List of top Mathematics Questions

Evaluate the integral: \[ \int \frac{1}{x^5 \sqrt{x^5+1}} dx. \]
Evaluate the integral: \[ I = \int (\tan^7 x + \tan x) dx. \]
Evaluate the integral: \[ I = \int \frac{x+1}{\sqrt{x^2 + x + 1}} dx. \]
Evaluate the integral: \[ I = \int \frac{\csc x}{3\cos x + 4\sin x} dx. \]
By considering \( 1' = 0.0175 \), the approximate value of \( \cot 45^\circ 2' \) is:
A point moves on the curve \( y = x^3 - 3x^2 + 2x - 1 \) and its y-coordinate increases at a rate of 6 units per second. When the point is at (2,-1), the rate of change of its x-coordinate is:
Evaluate the limit: \[ \lim_{x \to \infty} \left( \frac{3x^2 - 2x + 3}{3x^2 + x - 2} \right)^{3x - 2} \]
Let \( P(a, 4, 7) \) and \( Q(3, \beta, 8) \) be two points. If the YZ-plane divides the join of the points P and Q in the ratio 2:3 and the ZX-plane divides the join of P and Q in the ratio 4:5, then the length of line segment PQ is:
If \( (a, b) \) and \( (c, d) \) are the internal and external centres of similitude of the circles \[ x^2 + y^2 + 4x - 5 = 0 \] and \[ x^2 + y^2 - 6y + 8 = 0 \] respectively, then \( (a + d)(b + c) \) is:
If the coordinate axes are rotated by \( 45^\circ \) about the origin in the counterclockwise direction, then the transformed equation of \( y^2 = 4ax \) is:
A box contains 20 percent defective bulbs. Five bulbs are randomly chosen. Find the probability that exactly 3 are defective.
A random variable \( X \) follows a Poisson distribution with mean 5. Find the probability that \( X3 \).
The probability that a person goes to college by car,\(\frac{1}{5}\) bus,\(\frac{2}{5}\) or train \(\frac{3}{5}\) is given. If he reaches college on time, find the probability he traveled by car.
If 5 letters are to be placed in 5-addressed envelopes, then the probability that at least one letter is placed in the wrongly addressed envelope is:
In \( \triangle ABC \), given: \[ a = 26, \quad b = 30, \quad \cos C = \frac{63}{65} \] Find \( c \).
In a regular hexagon \( ABCDEF \), if \( \overrightarrow{AB} = \mathbf{a} \) and \( \overrightarrow{BC} = \mathbf{b} \), then find \( \overrightarrow{FA} \).
Find the value of \( x \) satisfying: \[ 1 + \sin x + \sin^2 x + \sin^3 x + \dots = 4 + 2\sqrt{3} \] where \( 0x\pi, x \neq \frac{\pi}{2} \).
The coefficient of \( x^5 \) in the expansion of \( (3 + x + x^2)^6 \) is:
If \(1\cdot3\cdot5 + 3\cdot5\cdot7 + 5\cdot7\cdot9 + \ldots\) to \(n\) terms is \(n(n+1)f(n)\), then \(f(2) =\)
If \(A\) is a non singular matrix, then \(\text{Adj}(A^{-1}) =\)
If the homogeneous system of linear equations \(x - 2y + 3z = 0\), \(2x + 4y - 5z = 0\), \(3x + \lambda y + \mu z = 0\) has a non-trivial solution, then \(8\mu + 11\lambda =\)
If \( \alpha \) is a root of the equation \( x^2 - x + 1 = 0 \), then \(\left(\alpha + \frac{1}{\alpha}\right)^3 + \left(\alpha^2 + \frac{1}{\alpha^2}\right)^3 + \left(\alpha^3 + \frac{1}{\alpha^3}\right)^3 + \left(\alpha^4 + \frac{1}{\alpha^4}\right)^3 =\)

If \[ z = \frac{(2-i)(1+i)^3}{(1-i)^2} \] then \[ \text{Arg}(z) = ? \]

The solution set of the inequality \( \sqrt{x^2 + x - 2}>(1 - x) \) is:
If \( \alpha, \beta, \gamma \) are the roots of the equation \( 4x^3 - 3x^2 + 2x - 1 = 0 \), then \( \alpha^3 + \beta^3 + \gamma^3 = \)