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If $8\sin \theta \cos \theta \cos 2\theta \cos 4\theta =\sin x$, then $x=$

The equation of the plane passing through the point (1,1,1) and perpendicular to the planes 2x+y-2z=5 and 3x-6y-2z=7 is

The number of terms in the expansion of $(a+b+c{)}^{20}$ is

Least positive integral value of x satisfying

$(e^x-2)(sinx-cosx)(x-lo{g}_{e}2)(cosx-\frac{1}{\sqrt{2}})<0$ is

Prove that:

$3(sinx-cosx{)}^4+6(sinx+cosx{)}^2+4(si{n}^{6}x+co{s}^{6}x)=13$

If $y=ta{n}^{-1}\left(\frac{3x-x^3}{1-3x^2}\right),-\frac{1}{\sqrt{3}}<x<\frac{1}{\sqrt{3}},then\frac{dy}{dx}=$

If x = a cos A - b sin A and y = b cos A + a sin A, prove that x² + y² = a² + b² .

If $\int (e^{2x}+2e^x-e^{-x}-1)e^{(e^x+e^{-x})}dx=g\left(x\right)e^{(e^x+e^{-x})}+c$, where $c$ is a constant of integration, then $g\left(0\right)$ is equal to :

Let a vertical tower $AB$ have its end $A$ on the level ground. Let $C$ be the mid-point of $AB$ and $P$ be a point on the ground such that $AP=2AB$. If $\angle BPC=\beta$ , then $\tan \beta$ is equal to:

If $\arg \left(z\right)<0,$ then $\arg \left(\frac{z-\overline{z}}{2}\right)$ is equal to

If $f:R\to R$ is a continuous function such that $f(x+y)=f\left(x\right)+f\left(y\right)\forall x,y\in R$ and, $f\left(1\right)=2,$ then $f\left(200\right)$ is

Which of the following is(are) equal to $\underset{0}{\overset{3}{\int }}{x}^{2}dx$

The sum of $n$ terms of the series $2\cdot 5+5\cdot 8+8\cdot 11+\dots$ is

State with reason whether given function has inverse:
(i) g:{5,6,7,8} $\to$ {1,2,3,4} with g={(5,4),(6,3),(7,4),(8,2)}

Find the value of x if ${|x+1|}^2$ - 25 = 0

A curve passes thorugh the point $(x=1,y=0)$ and satisfies the differential equation $\frac{dy}{dx}=\frac{x^2+y^2}{2y}+\frac{y}{x}$

The equation that decribes the curve is

Which of the given values of x and y make the following pairs of matrices equal $\left[\begin{array}{cc}3x+7& 5\\ y+1& 2-3x\end{array}\right],\left[\begin{array}{cc}0& y-2\\ 8& 4\end{array}\right]?$

$\left(a\right)x=\frac{-1}{3},y=7$
(b) Not possible to find
$\left(c\right)y=7,x=\frac{-2}{3}\left(d\right)x=\frac{-1}{3},y=\frac{-2}{3}$

Given two complex number $z_1=5+\left(5\sqrt{3}\right)i$ and $z_2=\frac{2}{\sqrt{3}}+2i$, the argument of $\frac{z_1}{z_2}$ in degree is

Prove that
the product of the lengths of the perpendiculars drawn from the
points

Solve the given inequality for real x: 2(2x + 3) – 10 < 6 (x – 2)

If the number of ways of selecting $3$ numbers out of $1,2,3,\dots ,2n+1$ such that they form an increasing arithmetic progression is $441,$ then the sum of the divisors of $n$ is equal to

If p is a real number and if the middle term in the expansion of ${(\frac{p}{2}+2)}^8$ is 1120, find p.

Given two sets $A=\{a,b,c,d\},B=\{b,c,d,e\}$, then $n\left[\right(A\times B)\cap (B\times A\left)\right]$ is

If A={$x:xϵM$, x is a factor of 6}$=\{1,2,3,6\}$
and B={$x:xϵN$, x is a factor of 8} = $\{1,2,4,8\}$. Then find:

$\left(i\right)A\cup B$

$\left(ii\right)A\cap B$

$\left(iii\right)A-B$

$\left(iv\right)B-A$

The scalar product of the vector $\hat{i}+\hat{j}+\hat{k}$ with a unit vector along the sum of vectors $2\hat{i}+4\hat{j}-5\hat{k}and\lambda \hat{i}+2\hat{j}+3\hat{k}$ is equal to one. Find the value of $\lambda$.

1. 0.375

The solution set of the inequality ${\log }_{10}(x^2-16)\le {\log }_{10}(4x-11)$ is