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what is the difference between the two ?

The prefix poly means many. So the word polynomial refers to one or more than one term in an expression. The relationship between these terms may be sums or differences. You call expression with a single term a monomial, an expression with two terms is a binomial, and expression with three terms is a trinomial. Here we are only discussing Binomial along with their exponents.
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$\\1.\int \sqrt{\left ( \frac{\sin(x-a)}{\sin(x+a)} \right )}dx\\2.\int \frac{2\sin2x-\cos x}{6-\cos^2x-4\sin x}$

@Vinod

$\\\int \sqrt{\frac{\sin \left(x-a\right)}{\sin \left(x+a\right)}}dx\\rationalize\;it\\\int \sqrt{\frac{\sin \left(x-a\right)\sin \left(x-a\right)}{\sin \left(x+a\right)\sin \left(x-a\right)}}dx\\\int \frac{\sin \left(x-a\right)}{\sqrt{\sin \:\left(x+a\right)\sin \:\left(x-a\right)}}dx\\\because \sin \left(A+B\right)\sin \left(A-B\right)=\sin ^2A-\sin ^2B\\\int \frac{\sin x\:\cos a-\sin a\:\cos x}{\sqrt{\sin ^2x-\sin ^2a}}dx\\\cos a\int \frac{\sin x\:}{\sqrt{\sin ^2x-\sin ^2a}}dx\:-\sin a\int \:\frac{\:\cos \:x}{\sqrt{\sin \:^2x-\sin \:^2a}}dx\:\:\:$

$\\\cos a\int \frac{\sin x\:}{\sqrt{\sin ^2x-\sin ^2a}}dx\:\\\cos \:a\int \frac{\sin \:x\:}{\sqrt{1-\cos ^2x-1+\cos ^2a}}dx\:\\\Rightarrow \cos \:a\int \frac{\sin \:x\:}{\sqrt{\cos \:^2a-\cos ^2x}}dx\:\\put\;\cos x=t,and\;solve\\same\;method\;apply\;for\;\sin a\int \:\frac{\:\cos \:x}{\sqrt{\sin \:^2x-\sin \:^2a}}dx\:\:\:$

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Let and   be the roots of equation

is equal to:

• Option 1)

6

• Option 2)

-6

• Option 3)

3

• Option 4)

-3

3

If in a parallelogram ABDC, the coordinates of A,B and C are respectively (1,2), (3,4) and (2,5) , then the equation of the diagonal AD is:

• Option 1)

$5x-3y+1=0$

• Option 2)

$3x-5y+1=0$

• Option 3)

$5x+3y-11=0$

• Option 4)

$3x+5y-13=0$

Mid-point formula -   - wherein If the point P(x,y) is the mid point of line joining A(x1,y1) and B(x2,y2) .     Two – point form of a straight line -   - wherein The lines passes through    and    As BD and AC are parallel ..............................(1) As AB and CD are parallel ..............................(2) Solving (1) and (2) m=4 and n=7              Option 1)Option 2)Option...

In an ellipse, with centre at the origin, if the difference of the lengths of major axis and minor axis is $10$ and one of the foci is at $\left ( 0,5\sqrt{3} \right )$, then the length of its latus rectum is :

• Option 1)

$10$

• Option 2)

$5$

• Option 3)

$8$

• Option 4)

$6$

focus is at   given difference of major axis-minor axis  Length of LR = Option 1)Option 2)Option 3)Option 4)

Let $f(x)=a^{x}(a>0)$ be written as $f(x)=f_{1}(x)+f_{2}(x)$, where $f_{1}(x)$ is an even function and $f_{2}(x)$ is an odd function. Then $f_{1}(x+y)+f_{1}(x-y)$ equals:

• Option 1)

$2f_{1}(x)f_{1}(y)$

• Option 2)

$2f_{1}(x+y)f_{1}(x-y)$

• Option 3)

$2f_{1}(x)f_{2}(y)$

• Option 4)

$2f_{1}(x+y)f_{2}(x-y)$

Now,     Option 1) Option 2) Option 3) Option 4)

If $S_{1}\; and\; S_{2}$ are respectively the sets of local minimum and local maximum points of the function,$f(x)=9x^{4}+12x^{3}-36x^{2}+25,x\: \epsilon \: \mathbb{R},$ then :

• Option 1)

$S_{1}=\left \{ -2 \right \};S_{2}=\left \{ 0,1 \right \}$

• Option 2)

$S_{1}=\left \{ -2 ,1\right \};S_{2}=\left \{ 0 \right \}$

• Option 3)

$S_{1}=\left \{ -2 ,0\right \};S_{2}=\left \{ 1 \right \}$

• Option 4)

$S_{1}=\left \{ -1\right \};S_{2}=\left \{ 0,2 \right \}$

Option 1) Option 2) Option 3)   Option 4)

A person throws two fair dice. He wins Rs. 15 for throwing a doublet

( same numbers on the two dice), wins Rs. 12 when the throw results

in the sum of 9 , and loses Rs. 6 for any other outcome on the throw.

Then the expected gain / loss (in Rs.) of the person is :

• Option 1)

$\frac{1}{2}$  gain

• Option 2)

$\frac{1}{4}$ loss

• Option 3)

$\frac{1}{2}$ loss

• Option 4)

2 gain

Option 2) 1/4 loss

The Boolean expression $\sim (p\Rightarrow (\sim q))$ is equivalent to :

• Option 1)

$p \wedge q$

• Option 2)

$q\Rightarrow \sim p$

• Option 3)

$p\vee q$

• Option 4)

$(\sim p)\Rightarrow q$

1

If the angle of intersection at a point where two circles with radii $5\: cm$ and $12\: cm$ intersects is $90^{\circ}$, then the length (in cm) of their common chord is :

• Option 1)

$\frac{13}{2}$

• Option 2)

$\frac{13}{5}$

• Option 3)

$\frac{120}{13}$

• Option 4)

$\frac{60}{13}$

Length of common chord =  Option 1)Option 2)Option 3)Option 4)

The value of $\sin ^{-1}\left ( \frac{12}{13} \right )-\sin ^{-1}\left ( \frac{3}{5} \right )$  is equal to :

• Option 1)

$\frac{\pi }{2}-\cos ^{-1}\left ( \frac{9}{65} \right )$

• Option 2)

$\pi -\sin ^{-1}\left ( \frac{63}{65} \right )$

• Option 3)

$\frac{\pi }{2}-\sin ^{-1}\left ( \frac{56}{65} \right )$

• Option 4)

$\pi -\cos ^{-1}\left ( \frac{33}{65} \right )$

Option 1) Option 2) Option 3)   Option 4)

The angles A,B and C of a triangle ABC are in A.P.  and $a:b=1:\sqrt3$.

If c = 4 cm , then the area ( in sq. cm) of this triangle is:

• Option 1)

$\frac{2}{\sqrt3}$

• Option 2)

$4\sqrt3$

• Option 3)

$2\sqrt3$

• Option 4)

$\frac{4}{\sqrt3}$

In  , A,B,C are in A.P. =>  Now, it is given that a:b= Now, Area of                                                                                         Option 1) Option 2) Option 3) Option 4)

If $\int \frac{dx}{(x^{2}-2x+10)^{2}}=A(\tan^{-1}(\frac{x-1}{3})+\frac{f(x)}{x^{2}-2x+10})+C$

Where C is a constant of integration , then :

• Option 1)

$A=\frac{1}{54}\: \: and\: \: f(x)=3(x-1)$

• Option 2)

$A=\frac{1}{81}\: \: and\: \: f(x)=3(x-1)$

• Option 3)

$A=\frac{1}{27}\: \: and\: \: f(x)=9(x-1)$

• Option 4)

$A=\frac{1}{54}\: \: and\: \: f(x)=9(x-1)^{2}$

put              correct option is (1)    Option 1) Option 2) Option 3) Option 4)

All the pairs ( x, y ) that satisfy the inequality

$2^{\sqrt{sin^{2}x-2sinx+5}\cdot \frac{1}{4^{sin^{2}y}}}\leq 1$  also satisfy the equation :

• Option 1)

$2|sinx|=3siny$

• Option 2)

$2 sinx=siny$

• Option 3)

$sinx=2siny$

• Option 4)

$sinx=|siny|$

=>  &  So, correct option is (4). Option 1) Option 2) Option 3) Option 4)

If the line $x-2y=12$ is the tangent to the ellipse

$\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$ at the point $(3,\frac{-9}{2})$ , then the length

of the latus rectum of the ellipse is :

• Option 1)

9

• Option 2)

$12\sqrt2$

• Option 3)

5

• Option 4)

$8\sqrt3$

Tangent to a given ellipse at  Equation of tangent at  Now compare this equation with given equation of tangent  x - 2y = 12 Length of LR =  So, correct  option is (1). Option 1) 9 Option 2) Option 3) 5 Option 4)

If the circles $x^{2}+y^{2}+5Kx+2y+K=0$ and

$2(x^{2}+y^{2})+2Kx+3y-1=0$ , $(K\epsilon R)$ , intersect

at the points P and Q , then the line $4x+5y-K=0$ passes

through P and Q , for :

• Option 1)

infinitely many values of $K$

• Option 2)

no value of $K$

• Option 3)

exactly two values of $K$

• Option 4)

exactly one value of $K$

Given two circles are      Equation of common chord  => ................(1) Given equation of chord is  ..................................(2) On Comparing (1) & (2) There is no value of k  So, option (2) is correct. Option 1) infinitely many values of  Option 2) no value of  Option 3) exactly two values of  Option 4) exactly one value of

For any two statements $p$ and $q$ , the negation of the expression $p\vee \left ( \sim p\wedge q \right )$ is :

• Option 1)

$\sim p\; \wedge \sim q$

• Option 2)

$p\; \wedge q$

• Option 3)

$p\; \leftrightarrow q$

• Option 4)

$\sim p\; \vee \sim q$

Option 1)      Option 2)       Option 3) Option 4)

If the line $y=mx+7\sqrt{3}$ is normal to the hyperbola $\frac{x^{2}}{24}-\frac{y^{2}}{18}=1$   , then a value of $m$ is :

• Option 1)

$\frac{\sqrt{5}}{2}$

• Option 2)

$\frac{\sqrt{15}}{2}$

• Option 3)

$\frac{2}{\sqrt{5}}$

• Option 4)

$\frac{3}{\sqrt{5}}$

given hyperbola       Normal to hyperbola is slope form            compare this                       Option 1)            Option 2) Option 3) Option 4)

The common tangent to the circle $x^{2}+y^{2}=4\:\:and\:\:x^{2}+y^{2}+6x+8y-24=0$  also passes through the point :

• Option 1)

$(4,-2)$

• Option 2)

$(-6,4)$

• Option 3)

$(6,-2)$

• Option 4)

$(-4,6)$

common tangent will  be   Option 1) Option 2) Option 3) Option 4)

Which one of the following statements is not a tautology?

• Option 1)

$(p \vee q)\rightarrow (p\vee (-q))$

• Option 2)

$(p\wedge q)\rightarrow (\sim p)\vee q$

• Option 3)

$p\rightarrow (p\vee q)$

• Option 4)

$(p\wedge q)\rightarrow p$

Option 1) Option 2) Option 3) Option 4)
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