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Determine P(E|F) Mother, father and son line up at random for a family picture﻿ E : son on one end,﻿ F : father in middle﻿

Find the second order derivatives of the functions e^(6x) cos 3x

Apply Binomial Theorem to find the value of (1.01)^5

If alpha, beta, gamma are the roots fo x^(3)-x^(2)+ax+b=0 and beta, gamma, delta are the roots of x^(3)-4x^(2)+mx+n=0. If alpha, beta, gamma and delta are INAP with common difference d then

The slopes of the focal chords of the parabola y^(2)=32 x which are tangents to the circle x^(2)+y^(2)-4 are

If f (x) =x ^(2) +1, then| f ^(-1) (17) |+| f ^(-1) (-3)| will be

If the angle between veca and vecb is 2pi//3 and the projection of veca in the direction vecb is -2, the |veca|=

(1)/(x(x+1)(x+2).....(x+n))=(A_(0))/(x)+(A_(1))/(x+1)+...+(A_(n))/(x+n) rArr A_(r)=(0 le r le n)

Probability of solving specific problem independently by A and B are (1)/(2)﻿ and﻿ 3(1)/(3) respectively. If both try to solve the problem independently, find the probability﻿ that﻿ (i) the problem is solved (ii) exactly one of them solves the problem.﻿

Solve the following differential equations.dy/dx=y+2

The polar of a point P w.r.t. a circle of radius a touching both x and y axis and lying in the first quadrant is x+2y=4a. The coordinate of P are

If z is a complex number such that Re(z)=Im(z), then

Examine the consistency of the system of linear equtions in 1 to 6 x+3y=5 2x+6y=8

Let ** be a binary operation on the set Z of integers as a**b=a+b+1. Then find the identity element:

Find which of the following of the operations given above has identity.

int (x^(2) +1)/(x^(4) + x^(2) + 1)dx =

If(1+ 2x+3x^2 ) ^(10)=a _ 0 +a _ 1 x +a _2 x ^ 2 + … +a _(20) x ^ (20), then(a _ 2)/(a_1)isequal to

A person takes 1//2 kg of cheese sandwitches of energy equivalent to 813 kJ. Suppose that all the energy is lost only through perspiration, what mass of water would he need to perpire in order to maintain his original temperature. Given : Enthalpy of vapurisation of water is 40.65 kJ mol^(-1).

Evaluate the following integrals. int(2sinx+3cosx+4)/(3sinx+4cosx+5)dx

S is a relation over the set R^(+) of all real numbers and it is given by (a,b)in S iff ab gt 0 Then S is

Evaluate int(x)/(x^(4)+1)dx

How many 5 digited numbers can be made with odd digits so that no two consecuitive digits are same.

If 1 is multiple root of order 3 for the equation x^(4)-2x^(3)+2x-1=0, then the other root is

If the area bounded by circle x^(2) + y^(2) = 4 the parabolay = x^(2) + x+ 1 and the curve y = [sin^(2) (x)/(4) + cos (x)/(4)]. Where [.] denotes the greatest integer function) and x-axis is (sqrt(3) + (2pi)/(3) - (1)/(k)) then the numerical quantity k should be ________

If X denotes number of heads obtained in tossing two coins. Then which of the following is false a) X(HH) = 2 b)X(HT) = 1 c)X(TH) = 0 d)X(TT) = 0

Two squares are inscribed in a circle of diameter sqrt2 units. Prove that the area of the common region of the squares is atleast 2(sqrt2-1).

Find the sum of all 4 digited numbers that can be formed using the digits 1,2,4,5,6 without repetition.

Evaluate the following inegrals intx^(3)(4+x^(2))^(2)dx

A stone is thrown in upward direction. Its equation is S=80 t-16 t^(2). The time to attain maximum height is …………. second.

Discuss the continuity of the function f given by f(x)= x^(3) + x^(2)-1

Let all chords of parabola y^(2)=x+1 which subtends right angle at (1,sqrt(2)) passes through (a,b) then the value of a+b^(2) is

If |z_1|=1,|z_2|=1and A = Arg(z_1,z_2),B=Arg(z_1//z_2),C=Arg(z_1+z_2),D=(z_1-z_2)arrange A,B,C,D in ascending order

If a,b and c are distinct positive real numbers in A.P, then the roots of the equation ax^(2)+2bx+c=0 are

Number of points ofdiscontinuity of f(x) =[x^(3)+3x^(2)+7x+2], where[.]representsthegreatest integer function in [0,1] is ___________.

Match the Section (A) with the Section (B) properly.

For the vectors vec(x) and vec(y),vec(x)+vec(y)=vec(a),vec(x)xx vec(y)=vec(b) and vec(x).vec(a)=1 then vec(x) = ………….., vec(y) = ……….

If a,b,c are noncoplanner vectors then (a.(b xx c))/((c xx a). B) + (b. (a xx c))/(c. (a xx b)) =

If the area of a circle increases at a uniform rate, then prove that perimeter varies inversely as the radius.

If a and b are the maximum and minimum values of the quadraticexpressions 1-2x - 5x^(2) and x^(2) - 2x + 5 respectively, then the set of all values of x for which the expression 5 ax^(2) + bx + 7 is positive, is

A point P moves such that the sum of the slopes of the normals drawn from it to the hyperbola xy = 16 is equal to the sum of ordinates of feet of normals . The locus of P is a curve C. If the tangent to the curve C cuts the corrdinate axes at A and B, then the locus of the middle point of AB is

A point P moves such that the sum of the slopes of the normals drawn from it to the hyperbola xy = 16 is equal to the sum of ordinates of feet of normals . The locus of P is a curve C. The area of the equilateral triangle inscribed in the curve C having one vertex as the vertex of curve C is

Let a_1,a_2,... a_49 be in A.P. Such that sum_(k=0)^12a_(4k+1)=416 and a_9+a_43=66.if a_1^2+a_2^2+...+a_17^2=140m, then m is equal to

Which of the following set are finite and which are infinite ?The set of prime number .

Given the graph of f(x), draw the graph each one of the following functions : (a) y=f(x)+3 "(b) " y= -f(x)+2 (c ) y=f(x+1)-2 "(d) " y= -f(x-1) (e ) y=f(-x) "(f) " y=f(|x|) (g) y=f(1-x)

If A is a square matrix of order 3, then |adj(adjA^2)| is equal to

Find the derivatives of the following functions :(1 xx)

Integration using trigonometric identities : int (cos^(8)x-sin^(8)x)/(1-2sin^(2)xcos^(2)x)dx=...+c

If a_(1), a_(2), a_(3), ......... , are in A.P. with common difference 5 and if a_(i)a_(j) != - 1 for i ,j = 1, 2, .... , n, then tan^(1)(5/(1 + a_(1) a_(2))) + tan ^(1)(5/(1 + a_(2)a_(3))) + ...... + tan^(-1)(5/(1 + a_(n - 1)a_(n))) is equal to

Determine P(E|F) Mother, father and son line up at random for a family picture E : son on one end, F : father in middle

Probability of solving specific problem independently by A and B are (1)/(2) and 3(1)/(3) respectively. If both try to solve the problem independently, find the probability that (i) the problem is solved (ii) exactly one of them solves the problem.

Let be a binary operation on the set Z of integers as ab=a+b+1. Then find the identity element: