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Which of the following is a graph of f(x)= tan^(-1) x , ( x in R) ?

f(x) = {{:((a^(sin x)-a^(tanx))/(tan x-sin x), "for",x gt 0),((ln(1+x+x^(2))+ln(1-x+x^(2)))/(sec x - cos x), "for", x lt 0):} if f is continous at x=0, find 'a'. Now if g(x) = ln(2-x/a) cot(x-a) for x ne a, a ne 0, a gt 0. If g is continous at x=a then show that g(e^(-1)) = -e.

L = (2, 4) and L^(1) (2, -4) are ends of latus- rectum and P is any point on the directrix of parabola then area of DeltaPLL^(1) in sq. units is

The number of ways of selecting 6 objects from eight objects is

Let S = {1, 2, … 100}. The probability of choosing an integer k, 1lekle100 is proportional to log k. The conditional probability of choosing the integer 2, given that an even integer is chosen is

Find the value of Lim_(x rarr 0)(1)/(x^(3)) int_(0)^(x) (t(ln (1+t)))/(t^(4) + 4)dt

Write the value ofd/dxsec^-1(1/(2x^2-1)), for x in(0,1/sqrt2).

If the curves ax^2+4xy+5y^2-2x+2y+p+2=0 and ax^2-2xy-2y^2-3x-4y-1=0 intersect at four concyclic points and the circle thus formed does not touch or intersect the coordinate axes, and point (3,2) lies inside it , then p can be

If the line x cos theta+y sin theta=P is the normal to the curve (x+a)y=1,then theta may lie in

If the point (a,2,3),(3,b,7)and(-3,-2,-5) are collinear, the values of a and b respectively are

A man is known to speak truth 3 out of 4 times. He throws a die and﻿ reports that it is a six. Find the probability that it is actually a six.

A dice is thrown three times. Let X be 'the number of two seen'. Find the expectation of X.

For- (pi)/(2) lt x lt (3pi )/( 2),the vlaue of { tan ^(-1) "" (cos x )/( 1 + sin x )}is equal to

If r_(1), r_(2), r_(3) are radii of the escribed circles of a triangle ABC and r it the radiusof its incircle, then the root(s) of the equation x^(2)-r(r_(1)r_(2)+r_(2)r_(3)+r_(3)r_(1))x+(r_(1)r_(2)r_(3)-1)=0 is/are :

Eric and Ortega and their teammates watch a movie. They all sit in a row, and they can sit in n different ways. In how many of the ways can Eric sit to the right of Ortega?

Determine if the set A ={1,2,3,4}is a proper subset of the set B={n in N, n is a divisor of 60}

Find the asymptotes of the hyperbola xy-3y-2x=0

Differentiate w.r.t x the function x^(x^(2)-3) + (x-3)^(x^(2)), for x gt 3

Let M be the foot of the perpendicular from a point P on the parabola y^(2)=8(x-3) onto its directrix and let S be the foucs of the parabola. If triangleSPM is an equilateral triangle, then P is equal to

A circle of radiu 4, drawn on a chord of the parabola y^(2)=8x as dimater, touches the axis of the parabola. Then, the slope of the chord is

If m is a natural number such that m le 5 , then the probability that the quadratic equation x^(2)+mx+(1)/(2)+(m)/(2)=0 has real roots is

Consider a fixed parabola C _(1) -=x ^(2) + y =0. A set of varying parabola (s) C thouches C _(1) at origin. Out of such curves C, a set of parabola (s)C_(2) are selected having vertex (-9,3). The possible coordinate of foci of parabola (s) C_(2) is/are

If A= [ (3,-3,4),(2,-3,4),(0,-1,1)]then A^(-1) equals :

Consider a fixed parabola C _(1) -=x ^(2) + y =0. A set of varying parabola (s) C thouches C _(1) at origin. Out of such curves C, a set of parabola (s)C_(2) are selected having vertex (-9,3). The locus of focus of curves C having same latus rectum as C _(1) will be

Find the derivative of xsin x from first priciple.

For |x| lt 1, the constant term in the expansion of (1)/((x-1)^(2)(x-2) is :

How many ways are there of getting from Alphaville to Gammerburg via Betancourt, if there are 3 roads between Alphaville and Betancourt and 4 roads between Betancourt and Gammerburg?

A box contain three coins, one coin is fair, one coin is two-headed, and one coin is weighted so thatthe probabilityof heads, appearing is 1/3 . Acoin is selected at random and tossed. Then theprobability that heads appears is

Write down a unit vector in XY-plane, making an angle of 30^(@) with the positive direction of x-axis.

If the 21^(st) and 22^(nd) terms in the expansion of (1 + x)^(44) are equal, then x =

If int (10x^(9)+a10^(x-1))/(x^(10)+10^(x)) dx=log(x^(10)+10^(x))+c then a=......

If the marginal revenue function of a commodity is MR=2x-9x^(2) then the revenue function is

Find (dy)/(dx) in the following ax + by^(2) = cos y

If "sin 6A + sin 2A"/"cos 6A + cos 2A"=tan (lambdaA) where lambda in I, then lambda is :-

If a and b are the natural numbers such that a + b = ab, then equation of the chord of the ellipse x^2+4y^2=4 with (a,b) as the mid point is :

If P = (1/x_p,p),Q=(1/x_q,q),R=(1/x_r,r)where x_kne0,k =p,q , r ne N , denotes the k^(th) term of a Harmonic progression , then

For thefucntionf(x) =x cot^(-1) x , x ge 0

Examine the continuity of the function f(x) = {(|x|.cos ((1)/(x))",","if" x ne 0),(0",","if" x = 0):} at x= 0

It is possible to express every set through a defining property? Justify your answer.

If alpha and beta satisfy sinalpha cos beta=-1/2, then the greatest value of 2cos alpha sin beta is ……….

What is the hybridisation of Fe in sodium thionitroprusside.

If the lines 2x-y+3z + 4 = 0=ax + y-z + 2 and x-3y + z=0 =x + 2y + z +1 are coplannar then the value of a is ...........

A group of students comprises of 5 boys and n girls. If the number of ways, in which a team of 3 students can randomly be selected from this group such that there is at least one boy and at least one girl in each team, is 1750, then n is equal to

Verify Rolle's theorem for the following functions: f(x)= a^(sin x), x in [0, pi], a gt 0

A man is known to speak truth 3 out of 4 times. He throws a die and reports that it is a six. Find the probability that it is actually a six.