Explore topic-wise InterviewSolutions in .

If int(e^(x-1))/((x^(2)-5x+4))2xdx=AF(x-1)+BF(x-4)+c and F(x)=int (e^(x))/(x)dx, then-

If the area of the triangle with vertices (x,0) and C(1,2,4) are the vertices of the triangle ABC, then the length of its median through the vertex A is -

An ellipse having the coordinate axes as its axes and its major axis along Y-axis, passes through the point (-3,1) and has eccentricity sqrt((2)/(5)). Then its equation is

Find a unit vector perpendicular to each of the vectors veca+vecb and veca-vecb when veca= 3hati+2hatj+2hatk, vecb=hati+2hatj- 2hatk

Evalute the following integrals int (x^(2) + 1)/(x^(4) + 1)dx

Solve system of linear equations , using matrix method if exists 3x-y=5 6x-2y=3

Evaluate the following definite intergrals . overset(3) underset(2)int x^(2)dx

Check the continuity of the following functions : f(x)=x^(2)" at "x=0.

Statement-I : The combined equatioin of the pair of asymptotes of the hyperola 2xy+6x+y+5=0 is 2xy+6x+y+3=0 Statement II: The angle between the asymptotes of the hyperola xy-2y+3x+sqrt3=0 is 60^(@). Which of above statement is true.

Evaluate {:[(x,x+1),(x-1,x)]:}

Solve x^(2) - 10x + 21 lt 0 by algebric method and graphical method.

Differentiate a^(x) w.r.t. x, where a is a positive constant.

Evaluate the following integrals int_(2)^(6)sqrt((6-x)(x-2))dx

Using elementary row transformations find the inverse of the matrix [{:(3,0,-1),(2,3,0),(0,4,1):}]

Ifalpha, beta , gammaare therootsof theequationx^3 - px^2 + qx +r=0then( alpha+ beta ) ( beta + gamma) ( gamma+ alpha)=

Evaluation of definite integrals by subsitiution and properties of its : int_(-2)^(0)(x^(3)+3x^(2)+3x+3+(x+1)cos(x+1))dx=...............

A rectangle with altitude x is inscribed in a triangle ABC with the bae b and altitude h. Express the perimeter P and area S of the rectangle as fuction of x.

The mean of n items is bar(x). If the first item is increased by 1, second by 2 and so on, then the new mean is

If f(x)=5x^3+4x^2 - 13 x-25 andf(x-3)= 5x^3 - 41x^2 + 98x + kthenk=

Find the number of ways of arranging 4 boys and 3 girls around a circle so that all the girls sit together.

The set of all point for which f(x) = (|x-3|)/(|x-2|) + 1/[1+x] is continuous is (where [*] represents greatest integer function)

The order and degree of the differential equation [1 + ((dy)/(dx))^(2) + sin((dy)/(dx))]^(3//4)= (d^(2)y)/(dx^(2))

A function y=f(x) is given by x = phi (t)=t^(5)-5t^(3)-20t+7y= Psi (t)=4t^(3)-3t^(2)-18t+3, -2 lt t lt 2Find the maximum and minimum value of the function.

If (2,-1,2) and (K,3,5)are the traidsof directionratiosof twolines and the anglebetween them is 45^(@) , then is a value of k is

A and B are among 20 persons sit at random along a round table. Find the probability that there are any 6 persons between A and B.

Using differentials, find the approximate value of each of the following upto 3 place of decimal. (iii) sqrt(0.6)

If one root of 24x^(3) - 14x^(2) - 63x + 45 = 0is the double the other then the roots are

Let a, b and c be three non-coplanar vectors and let p,q and r be the vector defined by p=(b xx c)/([abc]), q=(c xx a)/([abc]), r=(a xx b)/([abc]). Then, (a+b). p+(b+c).q +(c+a).r is equal to

If a and b(a gt b) are points of discontinuity of the function f(x)={:{(3-2x^2, "for", x le 0),(2x+3, "for" ,0 lt x le 1),(2x^2-3x,"for",1 lt x lt 2),(2x-3,"for", 2 le x lt 3),(|x|,"for" , ge 3):} then 3a-b =

y gex + 2 2x + 3y le6 In which of the following does the shaded region represent the solution set in the xy-plane to the system of inequalities above?

If (-2,-1) is a limiting point of a coaxal system of whichx^(2) + y^(2) + 2x + 4y + 7 = 0 is a member, then the equation of the or the gonal system is

The product of the distinct (2n)^(th) roots 1+isqrt3 is

Let the transverse axis ofa varying hyperbola be fixed with length of transverse axis being 2a. Then the locus of the point of contact of any tangent drawn to it from a fixed point on conjugate axis is

The value of sin 10^(@) + sin 20^(@) + sin 30^(@) + …. + sin 360^(@) is equal to

The functions f and g are defined as follow : f = {(1,2),(3,5),(4,1) } and g = {(2,3),(5,1),(1,3)}. Find the range of f and g . Also find the composition function fog and gof.

Equation of the line through the point (1, 1, 1) and intersecting the lines 2x-y-z-2=0=x+y+z-1 and x-y-z-3=0=2x+4y-z-4.

Two tangents are drawn from a point(-2,-1)to the curve y^(2) =4x,If alphais the angle between them , then| tan alpha |is equal to

intxtan^-1xdx

Represent as limit of sum : overset(2)underset(0)int(x^(2)+3)dx

If f: Rrarr R given by f(x) = (x^3) + 3, then f^-1(x) equals·:

If the absolute error while calculating the absolute error in volume of a sphere of radius 10 cm is 0.1 cm. Which is the absolute error in volume of the sphere ?

The tangent to the curve y=f (x) at the point with absicsa x =1 from an angle of pi//6 and at the point x=2 an angle of pi//3 and at the point x=3 and angle of pi//4 . If f''(x) is contnuous, then the value of int_(1)^(3) f''(x)f'(x)dx+int_(2)^(3)f''(x)dx is

Find the area of the parallelogram formed by the lines2x^2+5xy+3y^2=0 and 2x^2+5xy+3y^2+3x+4y+1=0

Find the sum of all four digit numbers formed by the digits {1,2,3,….9} in which exactly two digits are prime and repetition of digits is not allowed

Solve : (i) |x^(2)-2x|le x , (ii) (x^(2)-9)(|x|-2)le0

Integrate the function in Exercise. ((x-3)e^(x))/((x-1)^(3))

Find the polynomial P(x) of the least degree whose graph has three points of inflection : (-1,-1),(1,1)and a point withabscissa 0 at whichthe curve is inclined to the axisof abscissas at an angle of 60^(@).

Let A, B be two 3xx3 matrices with entries from real number . Which one of the follwing is true ?