Mathematics Tes...

If the progressions 3, 10, 17, ....... and 63, 65, 67, ....... are such that their n^th terms are equal, then n is equal to

Directions: The following question has four choices, out of which ONE or MORE are correct. If $\overrightarrow{a},\overrightarrow{b}$ and $\overrightarrow{c}$ are unit vectors satisfying $\overrightarrow{a}\times (\overrightarrow{b}\times \overrightarrow{c})=\frac{\overrightarrow{b}}{\sqrt{2}},$ then

The tangent to the circle $x^2+y^2=5$ at the point (1,-2) also touches the circle $x^2+y^2-8x+6y+20=0$. Then its point of contact is

The equation $x^3-3x+[a]=0,$ will have three real and distinct roots if $-$

(where [] denotes the greatest integer function)

In $\mathrm{\Delta }ABC,a,b,A$ are given and $c_1,c_2$ are two values of the third side $c$. The sum of the areas of the two triangles with sides $a,b,c_1$ and $a,b,c_2$ is

The equation of the plane through the line of intersection of planes $x+y+z+3=0$ and $2x-y+3z+1=0$ and parallel to the line $\frac{x}{1}=\frac{y}{2}=\frac{z}{3}is$

Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have at least one letter repeated is

There are 4 balls of different colours & 4 boxes of colours same as those of the balls. The number of ways in which the balls, one in each box, could be placed such that exactly no ball go to the box of its own colour is:

If $g(f(x))=|\sin x|$ and $f(g(x))=(\sin \sqrt{x}{)}^2,$ then

Directions: The following question has four choices, out of which ONE or MORE are correct. Let $f(\theta )={\cos }^2\theta +{\sin }^4\theta .$ Then, for all the values of $\theta$

Directions: The following question has four choices, out of which ONE or MORE are correct. If $f(x-y),f(x)\cdot f(y)$ and $f(x+y)$ are in $\mathrm{AP}$ for all $x,y$ and $f(0)\ne 0,$ then

A box contains 6 red marbles numbers from 1 to 6 and 4 white marbles 12 to 15. Find the probability that marble is drawn ‘at random’ is white and odd-numbered.

If ${\int }_{-1}^{-4}f(x)dx=4$ and ${\int }_2^{-4}(3-f(x))dx=7$

then the value of ${\int }_{-2}^{1}f(-x)dx$ is

$\int e^{3\log x}{(x^4+1)}^{-1}dx$ is equal to

Given vectors $\overrightarrow{x}=3\hat{i}-6\hat{j}-\hat{k},\overrightarrow{y}=\hat{i}+4\hat{j}-3\hat{k}$ and

$\overrightarrow{z}=3\hat{i}-4\hat{j}-12\hat{k}$ then the projection of $\overrightarrow{x}\times \overrightarrow{y}$ on $\overrightarrow{Z}$ is