Explore topic-wise InterviewSolutions in Current Affairs.

John, a United States resident, is on vacation in Spain and is trying to decide if the should use his own credit card from the U.S. or to purchase a prepaid credit card for 500 euros in Spain.

If 2, -3 , 5 are the roots of ax^(3) + bx^(2) + cx + d = 0 then the roots of a(x - 1)^(3) + b (x -1)^(2) + c(x - 1) + d= 0 are

Find the maximum value of the 8cosx-15sinx-2

Let the popultion of rabbits surviving at a time t be governed by the differential equation (dp(t))/(dt) = (1)/(2) p (t) - 200. If p(0) = 100, the p(t) equals

r :Two chords of a circle are equidistant from the centre if and only if they are equal in length Statements r can be interpreted as

Given that the marginal cost MC and average cost AC for a product are equal. Then thetotal cost C is a(i) constant function(ii) linear function of number of units (x) produced(iii) quadratic function of number of units (x) produced(iv) None of these

Find the volume of the solid generated by revolving about the x-axis the figure enclosed by the astroid : x= a cos^(3)t , y= a sin^(3)t.

If y=x^(x)+x^(a)+a^(x)+a^(a)," find "(dy)/(dx)

Find an approximation of (0.99)^(5) using the first three terms of its expansion.

Find the slope of the tangent to the curve. y=(x-1)/(x-2) x ne 2 at x=10

Evaluate the following integrals. int(1)/(x)(logx)^(2)dx

Let a=2hati+hat j and b=hat i+2hatj+hatk be two vectors. Consider a vector c=alphaa +betab,alpha,beta in R. If the projection of c on the vector (a+b) is 3sqrt(2), then the minimum value of (c-(axxb))).c equals...........

If A and B are two events such that P (barA)=0.3 P(B) =0.4 and P(A cap barB)=0.5 "then" P (B /A cup barB)=

A random variable X has the following probability distribution : P(X ge2)

If A = [(5,-1,3),(0,1,2)] .B = [(0,2,3),(1,-1,4)], then (AB') ' equals :

If n gt 3, then xyz^(n)C_(0)-(x-1)(y-1)(z-1)""^(n)C_(1)+(x-2)(y-2)(z-2)""^(n)C_(2)- (x-3)(y-3)(z-3)""^(n)C_(3)+…..+(-1)^(n)(x-n)(y-n)(z-n)""^(n)C_(n) equals :

Find the value of k if x+ky-5=0 is a tangent to the ellipse 4x^2+9y^2=20

In a certain college 25% boys and 10% girls are studying mathematics the girls constitute 60% of the student body. What is the probability that mathematics is being studied ?

If alpha-beta is constantprove that the chord joining the pointsalpha and beta on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 touchesa fixed ellipse

Evaluate the following determinants. [[1,1],[2,3]]

Ifcos alpha + cos beta + cosgamma = 0 sin alpha + sin beta + sin gamma, Prove that cos^(2) alpha + cos^(2) beta + cos^(2) gamma = 3/2 = sin^(2) alpha + sin^(2) beta + sin^(2) gamma.

If a=6hat(i)+7hat(j)+7hat(k), b=3hat(i)+2hat(j)-2hat(k), P(1, 2, 3) Q. If A is the point with position vector a then area of the triangle trianglePLA is sq. units is equal to

Differentiate the following w.r.t. x : e^(x) + e^(x^3)+"……….."+e^(x^3).

Show that +: R xx R to and x : R xx R to R are communtative binary opertions , but- : R xx R to R and div : R _(**) xx R _(**) are not commutative.

Consider the probability distribution of a random variable X: Calculate (i) V((X)/(2)) (ii) Variance of X.

If a,b,c are vectors of equal magnitude such that (a,b)= alpha, (b,c)= beta, (c,a)= gamma,then the minimum value of cos alpha +cos beta +cos gamma is

If 8x+5y le 40, 5x+4y le 40, x ge 0 , y ge 0 then the maximum value of f=3x+2y is

Find the equation of the circle which cuts the following circles orthogonally. x^2 + y^2 + 2x + 4y + 1 =0, 2x^2 + 2y^2 + 6x + 8y - 3 = 0, x^2 + y^2 - 2x +6y - 3 = 0.

Determine whether or not each of the definitions of ** given below gives a binary operation. In the event that ** is not a binary operation, give justification for this on R, define ** by a**b=ab^2

Oesophagous is a thin, long tube which extends ______ passing thought the Neck, Thorax and diaphragm.

If x^3+12x^2+10ax+1999 definitely has positive zero , if and only if ............

If a normal makes an angle theta with positive x-axis then the slop of the curve at the point where the normal is drawn is ……………

The sine of the angle between the straight line (x-2)/(3)=(y-3)/(4)=(z-4)/(5) and the plane 2x-2y+z=5 is …........

Find the sum of the coefficients of integral powers of x in (1+3sqrtx)^20

vec(OA)andvec(BO) are two vectors of magnitudes 5 and 6 respectively. If angleBOA=60^(@),"then "vec(OA).vec(OB) is equal to

if lim_(zto-1)(sqrt(z)-1)/(1-z)=

Solve in R and represent the solution on the number line. (x-1)/2 le (x+1)/3 lt (3x-1)/6

Draw the graph of y=cos^(-1){x}," where "{*}" represetns the fractional part function".

If m and M denotes the minimum and maximum value of |2z+1|, where |z-2i|le1 and i^(2)=-1, then the value of (M-n)^(2) is equal to

If sum _(r =1) ^(n ) T _(r) = (n +1) ( n +2) ( n +3) then findsum _( r =1) ^(n) = (1)/(T _(r))

Differentiate the following functions with respect to x. y= x^(x).sin x+ (sin x)^(x)

Show that f(x)={(xsinfrac{1}{x},xne0),(0,x=0):} is not differentiable x=0

If1 , omega , omega^(2) are the cube roots of unity , then find the values of the following . (a + 2 b)^(2) + ( a omega^(2) + 2 b omega)^(2) + ( a omega + 2 b omega^(2))^(2)

One of the closed points on the curve x^(2) - y^(2)=4 to the point (6,0) is………

If cos alpha+cos beta+cos gamma=0 & sin alpha +sin beta +sin gamma=0. Then Prove thatsin2alpha+sin2beta+sin2gamma=0

Let f(x) ={{:(x^(2)+a, 0 le x lt1),( 2x+b, ale x le 2):} andg(x) ={{:(3x+b,0 le xlt1),( x^(3), 1le x le 2):} if (df)/(dg) exists at x=1, then

If |{:(a-b,b-c,c-a),(x-y,y-z,z-x),(p-q,q-r,r-p):}|=m|{:(c,a,b),(z,x,y),(r,p,q):}|," then m"=

If P(A) = 4//5, P(B) = 2//4, P(A nn B) = 3//5, then find P(bar(A uu B)).

The perpendicular distance of the point P (6, 7, 8) from XY - plane is

Show that +: R xx R to and x : R xx R to R are communtative binary opertions , but- : R xx R to R and div : R _() xx R _() are not commutative.

Determine whether or not each of the definitions of given below gives a binary operation. In the event that is not a binary operation, give justification for this on R, define by ab=ab^2