Explore topic-wise InterviewSolutions in Current Affairs.

Evaluate int (x + (1)/(x))^((3)/(2))((x^(2) -1)/(x^(2)) )dx

C_(1) + 4.C_(2) + 7.C_(3) +......+(3n - 2).C_(n) =

Define binary operation on a set. Verify whether the operation * defined on Q set of rational number by a*b= ab+1 AA a,b in Q is commutative or assosiative.

The value of 50 sum_(r=1)^(49)(2r^(2) - 48r +1)/((50-r).""^(50)C_(r)) is "_____".

On the set of positive rationals, a binary operation * is defined by a*b=(2ab)/5 . If 2 * x=3^(-1) then x=

Integrate the following functions : e^(x)(1+x)log(xe^(x))

In the parabola y^(2)-2y +8x -23 =0the length of double ordinate at a distance of 4 units from its vertex is

Prove that the area of the triagle only if z_1^2+z_2^2+z_3^2=3 z_0^2

A :sin^(2) 5^(@) + sin^(2) 10^(@) + ..... + sin^(2) 85^(@) =17//2 R : If A+B=90^(@) , thensin^(2) A + sin^(2) B=1

A cylinder is heated in such a way that its radius always remains twice of its height when the radius is 3 cm, find the rate of increase of its volume. The radius is increased at the rate of 2 cm/s. Also find the rate of increase of its total surface area.

Evaluate int(1)/((x+1)sqrt(x+2))dx

State the converse, inverse and contrapositive ofprarr~~q propositions. Stating it as a conditional, wherever necessary.

If vecE and vecF are complementary events of events E and F respectively and 0lt P(F) lt 1 , then :

If the arithmetic mean of the roots of quadratic equation is (8)/(5) and the arithmetic mean of theirreciprocals is (5)/(8) then the equation is

The system of linear equations x+y+z=2 2x+y-z=3 3x+2y+kz=4 has a unique solution if

It is given that at x = 1, the function x^(4)-62x^(2)+ax+9 attains its maximum value, on the interval [0, 2]. Find the value of a.

Solve as directed : 7(x-3) le 4 (x +6 ), for non-negative integral values.

Express the following as trigonometric ratios of some acute angles. cosec (-60^@)

A six letters word is formed using the letters of the word LOGARITHEM with or without repetition. Find the number of words that contain exactly three different letters.

If the inverse of the matrix A=[{:(3, 4, 5), (2, -1, 8), (5, -2, 7):}] is B, then B^(T)=

Find the rate of change of the area of a circle with respect to its radius r when r=5cm.

A factory is operating in two shifts, day and night with 70 and 30 workers respectively. If per day mean wage of the day shift workers is rupes 54 and per day mean wages of all the workers is rupes 60 , Then per day mean wages of the night shift (in Rs.)is :

The vectors, p=(a+1)i+aj+ak, q=ai+(a+1)j+ak" and "r=ai+aj+(a+q)k. If 3(p.q)^(2)-lambdaabs(r times q)^(2)=0, then the value of lambda is _______

If y = sqrt(((x-1)(x-2))/((x-3)(x-4)(x-5))) find (dy)/(dx)

If f : [0,3] to [0,3] is defined by f (x) ={{:(1+x,0lt=xlt=2),(3-x,2ltxlt=3):}then fofo is

Let f(x) = (arc tan x)^(3) + (arc cot x)^(3) .If the range of f (x) is [a,b), then find the value of b/(7a).

Let f(x) = tan^(-1) x and g(x) = (x)/(1 + x^(2)), x gt 0 then

Find the area of the triangle formed by the tangent at P(x_(1), y_(1)) to the circle x^(2) +y^(2) = a^(2) with co-ordinate axes where x-(1) y_(1) ne 0.

Is ** defined on the set {1,2,3,4,5} by a ** b =L.C.M. of a and b a binary opertion ? Justified your answer.

Compute theintegrals I = int_(0)^(1) sqrt(2 x - x^(2)) dx

If A is a matrix of order 3xx3, then (A^2)^(-1)="........."

Sum of the focal distance of the ellipse (x^2)/(a^2) + (y^2)/(b^2) = 1 is

The system of equations 2x-y+z=0 x-2y+z=0 x-y+2z=0 has infinite of nontrivial solutions for

If A+B+C+D=360^(@) then show that sinA-B+sinC-sinD= -4cos((A+B)/2)cos((A+D)/2)sin((A+C)/2)

Let veca = 2hati+hatj, vecb = -hati+3hatj+hatk and vecc = hati+2hatj+5hatk be three vectors. Find (veca-vecb)xx(vecc-veca)

At an election, a voter may vote for any number of candidates, not greater than the number to be elected. There are 10 candidates and 4 are to be elected. If a voter votes for at least one candidate, then the number of ways in which he can vote is

Evaluate int sin^(4) x cos^(5) x dx

Rob spends (1)/(2) of his monthly paycheck, after taxes,on rent. He spends (1)/(3) on food and (1)/(8) on entertainment. If he donates the entire remainder, $500, to charity, what is Rob's monthly income, after taxes?

If the Roofean expression ( p oplus q ) ^^ ( ~ p odot q ) is equivelent ot p ^^ q where oplus , odot in( ^^ , vee ) , then the ordered pair (oplus, odot)is equal to

Let P(x)=|(x^(2)-13,4,2),(3,x^(2)-13,7),(6,5,x^(2)-13)| If x=-2 is a zero of P(x), then sum of the remaining five zerord id

Find the transberes common tangents of the circles x^(2) + y^(2) -4x -10y + 28 = 0and x^(2) + y^(2)+ 4x - 6y + 4 0.

The perimeter of a DeltaABC is 48 cm and one side is 20 cm. Then remaining sides of DeltaABC must be greaterthan :

Let f(x)=int_(0)^(x) (sint-cost)(e^t-2)(t-1)^3(t-1)^3(t-2)^5 dt , 0lt xle4 Then , the number of points where f(x) assumes local maximum value , is

If A and B are two events such that P(A|B)=0.6, P(B|A)=0.3, P(A)=0.1 then P(barAnnbarB)=

If C=[{:(,1,4,6),(,7,2,5),(,9,8,3):}] [{:(,0,2,3),(,-2,0,4),(,-3,-4,0):}] [{:(,1,7,9),(,4,2,8),(,6,5,3):}] Then trace of C+C^(3)+C^(5)+……+C^(99) is

A salesman has a 60% chance of making a sale to each customer. The behaviour of successive customers is independent. If two customers A and B enter. The probability that the salesman will make a sale to A or B is

Consider parabola P_(1)-=y=x^(2) and P_(2)-=y^(2)=-8x and the line L-=lx+my+n=0.Which of the following holds true (a point (alpha,beta) is called rational point if alpha and beta are rational)

Which of the following graphs represent function whose derivatives have a maximum in the interval (0,1) ?

On the set of positive rationals, a binary operation * is defined by ab=(2ab)/5 . If 2 x=3^(-1) then x=

Is defined on the set {1,2,3,4,5} by a b =L.C.M. of a and b a binary opertion ? Justified your answer.