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f(x)= (sqrt2 cos x-1)/(cot x-1), x ne (pi)/(4). If the function f(x) is continuous at x= (pi)/(4) then find f((pi)/(4))

If A=[{:(2,5,3),(3,4,-2),(4,-6,-2):}], find A^(-1) . Hence solve the system of equations 2/x+3/y+4/z =-3, 5/x+4/y-6/z=4, 3/x-2/y-2/z=6

If veca+vecb+vecc = vec0, |veca| = 3 , |vecb| = 5 and |vecc| = 7, find the angle between veca and vecb.

Let the complex number z_(1) , z_(2) , z_(3) be the vertices of an equilateral triangle . Let z_(theta) be the circumcentre of the triangle . Then z_(1)^(2) + z_(2)^(2) + z_(3)^(2) =

The unit vector parallel to the vecotr bar(a)-bar(b) is ……………. where bar(a)=(1,2,-3) and bar(b)=(-2,-4,-9)

Let A_(1), A_(2)…….A_(7) be a polygon and a(1), a_(2)……a_(7) be the complex numbers representing vertices A_(1), A_(2)……A_(7). If |a_(1)|=|a_(2)|=……….|a_(7)=R, then sum_(1le i lt j le 7)|a_(i)+a_(j)|^(2)

Prove that: |{:(a^(2)+1, ab, ac),(ab, b^(2)+1, bc):}|

Evaluate int_(0)^(1)x^5 (sqrt(1-x^2))^3dx

Let A be a non-singular square matrix of order 3×3.Then abs(adjA) is

If f(x)=x^(9)-6x^(8)-2x^(7)+12x^(6)+x^(4)-7x^(3)+6x^(2)+x-3,f(6)=

Solve the inequation sqrt(x+2) gt sqrt(8-x^(2)).

Integrate the functions x/(9-4x^(2))

Evaluate the following : [[37,-3,11],[16,2,3],[5,3,-2]]

If A+B+C=180^@ " then " sin^(2)""(A)/(2)-sin^(2)""(B)/(2)+sin^(2)""(C)/(2)=

A line passes through the point of﻿ intersection of the lines 100x + 50y-1=0﻿ and 75x + 25y + 3 = 0 and makes equal﻿ intercepts on the axes. Its equation is﻿

intsin^3xdx

If n is odd, then Coefficient of x^n in (1+ (x^2)/(2!) +x^4/(4!) + ....oo)^2 =

Evaluate the following (vi) int_(0)^(25) [sqrt(x)]dx

Solve: tan^(-1) ((1-2x)/(1+2x)) = 1/4 tan^(-1) ((4pi)/(1-4x^(2)))

The truth table of(~q) rArr~ p is

Write the order and degree of the differential equation given by : (d^2y)/dx^2=[1+(dy/dx)^2]^(4/3)

Let f:XtoY be a function and A_(y)={(f^(-1)(y))/(yinY)} Then A_(i)nnA_(i)=phi(i""nej)AAi,jinYanduu_(yiny)A_(y)=X, if

A black and a red dice are rolled.﻿ (a) Find the conditional probability of obtaining a sum greater than 9, given﻿ that the black die resulted in a 5.﻿ (b) Find the conditional probability of obtaining the sum 8, given that the red die﻿ resulted in a number less than 4.

Let X be the random variable with following probability distribution. therefore E(X^(2)) =..............

Find |vec(x)|, iif for a unit vector vec(a), (vec(x)-vec(a)).(vec(x)+vec(a))=12.

If the remainders of the polynomialf(x) when divided by x-1, x-2 are 2, 5 then the remainder of f(x) when divided by (x-1)(x-2) is

Find the 4th term of the extension (x - 1/x)^10

The mean and standard deviation of 10 observations are found to be 10 and 4 respectively. Later it was found that one itemis mistaken as 10 instead of 12. Findthe correct mean and standard deviation.

The polars of a point P w.r.t. two given circles meet in Q .The radical axis of the circles divide PQ in the ratio

Find derivatives of the following functionsIn (e^(n x) + e^(-n x))

Classify the following measures as scalars and vectors . (i)10 kg (ii) 2 meters north (iii)40^(@)(iv) 40 watt (v) 10^(19) coulomb (vi) 20m//s^(2)

Differentiate the functions with respect to x. (sin (ax+b))/(cos (cx+d))

If I is identify matrix of order two, then 3I would be which matrix ?

Lethata and hatc are unit vectors and |vecb|=4. If the angle between hata and hatc is cos^(-1)((1)/(4)), and hatb-2hatc=lambda hata, then the value of lambda can be :

Find the particular solution of (1+x^(3))dy - x^(2)y dx = 0 satisfying the initial conditions x = 1, y = 2.

Given that the two numbers appearing on throwing two dice are different. Find﻿ the probability of the event the sum of numbers on the dice is 4".﻿

For the expansion (x sin p + x^(-1)p)^(10), (p in R),

A tube of ...............

A = (1,2) , B= ( 6,-10 )locus of P such that PA- PB =13 is

Applying the iteration method , find all roots of the equation4x-5Inx = 5 accurate to four decimal places .

Evaluate the definite integrals int_(0)^(pi/2)sin2xtan^(-1)(sinx)dx

Number of triangle formed by joining the vertices of n sided polygn which has no side common with that on the polygon is

If a tower subtends equal angles at four points P, Q , R and S that lie in a plane containing the foot of the tower , the which fo the following statements is always true (here, the tower is perpendicular to the plane containing the points P, Q,R,S)

If a set A has n elements and another set B has m elements, what is the number of relations from A to B ?

Out of 100 students, two sections of 40 and 60 are formed. If you and your friend are among the 100 students, find the probability that (i) you both enter the same section (ii) you both enter the different sections.

which ofthefollowinginequalities are valid-

Which of the following function (s) is/are even ?

The solution of tan y (dy)/(dx) = sin (x+y) + sin(x-y) is

The product of the perpendiculars from the foci on any tangentto the ellipse x^(2)//a^(2)+y^(2)//b^(2)=1 is

If alpha is a non-real and alpha=(1)^(1//5) then the value of 2^(|1+alpha+alpha^2+alpha^(-2)+alpha^(-1)|) is equal to

A line passes through the point of intersection of the lines 100x + 50y-1=0 and 75x + 25y + 3 = 0 and makes equal intercepts on the axes. Its equation is

A black and a red dice are rolled. (a) Find the conditional probability of obtaining a sum greater than 9, given that the black die resulted in a 5. (b) Find the conditional probability of obtaining the sum 8, given that the red die resulted in a number less than 4.

Given that the two numbers appearing on throwing two dice are different. Find the probability of the event the sum of numbers on the dice is 4".