List of top Mathematics Questions

A differentiable function \( f(x) \) has a relative minimum at \( x = 0 \), then the function \( y = f(x) + ax + b \) has a relative minimum at \( x = 0 \) for
The sum \[ \sum_{k=0}^5 \left( 5C_k \right)^2 \] is equal to
Three points are chosen randomly and independently on a circle. What is the probability that all three pairwise distances between the points are less than the radius of the circle?

Choose the most appropriate options. 
If the SD of a set of observations is 8 and each observation is divided by -2, then the SD of the new set of observation will be:

If \( |a| < 1 \) and \( |b| < 1 \), then the sum of the series $$ a(a + b) + a^2(a^2 + b^2) + a^3(a^3 + b^3) + \cdots $$ 
The equation of a straight line passing through the point of intersection of \( x - y + 1 = 0 \) and \( 3x + y - 5 = 0 \) and perpendicular to one of them, is:
The mid-point of the chord $2x + y - 4 = 0$ of the parabola $y^2 = 4x$ is
Choose the most appropriate option. \[ \lim_{x \to 1} \sin(x - 1) \cdot \tan\left( \frac{\pi}{x} \right) \]
The integral \[ \int_0^{\frac{\pi}{2}} \frac{\sqrt{\sin x + \cos x}}{\sin x + \cos x} \, dx \] is equal to
The area bounded by the curves \( y = \cos x \) and \( y = \sin x \) between the ordinates \( x = 0 \) and \( x = \frac{3\pi}{2} \) is
Choose the most appropriate option.

\[ \lim_{x \to 0} \frac{\ln \cos 2x}{\sin 2x} \]

The function \( f:[0,3] \to [1,29] \) defined by \[ f(x) = 2x^3 - 15x^2 + 36x + 1 \] is
The value of \[ \int_0^{\frac{\pi}{2}} \sin^7 \theta \cos^4 \theta \, d\theta \] is

Choose the most appropriate options. 
Let \( f(x) = ax^3 + 5x^2 - bx + 1 \). If when divided by \( x - 1 \) it leaves a remainder of 5, and \( f(x) \) is divisible by \( 3x - 1 \), then

The number of integral values of \( \lambda \) for which the equation \[ x^2 + y^2 - 2\lambda x + 2\lambda y + 14 = 0 \] represents a circle whose radius cannot exceed 6 is:

If $x^{2}-ax-21=0$ and $x^{2}-3ax+35=0$ with $a>0$ have a common root, then $a$ equals:

If $a,b,c$ are distinct positive real numbers and $a^2+b^2+c^2=1$, then $ab+bc+ca$ is

On dividing $x^{3} - 3x^{2} + x + 2$ by a polynomial $g(x)$, the quotient and remainder were $x - 2$ and $-2x + 4$ respectively. Find $g(x)$.
 

If $\, {{^n C}_{12}}$ =$\, {{^n C}_8}$ then $n$ is equal to
The solution of the differential equation log x $\frac{d y}{d x}+\frac{y}{x} =$ sin 2x is
If $z=\frac{7-i}{3-4i} \, then\, z^{14}=$
The value of x obtained from the equation $\begin{vmatrix}x+\alpha&\beta&\gamma\\ \gamma&x+\beta&\alpha\\ \alpha&\beta&x+\gamma\end{vmatrix}=0$ will be
Let $l_n = \int \tan^{n} x \, dx , (n > 1) . l_4 + l_6 = a \, \, \tan^5 \, x + bx^5 + C$, where $C$ is a constant of integration, then the ordered pair $(a, b)$ is equal to :
The integral $\int\limits^{\frac{3\, \pi}{4}}_{\frac{\pi}{4}} \frac{dx}{ 1 + \cos \, x}$ is equal to :
If \[ y(x) = \int_{\sqrt{x}}^x e^t \, dt, \quad x>0 \] then \( y'(1) = \) .............