Explore topic-wise InterviewSolutions in .

Prove that x^(2)-y^(2)=c(x^(2)+y^(2))^(2) is the general solution of differential equation (x^(3)-3xy^(2))dx=(y^(3)-3x^(2)y)dy, where c is a parameter.

The sum of all numbers formed taking all the digits {1, 2,3, 4} is

The unit vector in the direction of the sum of the vectors (1, 1, 1),(2, -1,-1) and (0, 2, 6) ………..

Check whether the relation R defined by R = {(a,b) : a le b^3} is reflexive , symmetric or transitive.

Show that the normals to the planes oversettor.(overset^i-overset^j+overset^k)=3and oversettor.(3overset^i+2overset^j-overset^k)=0 are perpendicular to each other.

f: [2,oo) rarr y, f(x) = x^(2)-4x +5 is a one and Onto function . If y in[a,oo)then the value of a is .........

Angle substended by common tangents of two ellipse 4( x-4) ^(2) +25y^(2)=100 and 4( x+1) ^(2) +y^(2)=4 at origin is

A company sells its product at Rs 10 per unit. Fixed costs are Rs 35000 and variable costs are estimated to run 30% of total revenue. Determine the (i) total cost function (ii) the quantity the company must sell to cover the fixed cost.

The number of words that can be made with the letters of the word CALCULATE such that suceach word starts and ends a consonant, is

If z is a complex number, then the locus of z such that : {:("List I","List II"),((A)|z|=1,"(1) Is a straight line "),((B)|z+2i|+|z-2i|=4,"(2) Is a ellipse "),((C) Re (z^2)=4,"(3) Is a hyperbola"),((D)zbarz=4,"(4)IS a pair of st. lines"),(,"(5) Is a circle"):} The correct match is

lim_(z to 0)[{ max( sin^(-1) x+ cos^(-1) x)^(2),min (x^(2) + 4x + 7))} . (sin^(-1)z)/z]is equal to ( where [.] denotes greatest integer function )

The mod -amplitude form of 1+itan theta is

(1)/(1.2)-(1)/(2.3)+(1)/(3.4)-(1)/(4.5)+....=

If alpha, beta, gamma are the cube roots of a negative number p, thenfor any three real numbers x,y,z the value of (x alpha+y beta+ z gamma)/(x beta +y gamma+z alpha) is

Value of S=2012+(1)/(3)(2011+(1)/(3)(2010+(1)/(3)(2009+(1)/(3)(2+(1)/(3)(1))....) is

Choose the correct answer.The value of overset^^i.(overset^^jxxoverset^^k)+overset^^j.(overset^^ixxoverset^^k)+overset^^k.(overset^^ixxoverset^^j) is :a)0b)-1c)1d)3

If vec(a)=2hat(i)+lambda hat(j)+hat(k) and vec(b)=-hat(i)+2hat(j)-3hat(k) are orthogonal, then value of lambda is

Verify mean value theorem for each of the functions: f(x) = (1)/(4x-1),x in [1, 4]

Find(dy)/(dx), if x = c t, y= ( c )/( t)

Ifsin A - sqrt(6)cos A= sqrt(7)cos A, thencos A+ sqrt(6)sin Aisequal

int(dx)/(sinx+sqrt(3)+cosx)=....

Find the value of lambda so that the three vectors are co-planar. hati+2hatj+3hatk, 4hati+hatj+lambdahatk and lambdahati-4hatj+hatk

Approximate value of sqrt(0.081) = ….....

Show that the equation of the line passsing through the points of intersection of the circles 3x^2+3y^2-2x+12y-9=0 and x^2+y^2+6x+2y-15=0 is 10x-3y-18=0

(i) Show that in the set of positive integer, the relation ' is greater than ' is transitive but it is not reflexive or smmetric. (ii) Let R be a relation on the set of natural numbers N defined as ""_(a)R_(b) impliesa divides B where a,b inN. IsR symmetric ?

Number of solution in [0, pi//2] of the equation cos 3xcdot tan 5x = sin 7x is

The values of k for which the system of equations x+ky-3z=0……..1 3x+ky-2z=0 ……….2 2x+3y-4z=0……………3 has non trivial solution is (are)

Which of the following expressions are meaningul :

Solve dy = x^(3) dy + 3x^(2) ydy- sec ( sec x + tan x ) dx

If the equatoin ax^(2)-y^(2)+bx+cy+d=0 represents a pair of lines whose slopes are m and m^(2), then value (s) of a is /are

If y(x) is the ..............

A symmetrical form of the line of intersection of the planesx= ay +b and z= cy +dis

Solve the differential equation (x)dy = ( 1 + y^(2))dx.

If A=[[1,2],[-2,3]]B=[[3,2],[1,4]],C=[[2,2],[1,3]]Calculate BC.

If veca = 3hati+hatj-2hatk, vecb = 2hati-3hatj+4hatk then verify that vecaxxvecb is perpendicular to both veca and vecb.

Evaluate : inte^(2x)*(-sinx+2cosx)dx.

If a, b, c are three vectors such that |a|=1,|b|=2,|c|=3and2a*b=b*c=c*a=2, Then, [a" "b" "c]^(2)=

If the lines ax + 2y + 1 = 0, bx + 3y + 1 = 0,﻿ cx + 4y + 1 = 0 are concurrent, then a, b, c﻿ are in

For the given statement identify the necessary and sufficent conditions r : If x is real number such that xgt0 " then " x+1/xge2

Let f be a periodic continuous function with period T gt 0. If I= int_(0)^(T) f(x) dx Then the value of I_(1) = int_(4)^(4+4T) f(3x) dx is

Find the values of p and q, so that f(x) = {(x^(2) + 3x + p,x le 1),(qx + 2,x gt 1):} is differentiable at x=1.

The number of ways in which 20 letters a_(11),a_(2),a_(3),.............,a_(10),b_(1),b_(2),b_(3),.........,b_(10)be arranged in a line so that suffixes of the letters 'a' and also those of 'b' are respectively in ascending orders of magnitude is………

Write the derivative of sin^(-1)(cosx) with respect to x.

Area of region enclosed by the region y^2 le 3x , x^2+y^2 le 4 and y ge 0 is :

In the (x,y) coordinate plane, what is the diameter of the circle having its center at (-6,1) and (0,9) as one of the endpoints of a radius ?

Evaluate the following determinates |{:(x,y),(-y,x):}|

f(x) = min { x+1 , sqrt((1-x))}the areaof theregionbounded by thecurvef(x)and X - axisis….Sq. unit

Find the area enclosed between the circles x^(2) + y^(2) = 4 and (x - 2)^(2) + y^(2) = 4.

If a, b, c are three vectors such that |a|=1,|b|=2,|c|=3and2ab=bc=c*a=2, Then, [a" "b" "c]^(2)=

If the lines ax + 2y + 1 = 0, bx + 3y + 1 = 0, cx + 4y + 1 = 0 are concurrent, then a, b, c are in