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The value of $x,$ which satisfy the equation $3^{{\log }_{a}x}+2\cdot x^{{\log }_{a}3}=9$ is

Equation of curve through point(1,0) which satisfies the differential equation $(1+y^2)dx-xydy=0$, is

If $\cos A=\frac{15}{17}$ then find $\sin A$.

$ta{n}^{-1}\sqrt{x}=\frac{1}{2}co{s}^{-1}\left(\frac{1-x}{1+x}\right),xϵ[0,1].$

The equation of the line perpendicular to the line $2x+3y+5=0$ and passing through $(1,1)$, is

For the function $e^{-x}$ the linear approximation around $x=2$ is

Find the equation of
the plane passing through the point (−1, 3, 2) and
perpendicular to each of the planes x + 2y + 3z
= 5 and 3x + 3y + z = 0.

Let the tangents drawn from the origin to the circle, $x^2+y^2-8x-4y+16=0$ touch it at the points $A$ and $B$. The $(AB{)}^2$ is equal to :

Let $f:R\to R$ be an invertible function. If $g\left(x\right)=2f\left(x\right)+5,$ then $g^{-1}\left(x\right)$ is

For any two sets $A\&B,A\cup B$ is represented as:

If ${}^{n+1}{C}_3={2.}^n{C}_2,$ then =

The
sum and sum of squares corresponding to length x
(in
cm) and weight y

(in
gm) of 50 plant products are given below:

Which
is more varying, the length or weight?

If $\alpha ,\beta \gamma ,ϵ(0,\frac{\pi }{2}),then\frac{sin(\alpha +\beta +\gamma )}{sin\alpha +sin\beta +sin\gamma }is$

If $\int \frac{\cos \left(4x\right)+1}{\cot x-\tan x}dx=f\left(x\right)+C,$ where $C$ is a constant of integration, then $f\left(x\right)$ is

Five cards are chosen at random from a pack of $52$ cards. Then the probability that at least one face card is chosen, is

Let a computer program generate only the digits $0$ and $1$ to form a string of binary numbers with probability of occurrence of $0$ at even places be $\frac{1}{2}$ and probability of occurrence of $0$ at the odd place be $\frac{1}{3}$. Then the probability that ${}^{\prime }{10}^{\prime }$ is followed by ${}^{\prime }{01}^{\prime }$ is equal to :

$\frac{1+sin{600}^{\circ }-cos{600}^{\circ }}{1+sin{600}^{\circ }+cos{600}^{\circ }}$ = ?

In which of the following pairs, the two species are isostructural

In any $△ABC$, the least value of $\left(\frac{si{n}^{2}A+sinA+1}{sinA}\right)$ is

The equation $y^2{e}^{xy}=9e^{-3}\cdot x^2$ defines $y$ as a differentiable function of $x.$ The value of $\frac{dy}{dx}$ for $x=-1$ and $y=3$ is

A box contains $12$ white and $12$ black balls. The balls are drawn at random from the box, one at a time with replacement. The probability that a white ball is drawn for the fourth time on the seventh draw, is

The range of the quadratic expression $y=3x^2+8x-3$ is

If for the matrix, $A=\left[\begin{array}{cc}1& -\alpha \\ \alpha & \beta \end{array}\right],A{A}^T=I_2,$ then the value of ${\alpha }^4+{\beta }^4$ is:

If a = b + c, then is it true that |a| = |b|+|c|? Justify your answer.

Find the eccentric angle of a point on the ellipse $\frac{x^2}{6}+\frac{y^2}{2}=1$ whose distance from centre is 2.

The balance of trade shows a surplus of Rs 10,000 crores and the import of merchandise is half of the export of merchandise. Find the value of exports.

If $\tan \frac{\alpha }{2},\tan \frac{\beta }{2}$ are the roots of $8x^2-26x+15=0$, then the value of $\cos (\alpha +\beta )$ is

In an acute angle triangle $ABC,$ if $\frac{\sin 3B}{\sin B}={\left(\frac{a^2-c^2}{2ac}\right)}^2,$ then $a^2,b^2,c^2$ are in

Solve
system of linear equations, using matrix method.

5x
+ 2y = 3

3x
+ 2y = 5