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Integrating factor of differential equation $\cos x\frac{dy}{dx}+y\sin x=1$ is

Find the eccentricity of a hyperbola whose latus rectum is half of its transverse axis.

The set of values of $m$ for which $f\left(x\right)=x^2-(m-3)x+m$ intersects the positive direction of $x-$axis atleast once, is

The Boolean expression $(p\wedge q)\Rightarrow \left(\right(r\wedge q)\wedge p)$ is equivalent to

The value of $\cos {12}^{\circ }\cos {24}^{\circ }\cos {36}^{\circ }\cos {48}^{\circ }\cos {60}^{\circ }\cos {72}^{\circ }\cos {84}^{\circ }$ is

(a) If A = {1, 3, 4, 8, 9, 12}, B = {1, 4, 9} and C = {2, 4, 8, 10}

Find (i) A ∪ (B ∩ C) (ii) A ∩ (B ∪ C) (iii) (A ∪ B) ∩ (A ∪ C) (iv) (A ∩ B) ∪ (A ∩ C)

(b) If A = (2, 4, 6, 8, 10}, B = {1, 2, 3, 4, 5, 6} and C = (1, 3, 5, 7, 9, 11, 13}

Verify (i) A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C) (ii) A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)

(iii) (A ∩ B) ∪ C = (A ∪ C) ∩ (B ∪ C) (iv) (A ∪ B) ∩ C = (A ∩ C) ∪ (B ∩ C)

(c) If X = {x : x is a prime number less than 12}

Y = {x : x is an even number less than 12}

Z = {x : x is an odd number less than 12}

Show that (i) union of sets of distributive over intersection of sets.

(ii) intersection of sets is distributive over union of sets.

Find the multiplicative inverse of the complex number 4 – 3i

If p be the length of the perpendicular from the origin on the line $\frac{x}{a}+\frac{y}{b}=1,$ then

The period of the function $f\left(x\right)=3\tan (\frac{x}{3}+\frac{\pi }{2})=$

If $\int e^{ax}cos\left(bx\right)dx=\frac{e^{ax}}{K}(acosbx+bsinbx)+C$, then the K here would be equal to -

The coefficient of $t^4$ in the expansion of ${\left(\frac{1-t^6}{1-t}\right)}^3$ is :

The area enclosed by the curve $y=\sin x+\cos x$ and $y=|\cos x-\sin x|$ over the interval $[0,\frac{\pi }{2}]$ is

${\sum }_{n=1}^{\infty }\frac{\tan \left(\frac{2n-1}{4}\right)\pi }{2^{n+1}}=$

Tap on the array which gives 20 as the answer.

Solve the given inequality for real x:

The minimized expression for the given boolean function F is

$F(w,x,y,z)=\Pi (0,1,4,5,8,9,11)+\sum d(2,10)$

The equation of sphere passing through points $(1,0,0),(0,1,0)$ and $(0,0,1)$ and having minimum radius, is

If the ratio of the roots of the equation $x^2-px+q=0,$ is $a:b,$ then the value of $p^{2}ab=$

If $(p+q{)}^{\text{th}}$ term and $(p-q{)}^{\text{th}}$ term of a G.P. be $m$ and $n,$ then the $p^{\text{th}}$ term will be ___.

The sum of real roots of the equation $\left|\begin{array}{ccc}x& -6& -1\\ 2& -3x& x-3\\ -3& 2x& x+2\end{array}\right|=0,$ is equal to :

A hyperbola having the transverse axis of length $2\sin \theta$ unit, is confocal with the ellipse $3x^2+4y^2=12$, then its equation is

1. 8

Cofunction of cot20 is

Plots of $log\left(\frac{x}{m}\right)$ vs $logC$ showing a straight line parallel to $X$-axis reveals that:

How many numbers lying between 10 and 1000 can be formed from the digits 1, 2, 3, 4, 5, 6, 7, 8, 9 (repetition is allowed)

In $\Delta ABC,\frac{b-c}{r_1}+\frac{c-a}{r_2}+\frac{a-b}{r_3}=$