List of top Mathematics Questions

Solve the differential equation \( \frac{dy}{dx} = \frac{x^2 - 1}{y^2 + 1} \).
Show that \( f(x) = |x| \) is continuous for all values of x.
A function \( f: \mathbb{R} \to \mathbb{R} \) is defined by \( f(x) = 3x \) for all \( x \in \mathbb{R} \). Then function \( f \) will be:
The value of \( \int \cos^2 x \, dx \) will be:
At which point is the slope of the curve \( y^2 = 4x \) equal to the slope of the line \( y = x + 3 \)?
Solve the following system of linear equations by matrix method:
\( x + y + z = 6 \)
\( y + 3z = 11 \)
\( x + z = 2y \)
Prove that: \( \int_0^{\pi} \log(1 + \cos x) dx = -\pi \log_e 2 \)
Evaluate: \( \int_0^{\pi} \frac{x \, dx}{a^2 \cos^2 x + b^2 \sin^2 x} \)
Find the particular solution of the differential equation \( \frac{dy}{dx} + y \cot x = 2x + x^2 \cot x, (x \neq 0) \). It is given that \( y = 0 \) if \( x = \frac{\pi}{2} \).
If the vector \( 2\hat{i} + 3\hat{j} + 4\hat{k} \) is perpendicular to the vector \( 5\hat{i} - \lambda\hat{j} + 2\hat{k} \), the value of \( \lambda \) is:
Find the shortest distance between the lines:
\( \frac{x+1}{7} = \frac{y+1}{-6} = \frac{z+1}{1} \) and
\( \frac{x-3}{1} = \frac{y-5}{-2} = \frac{z-7}{1} \).
Find the equations of the tangent and normal to the curve \( x^{2/3} + y^{2/3} = 2 \) at the point (1, 1).
There are three groups of children having 3 girls and one boy, 2 girls and 2 boys, one girl and 3 boys respectively. One child is selected at random from each group. Find the probability that the three selected children have one girl and 2 boys.
Find the area of the region enclosed by the parabola \( y^2 = 4ax \) and its latus rectum.
Solve the differential equation \( ydx - (x + 2y^2) dy = 0 \).
Find the maximum value of Z = 8x + 5y under the constraints \( 5x + 3y \le 15 \), \( 2x + 5y \le 10 \) and \( x \ge 0, y \ge 0 \) by graphical method.
Find the angle between the pair of lines \( \frac{x+3}{3} = \frac{y-1}{5} = \frac{z+3}{4} \) and \( \frac{x+1}{1} = \frac{y-4}{1} = \frac{z-5}{2} \).
The volume of a cube is increasing at the rate of 9 cm\(^3\)/s. If the length of its edge is 10 cm, then its surface area is increasing with which rate?
Show that the given function \( f(x) = \cos x \) is increasing in \( (\pi, 2\pi) \).
Find the area of a parallelogram whose adjacent sides are given by vectors \( \vec{a} = 3\hat{i} + \hat{j} + 2\hat{k} \) and \( \vec{b} = \hat{i} + 2\hat{j} - 2\hat{k} \).
If P(A) = 0.3, P(B) = 0.4, then find P(A/B) if A and B are independent events.
The value of \( \tan^{-1}\sqrt{3} - \sec^{-1}(-2) \) is :
The order of the differential equation \( \frac{d^3y}{dx^3} + \frac{d^2y}{dx^2} + y \cos x = 0 \) is :
Find the order and degree of the differential equation \( \frac{d^2y}{dx^2} + \frac{dy}{dx} + y \cdot \sin x = 0 \).
If \( A = \begin{bmatrix} \cos\alpha & -\sin\alpha
\sin\alpha & \cos\alpha \end{bmatrix} \) and \( A + A' = I \), then find the value of \( \alpha \).