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$\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+......+\frac{1}{(2n+1)(2n+3)}=\frac{n}{3(2n+3)}$

Calculate the correlation coefficient between X and Y and comment on their relationship:

$sin{163}^{\circ }cos{347}^{\circ }+sin{73}^{\circ }sin{167}^{\circ }=$

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

show that sin 19 ° + sin 41 ° + sin 83 °= sin 23 ° + Sin 37 °+ sin 79 °

The slope of the tangent to a curve $y=f\left(x\right)$ at $(x,f(x\left)\right)$ is $2x+1.$ If the curve passes through the point $(1,2)$ then the area of the region by the curve, the $x$ -axis and the line $x=1$ is

In triangle $ABC$ given $9a^2+9b^2=17c^2$
If $\frac{\cot A+\cot B}{\cot C}=\frac{m}{n}$ then the value of $(m+n)$ equals

If a skew-symmetric matrix of order $2\times 2$ is formed with zero and cube roots of unity, then the determinant of such matrices formed can be

The point on the line $\frac{x-2}{2}=\frac{y+1}{-2}=\frac{z+2}{-1}$ which is nearest to origin is

Five persons A, B, C, D& E are pulling a cart of mass 100 kg on a smooth surface and cart is moving with acceleration $3m/s^2$ in east direction. When person ‘A’ stops pulling, it moves with acceleration $1m/s^2$ in the west direction. When only person ‘B’ stops pulling, it moves with acceleration $24m/s^2$in the north direction. The magnitude of acceleration of the cart when only A & B pull the cart keeping their directions same as the old directions, is $\left(25/n\right)m/s^2,$ value of n is ___

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Set of values of $x$ in $(0,\pi )$ satisfying $1+{\log }_2\sin x+{\log }_2\sin 3x\ge 0$ is

Minimized expression for the Boolean function



$f(A,B,C,D)=\sum m(0,2,3,4,6,8,9,10,12,14)+\sum d(5,7,13,15)$

If $y=y\left(x\right)$ is the solution of differential equation $\frac{2+\sin x}{y+1}\left(\frac{dy}{dx}\right)=-\cos x,y\left(0\right)=1,$ then $y\left(\frac{\pi }{2}\right)$ equals

The value of $\sin 20°\sin 40°\sin 80°$ equals

If a, b be the roots $x^2+px-q$=0 and g,d be the roots of $x^2+px+r$=0 , q+r =1 then $\frac{(a-g)(a-d)}{(b-g)(b-d)}$ is ……

If x=a (cos 2t+2t sin 2t) and y=a (sin 2t - 2t cos 2t), then find $\frac{d^{2}y}{d{x}^2}$.

The set of real values of x for which $2^{{log}_{\sqrt{2}}(x-1)}>x+5$ is

Among the given options, the function $f\left(x\right)=tanx$ is discontinuous at .

Let $f\left(x\right)=a{x}^2+bx+c$. Then, match the following.

$\begin{array}{cc}\text{a. Sum of roots of f(x) = 0}& 1.–\frac{b}{a}\\ \text{b. Product of roots of f(x) = 0}& 2.\frac{c}{a}\\ \text{c. Roots of f(x) = 0 are real and distinct}& 3.b^2–4ac=0\\ \text{d. Roots of f(x) = 0 are real and identical.}& 4.b^2–4ac>0\end{array}$

If $0<x<y$, then $\underset{n\to \infty }{lim}{(y^n+x^n)}^{1/n}=$

Three machines $E_1,E_2,E_3$ in a certain factory produced 50%, 25% and 25%, respectively, of the total daily output of electric tubes. It is known that 6% of the tubes produced on each of machines $E_1$ and $E_2$ is defective and that 5% of those produced on $E_3$ is defective. If one tube is picked up at random from a day’s production, calculate the probability that it is defective.

If A is a matrix such that $\left(\begin{array}{cc}2& 1\\ 3& 2\end{array}\right)A\left(11\right)=\left(\begin{array}{cc}1& 1\\ 0& 0\end{array}\right)$ then A=

If $y_1\left(x\right)$ is a solution of the differential equation $\frac{dy}{dx}-f\left(x\right)y=0$, then a solution of the differential equation $\frac{dy}{dx}+f\left(x\right)y=r\left(x\right)$