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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 $f( x)=x^{2}+\frac{1}{x^{2}}$ and $g( x)=x^{}-\frac{1}{x^{'}}$ x $\in$ R - {-1,0,1}. If $h( x)=\frac{f( x)}{g( x)}$ , then the local minimum value of h(x) is

A) 3

B) -3

C) $-2\sqrt{2}$

D) $2\sqrt{2}$

A straight line through a fixed point ( 2,3) intersects the coordinate axes at distinct point P and Q, If O is the origin and the rectangle OPRQ is completed, then the locus of R is

A) $3x+2y=6$

B) $2x+3y=xy$

C) $3x+2y=xy$

D) $3x+2y=6xy$

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

The boolean expression $\sim (p\vee q) \vee (\sim p \wedge q)$ is equivalent to

A) $\sim p$

B) p

C) q

D) $\sim q$

If the system of linear equation x+ky+3z=0;3x+ky-2z=0; 2x+4y-3z=0 has a non-zero solution ( x,y,z), then $\frac{xz}{y^{2}}$ is equal to

A) -10

B) 10

C) -30

D) 30

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) $4\pi$

A bag contains 4 red and 6 black balls, a ball is drawn at random from the bag. Its colour is observed and this ball along with two additional balls of the same colour are returned to the bag. If now a ball is drawn at random from the bag, then the probability that this drawn ball is red, is

A) $\frac{3}{10}$

B) $\frac{2}{5}$

C) $\frac{1}{5}$

D) $\frac{3}{4}$

The length of the projection of the line segment joining the points (5,-1,4) and (4,-1,3) on the plane , x+y+z=7 is

A) $\frac{2}{\sqrt{3}}$

B) $\frac{2}{3}$

C) $\frac{1}{3}$

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

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

A farmer F₁ has a land in the shape of a triangle with vertices at P(0,0), Q(1,1), and R (2,0). From this land, a neighbouring farmer F₂ takes away the region which lies between the sides PQ and a curve of the form y=xⁿ(n>1). If the area of the region taken away by the farmer F₂ is exactly 30% of the area Δ PQR , then the value of n is........

A) 5

B) 4

C) 2

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 $f:R\rightarrow R $ and $g :R\rightarrow R $ e two non-constant differentiable functions. If $f'(x)=(e^{(f(x)-g(x)})g'(x)$ for all $x \in R$ and f(1)=g(2)=1, then which of the following statement(s) is (are) TRUE ?

A) $f(2)<1-\log_{e}{2}$

B) $f(2)>1-\log_{e}{2}$

C) $g(1)>1-\log_{e}{2}$

D) $g(1)<1-\log_{e}{2}$

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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