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If $9^7+7^9$ is divided by $64$, then the remainder is

$Domainofthefunctionf\left(x\right)=\sqrt{5|x|-x^2-6}is$

A differentiable function f(x) will have a local maximum at x = c if -

If $x^2+4y^2-8x+12=0$ is satisfied by real values of x and y then 'y' $ϵ$

Let $x+4y=4$ is any straight line. Sum of abscissa and sum of ordinates of the point of intersection of the line with coordinate axes is $p$ and $q$ respectively. Let $m$ be the digit at unit place of the number $(p+q{)}^{61}$ and $n$ be the number of integral terms in binomial expansion of $(\sqrt[4]{49}+\sqrt[6]{68}{)}^{500}.$ Then $n+m$ will be

If $y=\sqrt{\left(\frac{1+cos2\theta }{1-cos2\theta }\right)},\frac{dy}{dx}at\theta =\frac{3\pi }{4}$ is

If $z_1$ and $\overline{z_2}$ represent adjacent vertices of a regular polygon of n sides and if $\frac{Im\left(z_1\right)}{Re\left(z_1\right)}=\sqrt{2}-1$, Then n is equal to

Integrate the following functions.
$\int \frac{2cosx-3sinx}{6cosx+4sinx}dx$

The equation of the line perpendicular to the line x – 2y + 3 = 0 and passing through the point (1, -2) is

The slope of the normal to the curve $x=a(\theta –sin\theta ),y=a(1–cos\theta )at\theta =\frac{\pi }{2}$ is

The distance between the foci of a hyperbola is 16 and its ecentricity is $\sqrt{2},$ then equation of the hyperbola is

The equation of the ellipse with foci at $(\pm 5,0)$ and $x=\frac{36}{5}$ as one directrix, is

The radius of the sphere is expressed as (5.3±0.1) cm. Find the percentage error in the volume of the sphere

$1.2+2.3+3.4+....+n(n+1)=\frac{n(n+1)(n+2)}{3}$

Let $A=\{x:x^2-9\le 0,x\in Z\}$ and $B=\{x:|x-2|<3,x\in Z\}.$ Then the number of elements in $A\Delta B$ is

Using first principle find derivative of log ax+b

If x, y, z are positive, and x + y + z = 1, then the maximum value of xyz is

If $b,k$ are the intercepts of the focal chord of $y^2=4ax$, $a\ne b$ then $k$ is

If the point $(2,k)$ lies outside the circle's $x^2+y^2+x-2y-14=0$ and $x^2+y^2=13$ then range of $k$ is

For $a>b>c>0$, the distance between (1,1) and the point of intersection of the lines $ax+by+c=0$ and $bx+ay+c=0$ is less then $2\sqrt{2}$. Then

If $f\left(x\right)=cos\left(lo{g}_{e}x\right)$, then $f\left(\frac{1}{x}\right)f\left(\frac{1}{y}\right)-\frac{1}{2}\left\{f\right(xy)+f\left(\frac{x}{y}\right)\}$ is equal to

Let ‘F’ denote the set of all onto functions from $A=\{a_1,a_2,a_3,a_4\}$ to B = {x, y, z}. A function ‘f’ is chosen at
random from ‘F’. The probability that $f^{-1}${x} consists of exactly one element.

The value of $tan(ta{n}^{-1}\frac{1}{2}-ta{n}^{-1}\frac{1}{3})$=

Find the domain and the range of the real function, $f\left(x\right)=\frac{3}{(2-x^2)}$.

Find the intervals in which f (x) = 2 log (x - 2) - x² + 4x + 1 is increasing or decreasing

The equations x2− 4x + k = 0 and x2+ kx − 4 = 0, where k is a real number, have exactly one common root. What is the value Ofp k?

Getting difficulty in expressing a determinant as a product of two different determinants

The value of x in $(0,\pi )$ which satisfy the equation
$8^{-+|cosx|+co{s}^{2}x+|co{s}^{3}x|+\cdots to\infty }=4^3$ is

The domain of real function $f\left(x\right)=\sqrt{25-x^2}$ is

Let the length of the latus rectum of an ellipse with its major-axis along $x$-axis and centre at the origin, be $8$. If the distance between the foci of this ellipse is equal to the length of its minor axis, then which one of the following points lies on it?

For the differential equation in given question find the general solution.​​​​

$ylogydx-xdy=0$

Let $P,Q,R$ be three points on the ellipse $x^2+4y^2=4$ and $P^{\prime },Q^{\prime },R^{\prime }$ be the corresponding points on the auxiliary circle. Then Area of $△P^{\prime }{Q}^{\prime }{R}^{\prime }$ $:$ Area of $△PQR$ is

The domain of the definition of the function $\sqrt{{\log }_{10}\left(\frac{5x-x^2}{4}\right)}$ is

Write the total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants.

Solve the quadratic equation ix^{2 –} 3x ^- 2i = 0

If $\frac{5}{x-2}<5,x\ne 2$, then the interval(s) in which $x$ can be lie is/are

Show that the tangents to the curve $y=7x^3+11$ at the points where x=2 and x=-2 are parallel.

Prove that:

$cos4A=1-8co{s}^{2}A+8co{s}^{4}A$

if three persons are selected at random from n persons sitting at a round table then the probability that no two of them are adjacent to each other are

$ta{n}^{-1}\frac{x}{\sqrt{a^2-x^2}},|x|<a$

If sum of n terms of an A.P. is 3n2+5n and Tm= 164, m=?

The area of the pentagon formed by the vertices $(1,2),(4,1),(5,3),(3,7),(2,6)$ is