Explore topic-wise InterviewSolutions in Current Affairs.

If f(x)=|{:(1,x,x+1),(2x,x(x-1),x(x+1)),(3x(x-1),x(x-1)(x-2),x(x^2-1)):}| then f(100)= ………

If int _(0) ^(x) (x ^(3) cos ^(4) x sin ^(2)x)/(pi^(2) -3pix + 3x ^(2))dx = lamda int _( 0)^(pi//2)sin ^(2) x dx,then the value of lamda is:

If int e^(x) cos 4 x dx = A e^( 5x) (sin 4x + (5)/(4) cos 4x) + C then A is equal to

STATEMENT -1 : for the function y= f(x), f(x) ,({1+((dy)/dx)^(2)}^(3/2))/((d^(2)y)/(dx^(2))) = - ({1+ (dx/dy)^(2)}^(3/2))/((d^(2)x)/(dy^(2))) STATEMENT -2 :(dy)/(dx) = (1/(dx))/dyand (d^(2)y)/(dx^(2)) = d/dx (dy/(dx))

If f(x) is differentiable function in the interval (0,oo) such that f(1) = 1 and lim_(trarrx) (t^(2)f(x)-x^(2)(t))/(t-x)=1 for each x gt 0, then f((3)/(2)) is equal tv

A cylindrical tank of radius 10 m is being filled with wheat at the rate of 314 cubic metre per hour. Then the depth of the wheat is increasing at the rate of ………..

The vertex of the parabola y^2 + 4x = 0 is

Sketch the origin in which the points satisfying the following inequalities lie. (i)|x+y| lt 2 "(ii) " |2x-y| gt 3 "(iii) "|x| gt|y|

Equation of the tangent to the circle x^(2)+y^(2)=3, which is inclined at 60^(@) with the x-axis is

Find the equation of locus of a point, the sum of whose distances from (0 , 2) and (0 , -2) is 6 .

How many different words can be formed by jumbling the letters in the word MISSISSIPPI in which no two S are adjacent?

2sec^(2)theta - sec^(4)theta - 2cosec^(2)theta + cosec^(4)theta = 15/4 if tan theta is equal to ,

Area of the triangle formed by the radical axis of the circles x^2+y^2=4, x^2+y^2+2x+4y-6=0 with co-ordinate axes is

arg(bar(z))+arg(-z)={{:(pi",","if arg (z) "lt 0),(-pi",", "if arg (z) "gt 0):},"where" -pi lt arg(z) le pi. Let z_(1) and z_(2) be two non-zero complex numbers, such that abs(z_(1))=abs(z_(2)) " and " arg(z_(1),z_(2))-pi," then " z_(1) is equal to

(dy)/(dx) + (sec x)y = tan x (0 le x lt (pi)/(2))

Let alpha and betabe the roots of the equation x^(2)+x+1=0.The equation whose roots are alpha^(19), beta^(7) is

The x-axis, y-axis and a line passing﻿ through the point A(6,0) form a triangle﻿ ABC. If /_A = 30^(@), then the area of the﻿ triangle in sq.units, is﻿

f(x) = (x) /(1+("ln"x)("ln"x).. . oo)AAx in [1,3] is non-differentiableat x=K thenthe valueof [k^(2)] is ( where[.] representsthegreatest integer function )______.

Consider the following linear equations ax+ by + cz=0, bx + cy + az =0, cx+ ay +bz=0

If alpha , beta , gammaare the rootsof theequationx^3 -6x^2 +11 x +6=0thensumalpha^2beta =

The sum of distance of any point on the ellipse 3x^2 + 4y^2 = 24 from its foci is

If any two chords be drawn through two points on the major axis of the ellipse x^2/a^2+y^2/b^2=1 equidistant from the centre prove that tan""alpha/2 tan""beta/2 tan""gamma/2=1 where alpha,beta,gamma,delta are the eccentricity angles of the extremities of the chord.

If z_(1) = 1 , z_(2) = i and A = Arg (z_(1) z_(2)) B = Arg ((z_(1))/(z_(2))) , C = Arg (z_(1) + z_(2)) , D = Arg (z_(1) - z_(2)) arrange A , B , C , D in ascending order

A person wishes to make up as many different parties of 10 as he can out of 20 friends, each party consisting of the same number. The number of ways that the same man is found in different parties is

If x in (-3)/(sqrt(2)), thenint (x^(2))/(2x^(2) + 6 sqrt(2)x + 9) dx =

Find x and y, if 2[(1,3),(0,x)]+[(y,0),(1,2)]=[(5,6),(1,8)]

Solve the following equation x: 3x - 4 = 2(x - 5)

If x =3 + (4)/(2!) + (8)/(3!) + (16)/(4!) + .....oothen 1/x =

int_(0)^(2x)d^(x/2).sin(x/2+(pi)/4)dx=

A focal chordof y^(2)=4ax meets it in P and Q. If S is the focus, then (1)/(SP)+(1)/(SQ)=

If a_(n) = int_(0)^(pi//2) (sin^(2) nx)/( sin x) dx then a_(2) - a_(1) , a_(3)- a_(2), a_(4) - a_(3) are in

Evaluate the following definite integrals: int_(-1)^(1//2)|xcos pi x|dx

For each of the differential equations in find the particular solution satisfying the given condition : 2xy+y^(2)-2x^(2)(dy)/(dx)=0,y=2 when x=1

Find the area of the parallelogram whose diagonals are vectors 3hati+hatj-2hatk and hati-3hatj+4hatk.

If 3f(cosx)+2f(sinx)=5x, then f^(')(cosx) is equal to (where f^(') denotes derivative with respect tox)

A bead is moving on a frictionless fixed circular wire of radius 0.8 m in horizontal plane with constant speed & there is no interaction force between bead & wire & it is also connected with string & spring .

If two circles touching both the axes are passing through (2,3) then length of their common chord is

If |bar(a)|=2,|bar(b)|=4,|bar( c )|=1 and bar(a)+bar(b)=-bar( c ) then bar(a).bar(b)+bar(b).bar( c )+bar( c ).bar(a)=……………

inte^(2x)(log2x+(1)/(2x))dx=..........+c

Differentiate (x^(2)-5x + 8) (x^(3) + 7x + 9)By using product rule

A circle of radius 2 units rolls inside the ring of the circle x^(2)+y^(2)+8x-2y-19=0 then the locus of its centre is

The sum sumsum_(0leilejle10) (""^(10)C_(j))(""^(j)C_(r-1))is equal to

If xy =e -e ^(y)then (d ^(2) y )/( dx ^(2)) at x =0 is

A die is thrown and a card is selected at random from a deck of 52 playing cards. The probability of getting an even number on the die and a spade card is …………

Thetransformedequationx^3 -5/2 x^2 -(7)/(18 )x+(1)/( 108)=0byremovingfractionalcoefficientsis

2 int_(0)^(1) (tan^(-1)x)/(x) dx=

[.] represents greatest integer function:

The x-axis, y-axis and a line passing through the point A(6,0) form a triangle ABC. If /_A = 30^(@), then the area of the triangle in sq.units, is