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If $A$ is a $3\times 3$ non-singular matrix, then the value of $|5A|$ is

Evaluate $\int x\ln xdx$

(where $C$ is constant of integration)

Solve the inequality

If the last term in the binomial expansion of ${(2^{1/3}-\frac{1}{\sqrt{2}})}^n$ is ${\left(\frac{1}{3^{5/3}}\right)}^{{\log }_{3}8},$ then the $5^{\text{th}}$ term from the beginning is

If the sum of the coefficients in the expansion of ${(1-3x+10x^2)}^n$ is $a$ and if the sum of the coefficients in the expansion of ${(1+x^2)}^n$ is $b$, then

If two opposite vertices of a square are (1, 2) and (5, 8), find the coordinates of its other two vertices and the equations of its sides.

The number of solutions of $\sin 3x=\cos 2x,$ in the interval $(\frac{\pi }{2},\pi )$ is :

If $[x+[x+[x+[x+\left[x\right]]]]]=10$, then $x$ lies in

Find the equation of the tangent line to the curve y = x²
− 2x + 7 which is

(a) parallel to the line 2x − y + 9 = 0

(b) perpendicular
to the line 5y − 15x = 13.

In $\Delta ABC$, if $a,b$ and $A$ are given, then there are two triangles are formed with the third side $c_1$ and $c_2$ such that the sum of their areas is :

The point which lies in the half plane $3x-2y-2\ge 0$ is



[1 mark]

The function f(x) = [x], where [x] denotes greatest integer function is continuous at ………

Find the value of ${\sin }^n{1890}^{\circ }+{\text{cosec}}^n{1890}^{\circ }$. Where $n\in N$

The area (in sq. units) of the region bounded by the curves $y=2^x$ and $y=|x+1|,$ in the first quadrant is :

The equation of line passing through $(3,4)$ and parallel to $5x+9y+12=0$ is

Complete the table of products

$\begin{array}{cccc}\text{First Monomial}\to \text{Second Monomial}& {\text{a}}^2{\text{b}}^2& {\text{cd}}^2& -5{\text{p}}^2\\ -\text{ab}& & & \\ -\text{cd}& & -{\text{c}}^2{\text{d}}^3& \\ \text{abcd}& & & \end{array}$
[4 MARKS]

If $\overline{A}and\overline{B}$ are two vectors such that, $|\overline{A}+\overline{B}|=|\overline{A}-\overline{B}|$, the angle between $\overline{A}and\overline{B}$ is.

Count the number of triangles in the given figure.

The equation of the plane through the intersection of the planes $\overrightarrow{r}.(2\hat{i}+6\hat{j})+12=0$ and $\overrightarrow{r}.(3\hat{i}-\hat{j}+$ $4\hat{k})=0$ and at a unit distance from the origin, is

Each coefficient in the equation $a{x}^2+bx+c=0$ is determined by throwing an ordinary die. Find the probability that the equation will have equal roots.

The sum of series $4-9x+16x^2-25x^3+36x^4-49x^5+\dots +\infty$ is

If two adjacent vertices of a regular hexagon are $(1,2)$ and $(2,1),$ then equation of the circumcircle of the hexagon is

The number of ordered pairs $(x,y)$ satisfying $|x|+|y|=3$ and $\sin \left(\frac{\pi x^2}{3}\right)=1$ is less than equal to

If $f\left(x\right)$ is an even function and $a$ is a positive real number, then ${\int }_{-a}^{a}f\left(x\right)dx$ equals

If the expansion of $\frac{1}{(1-ax)(1-bx)}=a_0+a_{1}x+a_2{x}^2+\cdots +a_n{x}^n+\cdots$, then $a_n$ is (where $a\ne b,|ax|,|bx|<1$)

A set is defined as a __________________.