List of top Mathematics Questions

One card is drawn from a well-shuffled pack of 52 cards, find the probability of getting:
(i) A king of red colour
(ii) A face card

Prove that \[ \sqrt{\frac{1-\cos\theta}{1+\cos\theta}} = \csc\theta - \cot\theta \]

The zeroes of quadratic polynomial $6x^2 - 7x - 3$ will be:

The distance between the points $(2,3)$ and $(4,1)$ will be:

A solid is made by joining corresponding faces of two cubes each of side 10 cm. The surface area of the resulting cuboid will be:

The angle of a sector of a circle with radius of 6 cm is $60^\circ$. The area of the sector will be:

The $LCM$ of the numbers 12, 15 and 21 will be:

The value of $\cos 60^\circ$ is:

Which of the following cannot be the probability of any event?

Solve: \(\frac{dy}{dx} = \frac{x+y+1}{2x+2y+3}\).

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

If \( I = \int_{0}^{\pi} \frac{x \, dx}{a^2 \cos^2 x + b^2 \sin^2 x} \), find the value of I.

For the two vectors \( \vec{a} \) and \( \vec{b} \), prove that \( |\vec{a} + \vec{b}| \leq |\vec{a}| + |\vec{b}| \) when \( \vec{a} \neq \vec{0} \) and \( \vec{b} \neq \vec{0} \).

If x, y, z are three independent events, then prove that \(P(X \cap Y \cap Z) = P(X) \cdot P\left(\frac{Y}{X}\right) \cdot P\left(\frac{Z}{X \cap Y}\right)\).

Solve the following system of equations by matrix method :
2x + 3y + 3z = 5
x - 2y + z = -4
3x - y - 2z = 3

Find the shortest distance between the lines \(\vec{r} = \hat{i} + \hat{j} + \lambda(2\hat{i} - \hat{j} + \hat{k})\) and \(\vec{r} = 2\hat{i} + \hat{j} - \hat{k} + \mu(3\hat{i} - 5\hat{j} + 2\hat{k})\).

If \( I = \int_{\pi/6}^{\pi/3} \frac{dx}{1 + \sqrt{\tan x}} \), then prove that \( I = \frac{\pi}{12} \).

A car is started to move from a point P at time t = 0 and is stopped at the point Q. The distance x metre covered by the car in t second is given by \(x = t^2\left(3-\frac{t}{2}\right)\). Find the time required by the car to reach at the point Q and also find the distance between P and Q.

Find the area of a triangle whose vertices are A(2, 2, 2), B(2, 1, 3) and C(3, 2, 1).

Let function \( f:N \to Y \) is defined as \( f(x)=4x+3 \) where \( Y=\{y \in N : y=4x+3 \text{ for } x \in N\} \). Prove that f is invertible, also find the inverse of the function f.

Let A and B are independent events and P(A)=0.3 and P(B)=0.4 ; then find P(B/A).

Find the minimum value of the objective function \( Z = -50x + 20y \) by graphical method under the following constraints :
\( 2x - y \geq -5 \)
\( 3x + y \geq 3 \)
\( 2x - 3y \leq 12 \)
\( x \geq 0, y \geq 0 \)

Without cover a box is formed by 6 m x 16 m rectangular steel sheet on cutting the squares of length x m from its each corner. Then find the maximum volume of the box.