/6}^{\pi/3} \frac{dx}{1+\sqrt{\tan x}} = \frac{\pi}{12}$.

If $ A = \begin{bmatrix} 0 & -\tan{\frac{\alpha}{2}} \\[4pt] \tan{\frac{\alpha}{2}} & 0 \end{bmatrix} $, then prove that \[ (I + A) = (I - A)\begin{bmatrix} \cos{\alpha} & -\sin{\alpha} \\[4pt] \sin{\alpha} & \cos{\alpha} \end{bmatrix}. \]

Solve the system of equations by matrix method:
$ 3x - 2y + 3z = 8 $
$ 2x + y - z = 1 $
$ 4x - 3y + 2z = 4 $

If $LCM(35, 63) = 315$, the $HCF(35, 63)$ will be:

Find the inverse of the matrix $ A = \begin{bmatrix} 2 & 0 & -1 \\ 5 & 1 & 0 \\ 0 & 1 & 3 \end{bmatrix} $.

Let $ f, g : \mathbb{R} \to \mathbb{R} $ be two functions defined by \[ f(x) = \begin{cases} x |x| \sin \frac{1}{x} & \text{if } x \neq 0 \\ 0 & \text{if } x = 0 \end{cases} \] and \[ g(x) = \begin{cases} x^2 \sin \frac{1}{x} + x \cos \frac{1}{x} & \text{if } x \neq 0 \\ 0 & \text{if } x = 0 \end{cases} \] Then, which one of the following is TRUE?

Obtain the differential equation of the family of curves $y = \frac{2ce^{2x}}{1+ce^{2x}}$.

Solve: $(\tan^{-1}y - x)dy = (1+y^2)dx$.

Suppose $ t_1, t_2, t_3, \dots, t_{55} $ are in AP such that $ \sum_{l=0}^{18} t_{3l+1} = 1197 $ and $ t_7 + 3t_{22} = 174 $. If $ \sum_{l=1}^{9} t_l^2 = 947b $, then the value of $ b $ is

If $A$ is an identity matrix of order $n$, then $A (\text{Adj } A)$ is a/an:

$\triangle$ABC $\sim$ $\triangle$PQR. In $\triangle$ABC, AB = 3.6 cm, BC = 4 cm and AC = 4.2 cm. The corresponding sides of $\triangle$ABC and $\triangle$PQR are in the ratio 2 : 3, construct $\triangle$ABC and $\triangle$PQR.

How many 4-digit numbers can be formed using digits 1 to 6 if the digit 4 is never there in the number and the repetition of digits is not allowed?

For all $ n \in \mathbb{N} $, if $ 1^3 + 2^3 + 3^3 + \cdots + n^3>x $, then a value of $ x $ among the following is:

The maximum value of $Z = 3x + 4y$ subject to the constraints $x + y \leq 1$, $x \geq 0$, $y \geq 0$ is:

Find a particular solution of the differential equation $ (x - y) (dx + dy) = dx - dy $ when $ y = -1 $ if $ x = 0 $.

If $ R_1 $ and $ R_2 $ be two equivalence relations on a set A, then prove that $ R_1 \cap R_2 $ be also an equivalence relation.

If P(A) = 0.12, P(B) = 0.15 and P(B/A) = 0.18, then find the value of P(A $ \cap $ B).

Prove that $\displaystyle \frac{\sin A-\cos A+1}{\sin A+\cos A-1}=\frac{1}{\sec A-\tan A}$.

A relation R is defined in the set N as follows:
R = (x, y) : x = y - 3, y > 3
Then, which of the following is correct?

If $\begin{vmatrix} 2x & 3 \\ x & -8 \\ \end{vmatrix} = 0$, then the value of $x$ is:

If radius of cone is 5 cm and its perpendicular height is 12 cm, then the slant height is ...................... .

In the following figure DE$||$BC, then: If DE = 4 cm, BC = 8 cm, A($\triangle$ADE) = 25 cm$^2$, find A($\triangle$ABC).

If $ A = \begin{pmatrix} 2 & x + 9 \\ 1 & 2x \end{pmatrix} $ is invertible, then $ x \neq $: