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The degree of the differential equation satisfying $\sqrt{1-x^4}+\sqrt{1-y^4}=a(x^2-y^2)$, is

Find the number of ways in which a mixed doubles game can be organised from amongst $8$ married couples if no husband and wife play in the same team.

For the given sequence $21,16,11,6,1\dots$, which term is equal to $-54$?

Let $S\left(x\right)=\int \frac{dx}{e^x+8e^{-x}+4e^{-3x}},R\left(x\right)=\int \frac{dx}{e^{3x}+8e^x+4e^{-x}}$ and $M\left(x\right)=S\left(x\right)-2R\left(x\right).$ If $M\left(x\right)=\frac{1}{2}ta{n}^{-1}\left(f\right(x\left)\right)+c$ then f(0)=

The difference between the greatest and least values of the function

f (x) = sin(2x) – x, on $\left(-\frac{\pi }{2},\frac{\pi }{2}\right]$ is

Equation(s) of the tangents drawn from $(4,10)$ to the parabola $y^2=9x$ is/are

Let $n$ and $k$ be positive integers such that $n\ge {}^{k+1}{C}_2$. The number of integral solutions of $x_1+x_2+\cdots +x_k=n,$ $x_1\ge 1,x_2\ge 2,\cdots x_k\ge k$ is

Given f(x) = g(X) . h (x) and $f^{{}^{\prime }}\left(x\right)$=$g^{{}^{\prime }}\left(x\right)$h(x) + g(x)$h^{{}^{\prime }}\left(x\right)$ find f'(x) where f(x) = x sin x.

Cube root of 217 is

The solution set of $16-x^2\ge 0$ is

The figure given below shows a relation from $P$ to $Q.$ Find the relation, domain and range from the arrow diagram given?

The two curves $x^3-3x{y}^2+2=0and3x^{2}y-y^3-2=0$

The equation $\frac{x^2}{12-k}+\frac{y^2}{8-k}=1$ represents.

The sum of n terms of the series: 13+105+1007+10009.... is

Which among the following is\are function(s)

The centre of the circle passing through $(0,0)$ and $(1,0)$ and touching the circle $x^2+y^2=9$ can be

Let $\overrightarrow{a}=2\hat{i}+3\hat{j}-6\hat{k},\overrightarrow{b}=2\hat{i}-3\hat{j}+6\hat{k}$ and $\overrightarrow{c}=-2\hat{i}+3\hat{j}+6\hat{k}$. Let ${\overrightarrow{a}}_1$ be the projection of $\overrightarrow{a}$ on $\overrightarrow{b}$ and ${\overrightarrow{a}}_2$ be the projection of ${\overrightarrow{a}}_1$ on $\overrightarrow{c}$. Then, ${\overrightarrow{a}}_1.\overrightarrow{b}$ is equal to

If the mid-points of the sides of a triangle are $(1,1),(2,4)$ and $(3,5)$, then the area (in sq. units) of the triangle is

The range of the function $f\left(x\right)=|x-1|+|x-8|$ is

From the adjoining figure, $A\cap B$ is

Let R and S be two non-void relations on a set A. Which of the following statements is false

Find the equation of normal to the parabola $y^2=8x$ at (8, 8) using parametric form.

If both the roots of $a{x}^2+bx+c=0$ are negative and $b<0$, then which of the following statements is always true?

If the chords of the hyperbola $x^2-y^2=a^2$ touch the parabola $y^2=4ax,$ then the locus of the midpoints of the chords is the curve

$\int \frac{5}{x^4+1}dx$

The distance of the point (1, -5, 9) from the plane x - y + z = 5 measured along the line x = y = z is

The auxiliary circle of $\frac{x^2}{9}+\frac{y^2}{4}=1$ touches a parabola having axis of symmetry as $y-$axis at its vertex . If the latus rectum of parabola is equal to radius of director circle of auxiliary circle, then the equation of parabola can be

The means of five observations is 4 and their variance is 5.2. If three of these observations are 1, 2, and 6, then the other two are:

If the 2nd, 5th and 9th terms of a non-constant AP are in GP, then the common ratio of this GP is

A survey shows that 63% of the people watch news whereas 76% watch sports. If $x$% of people watch both sports and news, then

Consider the graph of the quadratic polynomial $y=a{x}^2+bx+c$ as shown below.



Which among the following is/are correct?

Let $D$ be the middle point of the side $BC$ of a triangle $ABC$. If the triangle $ADC$ is equilateral, then $a^2:b^2:c^2$ is equal to

If $A,B,C$ are acute positive angles such that $A+B+C=\pi$ and $\cot A\cot B\cot C=k$, then

Trigonometric series of the form

$\frac{\sin (A-B)}{\cos A\cdot \cos B}+\frac{\sin (B-C)}{\cos B\cdot \cos C}+\frac{\sin (C-D)}{\cos C\cdot \cos D}$

$=\tan A-\tan D$

As we know that,

$\frac{\sin (A-B)}{\cos A\cdot \cos B}=\tan A-\tan B$

Based on the above given information, find $n^{\text{th}}$ term of the series

$\frac{\sin x}{\cos 3x}+\frac{\sin 3x}{\cos 9x}+\frac{\sin 9x}{\cos 27x}+\cdots$ upto $n$ terms

If the $n\text{th}$ term of a sequence is given by $t_n=8n+3$, then the sum of first $20$ terms is

If A is a square matrix of order n such that |adj (adj A)|$=|A{|}^9$, then the value of n can be

The equation of the parabola whose vertex and focus lie on the $x-$axis at distances $a$ and $a_1$ $(0<a<a_1)$ from the origin respectively, is

The maximum value of $(\sin \theta \cos \theta {)}^{42}$ is

The domain of the function $f\left(x\right)=\frac{1}{[x{]}^2-7[x]+10}$ is

(where $[.]$ denotes the greatest integer function)