List of top Mathematics Questions

The area enclosed by the curves \( y = x^3 \) and \( y = \sqrt{x} \) is:
The area of the region bounded by the curves \( x = y^2 - 2 \) and \( x = y \) is:
If the area bounded by the curves \( y = ax^2 \) and \( x = ay^2 \) (where \( a>0 \)) is 3 sq. units, then the value of \( a \) is:
The solution of the differential equation \( (x + 1)\frac{dy}{dx} - y = e^{3x}(x + 1)^2 \) is:
If \( \frac{dy}{dx} - y \log_e 2 = 2^{\sin x} (\cos x - 1) \log_e 2 \), then \( y \) is:
Let \( \mathbf{a} = \hat{i} - \hat{k}, \mathbf{b} = x\hat{i} + \hat{j} + (1 - x)\hat{k}, \mathbf{c} = y\hat{i} + x\hat{j} + (1 + x - y)\hat{k} \). Then, \( [\mathbf{a} \, \mathbf{b} \, \mathbf{c}] \) depends on:}
Let \( ABC \) be a triangle and \( \vec{a}, \vec{b}, \vec{c} \) be the position vectors of \( A, B, C \) respectively. Let \( D \) divide \( BC \) in the ratio \( 3:1 \) internally and \( E \) divide \( AD \) in the ratio \( 4:1 \) internally. Let \( BE \) meet \( AC \) in \( F \). If \( E \) divides \( BF \) in the ratio \( 3:2 \) internally then the position vector of \( F \) is:
If \( \vec{a} = 2\hat{i} + \hat{j} + 2\hat{k} \), then the value of \( |\hat{i} \times (\vec{a} \times \hat{i})| + |\hat{j} \times (\vec{a} \times \hat{j})| + |\hat{k} \times (\vec{a} \times \hat{k})|^2 \) is equal to:}
The magnitude of projection of the line joining \( (3,4,5) \) and \( (4,6,3) \) on the line joining \( (-1,2,4) \) and \( (1,0,5) \) is:
The angle between the lines whose direction cosines are given by the equations \( 3l + m + 5n = 0 \) and \( 6m - 2n + 5l = 0 \) is:
Let the acute angle bisector of the two planes \( x - 2y - 2z + 1 = 0 \) and \( 2x - 3y - 6z + 1 = 0 \) be the plane \( P \). Then which of the following points lies on \( P \)?
Let the foot of perpendicular from a point \( P(1,2,-1) \) to the straight line \( L : \frac{x}{1} = \frac{y}{0} = \frac{z}{-1} \) be \( N \). Let a line be drawn from \( P \) parallel to the plane \( x + y + 2z = 0 \) which meets \( L \) at point \( Q \). If \( \alpha \) is the acute angle between the lines \( PN \) and \( PQ \), then \( \cos \alpha \) is equal to:
The probability of getting 10 in a single throw of three fair dice is:
In a binomial distribution, the mean is 4 and variance is 3. Then, its mode is:
The probability that certain electronic component fails when first used is 0.10. If it does not fail immediately, the probability that it lasts for one year is 0.99. The probability that a new component will last for one year is
If \( \vec{a} = \hat{i} - \hat{j} + \hat{k} \), \( \vec{b} = 2\hat{i} + \hat{j} + \hat{k} \) are two vectors and \( \vec{c} \) is a unit vector lying in the plane of \( \vec{a} \) and \( \vec{b} \), and if \( \vec{c} \) is perpendicular to \( \vec{b} \), then \( \vec{c} \cdot (\hat{i} + 2\hat{k}) = \):
Evaluate: \[ \cosh^{-1} 2 \]
For two events A and B, if \(P(A) = P(A/B) = \frac{1}{4}\) and \(P(B/A) = \frac{1}{2}\), then which of the following is not true?
In \( \triangle ABC \), evaluate: \[ \frac{r_2 (r_1 + r_3)}{\sqrt{r_1 r_2 + r_2 r_3 + r_3 r_1}}. \]
If the system of equations: $$ a_1 x + b_1 y + c_1 z = 0, \quad a_2 x + b_2 y + c_2 z = 0, \quad a_3 x + b_3 y + c_3 z = 0 $$ has only the trivial solution, then the rank of the matrix:  \[\left[ \begin{array}{ccc} a_1 & b_1 & c_1 \\ a_2 & b_2 & c_2 \\ a_3 & b_3 & c_3 \end{array} \right] \] is
Evaluate \( \cosh (\log 4) \):
Given the partial fraction decomposition: \[ \frac{4x^2 + 5}{(x - 2)^4} = \frac{A}{(x - 2)} + \frac{B}{(x - 2)^2} + \frac{C}{(x - 2)^3} + \frac{D}{(x - 2)^4} \] then the value of \[ \sqrt{\frac{A}{C} + \frac{B}{C} + \frac{D}{C}} \] is:
The range of the real-valued function \( f(x) = \sin^{-1} \left( \frac{1 + x^2}{2x} \right) + \cos^{-1} \left( \frac{2x}{1 + x^2} \right) \) is:
In a triangle ABC, if \( r : R = 1 : 3 : 7 \), then \( \sin(A + C) + \sin B = \)
The set of all values of \(k\) for which the inequality \(x^2 - (3k+1)x + 4k^2 + 3k - 3>0\) is true for all real values of \(x\) is