List of top Mathematics Questions

In how many ways can a committee of 5 be formed out of 6 men and 4 women containing at least one woman?
If \(T_0,T_1,T_2,\ldots,T_n\) represent the terms in the expansion of \((x+a)^n\), then \((T_0-T_2+T_4-\cdots)^2+(T_1-T_3+T_5-\cdots)^2=\)
The complex number \(z=z+iy\) which satisfies the equation \[ \left|\frac{z-3i}{z+3i}\right|=1 \] lies on:
The solution of \(\cos(2x)-1(3+2\cos x)=0\) in the interval \(0\le x\le2\pi\) is:
\(2^{3n}-7n-1\) is divisible by:
The greatest positive integer which divides \(n(n+1)(n+2)(n+3)\) for all \(n\in\mathbb{N}\), is:
\(\cos^2\!\left(\frac{\pi}{6}+\theta\right)-\sin^2\!\left(\frac{\pi}{6}-\theta\right)=\)
If \(z=x+iy,\; z^{1/3}=a-ib\), then \(\dfrac{x}{a}-\dfrac{y}{b}=k(a^2-b^2)\), where \(k\) is equal to:
\(i^{57}+\dfrac{1}{i^{25}}\), when simplified has the value:
The domain of the function \[ f(x)=\log_2\!\left(-\log_{\sqrt{2}}\!\left(1+\frac{1}{x^4}\right)-1\right) \] is:
The set \((A\setminus B)\cup(B\setminus A)\) is equal to:
If \[ \Delta_r = \begin{vmatrix} 2r - 1 & mC_r & 1 \\ m^2 - 1 & 2^m & m + 1 \\ \sin^2(m^2) & \sin^2(m) & \sin^2(m + 1) \end{vmatrix}, \] then the value of \[ \sum_{r=0}^{m} \Delta_r \text{ is:} \]
If \[ \Delta(x) = \begin{vmatrix} 1 & \cos{x} & 1 - \cos{x} \\ 1 + \sin{x} & \cos{x} & 1 + \sin{x} - \cos{x} \\ \sin{x} & \sin{x} & 1 \end{vmatrix}, \] then \[ \int_0^{\frac{\pi}{4}} \Delta(x) \, dx \text{ is equal to:} \]
Let \( f'(x) \) be differentiable for all \( x \). If \( f(1) = -2 \) and \[ f'(x) \geq 2 \quad \forall x \in [1, 6], \] then:
If the points \( (1, 2, 3) \) and \( (2, -1, 0) \) lie on the opposite sides of the plane \( 2x + 3y - 2z = k \), then \( k \) is:
The area in the first quadrant between \( x^2 + y^2 = 4 \) and \( y = \sin x \) is?
The area bounded by \( y = x \) and \( lines |x| = 1 \) is?
If there is an error of \( k% \) in measuring the edge of a cube, then the percent error in estimating its volume is:
If \( (m,n) \) is an integer solution of \( \int_1^\infty \left( 1 + y^2 \right) dy \), then the expression for \( (m, n) \) in terms of \( (m+1, n+1) \) is?
If \[ A = \begin{bmatrix} 3 & 4 \\ 5 & 7 \end{bmatrix}, \] then \( A \cdot \text{(adj A)} \) is equal to:
If the system of equations \[ x + ky - z = 0, \quad 3x - ky - z = 0, \quad x - 3y + z = 0, \] has a non-zero solution, then \( k \) is equal to:
If a plane meets the coordinate axes at \( A, B, C \) such that the centroid of the triangle is \( (1, 2, 4) \), then the equation of the plane is?
The volume of the tetrahedron included between the plane \( 3x + 4y - 5z = 60 \) and the coordinate planes is?
The equation of the chord of the hyperbola \( 25x^2 - 16y^2 = 400 \), which is bisected at the point \( (6, 2) \), is?
\( \int_0^\infty \left( \sin x + \left| \sin x \right| \right) dx \) is equal to?