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The sum of the coefficients of all odd degree terms in the expansion is

$(x+\sqrt{x^{3}-1})^{5}+(x-\sqrt{x^{3}-1} )^{5},(x>1)is$

A) -1

B) 0

C) 1

D) 2

If the curves $y^{2}=6x,9x^{2}+by^{2}=16$ intersect each other at right angles, then the value of b is

A) 6

B) $\frac{7}{2}$

C) 4

D) $\frac{9}{2}$

Let the orthocentre and centroid of a triangle be A ( -3,5) and B ( 3,3) respectively. If C is the circumcentre of this triangle, then the radius of the circle having line segment AC as diameter , is

A) $\sqrt{10}$

B) $2\sqrt{10}$

C) $3\sqrt{\frac{5}{2}}$

D) $\frac{3\sqrt{5}}{2}$

If the tangent at ( 1,7) to the curve $x^{2}=y-6$ touches the circle $x^{2}+y^{2}+16x+12y+c=0$, then the value of c is

A) 195

B) 185

C) 85

D) 95

Let $g(x)=\cos x ^{2}, f(x)=\sqrt{x}$ and $\alpha ,\beta (\alpha <\beta)$ be the roots of the quadratic equation

$18x^{2}-9\pi x +\pi^{2}=0$ .Then , the area (in sq units) bounded by the curve $y= (gof) (x)$ and the lines x=α, x=β

and y=0, is

A) $\frac{1}{2}(\sqrt{3}-1)$

B) $\frac{1}{2}(\sqrt{3}+1)$

C) $\frac{1}{2}(\sqrt{3}-\sqrt{2})$

D) $\frac{1}{2}(\sqrt{2}-1)$

The value of $\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \frac{\sin ^{2}x}{1+2^{x}}$ is

A) $\frac{\pi}{8}$

B) $\frac{\pi}{2}$

C) $\frac{\pi}{4}$

D) $4\pi$

The Integral

$\int_{}^{} \frac{\sin^{2}x cos^{2}x}{(\sin^{5}x+\cos^{3}x\sin^{2}x+\sin^{3}x\cos^{2}x+\cos^{5}x)^{2}}dx$

is equal to (where C is constant of integration)

A) $\frac{1}{3( 1+tan^{3}x)}+C$

B) $\frac{-1}{3( 1+tan^{3}x)}+C$

C) $\frac{1}{ 1+\cot^{3}x}+C$

D) $\frac{-1}{ 1+\cot^{3}x}+C$

Let A be the sum of the first 20 terms and B be the sum of first 40 terms of the series

1²+2.2²+3²+2.4²+5²+2.6²+........ If B-2A=100λ then λ is equal to

A) 232

B) 248

C) 464

D) 496

The number of 5 digit numbers which are divisible by 4, with digits from the set {1,2,3,4,5} and the repetition of digits is allowed, is...........

A) 625

B) 196

C) 525

D) 169

Let a,b,c be three non-zero real numbers such that the equation $\sqrt{3} a \cos x+2b \sin x= c$ , $x\in[-\frac{\pi}{2},\frac{\pi}{2}]$, has two distinct real roots $\alpha$ and $\beta$ with $\alpha$ + $\beta$= $\frac{\pi}{3}$ , Then , the value of $\frac{b}{a}$ is.....

A) 0.5

B) 0.75

C) 1.5

D) 1

Let E₁ E₂and F₁F₂be the chords of S passing through the point P₀(1,1) and parallel to the X-axis and the Y-axis, respectively. Let G₁G₂ be the chord of S passing through P₀and having slope -1. Let the tangents to S at E₁and E₂meet at E_3,then tangents to S at F₁and F₂meet at F_3, and the tangents to S at G₁and G₂ meet at G3. Then, the points E₃, F_3,and G₃ lie on the curve

A) x+y=4

B) $(x-4)^{2}+(y-4)^{2}=16$

C) (x-4)(y-4)=4

D) xy=4

Let s,t, r be non zero complex numbers and L be the set of solutions z=$ x + iy (x, y \in R$ ,i = $\sqrt{-1}$ ) of the equation $sz+i\bar{z}+r=0$ , where $\bar{z}=x-iy$ , Then , which of the following statement (s) is (are) TRUE ?

A) If L has exactly one element, then $\mid s\mid \neq \mid t\mid$

B) If $\mid s\mid = \mid t\mid$ , then L has infinitely many elements

C) The number of elements in $L \cap ({z:\mid z-1+i\mid=5})$ is at most 2

D) If L has more than one element then L has infinitely many elements.

Let X be a set with exactly 5 elements and Y be a set exactly 7 elements. If α is the numbers of one - one functions from X to Y and β is the number of onto functions from Y to X , then the value of $\frac{1}{5!}(\beta -\alpha) $ is ............

A) 118

B) 119

C) 121

D) 115

Let $f:R\rightarrow R$ be a differentiable function with f(0)=0, y=f(x) satisfies the differential equation

$\frac{\text{d}y}{\text{d}x}= (2+5y)(5y-2)$ , then the value of $\lim_{x \rightarrow \infty} f(x) $ is .............

A) 0.6

B) 0.4

C) 0.8

D) 0.1

Let P be a point in the first octant , whose image Q in the plane x+y= 3 (that is, the line segment PQ is perpendicular to the plane x+y=3 and the mid- point of PQ lies in the plane x+y=3) lies on the Z-axis. Let the distance of P from the X-axis be 5. If R is the image of P in the XY-plane, then the length of PR is .....

A) 4

B) 6

C) 12

D) 8

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