List of top Mathematics Questions

If \(A\) and \(B\) are two skew symmetric matrices of the same order then \(AB\) is skew symmetric if and only if

If \(C_r={}^{10}C_r\), then \[ 2C_0+\frac{2^2}{2}C_1+\frac{2^3}{3}C_2+\cdots+\frac{2^{11}}{11}C_{10} \] is equal to:

The largest value of the third determinant whose elements are equal to 1 or 0 is

If \(A=(a_{ij})\) is a \(3\times 3\) diagonal matrix such that \(a_{11}=1\), \(a_{22}=2\) and \(a_{33}=3\), then \(|A|\)

If \(A\) and \(B\) are two square matrices of order \(3\) such that \(|A|=-2,\ |B|=5\), then \(|4AB|=\)

If the determinant of the matrix \[ \begin{vmatrix} 1 & 3 & 2\\ 0 & 5 & -6\\ 2 & 7 & 8 \end{vmatrix} \] is \(26\), then the determinant of the matrix \[ \begin{vmatrix} 2 & 7 & 8\\ 0 & 5 & -6\\ 1 & 3 & 2 \end{vmatrix} \] is

The lines \(px+qy+r=0\), \(qx+ry+p=0\) and \(rx+py+q=0\) are concurrent if

The common roots of the equations \(x^3+2x^2+2x+1=0\) and \(1+x^{2002}+x^{2003}=0\) are (where \(\omega\) is a complex cube root of unity)

The area of the triangle whose vertices are \((3,8)\), \((-4,2)\) and \((5,1)\) is

Let \(R\) be a relation in \(N\) defined by \(R=\{(x,y): x+2y=8\\). The range of \(R\) is}

If \(a,b\) are the roots of \(x^2+px+1=0\) and \(c,d\) are the roots of \(x^2+qx+1=0\), the value of \(E=(a-c)(b-c)(a+d)(b+d)\) is

If \(\alpha,\beta\) are the roots of \(ax^2+bx+c=0\) and \(\alpha+h,\beta+h\) are the roots of \(px^2+qx+r=0\), then \(h=\)

Two finite sets have \(m\) and \(n\) elements. Then total number of subsets of the first set is \(56\) more than that of the total number of subsets of the second. The value of \(m\) and \(n\) are

If \(aN=\{ax:x\in N\}\) and \(bN\cap cN=dN\) where \(b,c\in N\) are relatively prime then

The domain of the function \(f(x)=\sqrt{x-1+\sqrt{6-x}\) is}

Solve the following pair of linear equations by the elimination method and the substitution method : 
(i) x + y = 5 and 2x – 3y = 4
(ii) 3x + 4y = 10 and 2x – 2y = 2 
(iii) 3x – 5y – 4 = 0 and 9x = 2y + 7 
(iv)\( \frac{x}{2} + \frac{2y}{3} = -1 \) and \(x- \frac{y}{3} = 3\)

$f\left(x\right) = \frac{x}{e^{x}-1} + \frac{x}{2} + 2 \cos^{3} \frac{x}{2} $ on $R-\left\{0\right\} $ is

$D = \left\{x\in\mathbb{R}: f\left(x\right) =\sqrt{\frac{x - \left|x\right|}{x - \left[x\right]}} \text{is defined} \right\}$ and $C$ be the range of the real function $g(x) = \frac{2x}{4 + x^{2}}$. Then $D \cap C$

Which of the following is a tautology?

The angle between the curves y = x3 and y = x5 at x = 0 is

Let $x = 2$ be a root of $y = 4x^2 - 14x + q = 0$. Then $y$ is equal to

The boolean expression corresponding to the combinational circuit is

If $f \left(z\right)=\frac{1-z^{3}}{1-z} ,$ where $z=x+iy$ with $z\ne1,$ then $Re\left\{\overline{f \left(z\right)}\right\}=0$ reduces to

Let $A (6, -1), B (1, 3)$ and $C (x, 8)$ be three points such that $AB = BC$. The values of $x$ are

If $ y={{\cot }^{-1}}\left( \tan \frac{x}{2} \right), $ then $ \frac{dy}{dx} $ is equal to