List of top Mathematics Questions

In a triangle $ ABC $, if angles $ A $, $ B $, and $ C $ are in A.P., then $ \frac{a + c}{b} $ is equal to:

For what values of $ \lambda $ and $ \mu $, the following system of equations has a unique solution? 
$ 2x + 3y + 5z = 9 $
$ 7x + 3y - 2z = 8 $ 
$ 2x + 3y + \lambda z = \mu $

Sum of the last 40 coefficients in the expansion of $ (1 + x)^{79} $, when expanded in ascending power of $ x $ is:
$ (666 \ldots \text{up to } n \text{ digits})^2 + (888 \ldots \text{up to } n \text{ digits}) $ is:
Out of 6 boys and 4 girls, a committee of 5 members is to be formed. In how many ways can this be done, if at least 2 girls are included?
For what value of $ n $, the curve \[ \left( \frac{x}{a} \right)^n + \left( \frac{y}{b} \right)^n = 2 \text{ touches the straight line } \frac{x}{a} + \frac{y}{b} = 2 \text{ at the point } (a, b)? \]
If $ f(x) $ and $ g(x) $ are two functions such that $ f(x) + g(x) = e^x $ and $ f(x) - g(x) = e^{-x} $, then:
The range of the function $ f(x) = 7 - x\cdot P_{x-3} $ is:

Let the function $ f(x) $ be defined as follows: $$ f(x) = \begin{cases} (1 + | \sin x |)^{\frac{a}{|\sin x|}}, & -\frac{\pi}{6}<x<0 \\b, & x = 0 \\ \frac{\tan 2x}{\tan 3x}, & 0<x<\frac{\pi}{6} \end{cases} $$ Then the values of $ a $ and $ b $ are:

The value(s) of $ c \in (1, 2) $, where the conclusion of Lagrange’s M.V.T. is satisfied for the function $ f(x) = x^2 + 3x + 2 $ in $[1,2]$, is/are:
Let $ \phi_1(x) = e^{\sin x, \phi_2(x)} = e^{\phi_1(x)}, \ldots, \phi_{n+1}(x) = e^{\phi_n(x)}, \forall n \geq 1$. Then for any fixed $ n $, the expression $ \frac{d}{dx} \left\{ \phi_n(x) \right\} $ is:
The equation of the circle of radius 3 units which touches the circles $ x^2 + y^2 - 6|x| = 0 $ is:
If the probability for A to fail in an examination is 0.2 and that for B is 0.3, then the probability that either A or B fails is:
The shortest distance between the lines \[ \frac{x + 1}{1} = \frac{y - 3}{-1} = \frac{z - 1}{-1} \quad \text{and} \quad \frac{x}{3} = \frac{y - 1}{2} = \frac{z + 1}{-1} \] is:

If l, m, n are the pth, qth and rth terms of a G.P. respectively and l, m, n > 0, then

\[ \begin{vmatrix} \log_l p & 1 \\ \log_m q & 1 \\ \log_n r & 1 \end{vmatrix} \]

The value of \[ \tan^{-1} \left( \frac{\sin 2 - 1}{\cos 2} \right) \] is:
The equation of the image of the line $ 2y - x = 1 $ obtained by the reflection on the line $ 4y - 2x = 5 $ is:
The function $ f(x) = x^3 - 3x $ is:
If $ A $ is the A.M. of the roots of the equation $ x^2 - 2ax + b = 0 $ and $ G $ is the G.M. of the roots of the equation $ x^2 - 2bx + a^2 = 0 $, $ a>0 $, then:
The area bounded by the curves $ y = \log_e x $ and $ y = (\log_e x)^2 $ is:
The mapping $ f: \mathbb{R} \to \mathbb{R} $ such that $ f(x) = |x - 1| $, $ x \in \mathbb{R} $ is:
Evaluate the integral: \[ \int_0^2 |x^2 + x - 2| \, dx \]
The differential equation of all circles of radius $ a $ is:
The period of \( 2 \sin 4x \cos 4x \) is:
The sum of all the 4-digit numbers formed by taking all the digits from 0, 3, 6, 9 without repetition is: