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If A and B are invertible matrices of same order then prove that (AB)^(-1) = B^(-1)A^(-1)

The three sides of a trapezium are equal, each being 6 cm long. Find the area of trapezium when it is maximum.

Let r be the range and S^(2)=(1)/(n-1) sum_(i=1)^(n) (x_(i)-overline(x))^(2) be the SD of a set of observations x_(1),x_(2),.., x_(n), then

Natural numbers k,l,p and q are such that if a and b are roots of x^(2) - kx + l=0, then a+1/b and b+1/a are roots of x^(2) -px + q=0. What is the sum of all possible values of q?

Two particles P and Q located at the points with coordinates P(t^3-16t-3),Q(t+1,t^3-6t-6) are moving in a plane. The minimum distance between them in their motion is

What is the standard enthalpy change at 298 K for the following reaction? CO_(2) (g)+ C("diamond") rarr 2CO(g) Given : DeltaH_(f)^(@)(CO,g) = - 110.5 kJ//mol : Delta H_(f)^(@)(CO_(2),g) = - -393.5 kJ//mol Delta H_("transition")^(@)[C("graphite")rarr C("diamond")] = 2.0 kJ//mol

Draw the graph of y = sin pisqrt(x).

Line A passes through the cooredinate points (-2/5, 0) and (0,1). Which of the following lines will line A never intersect ?

A cyclist covers his first three miles at an average speed of 8 m.p.h. Anoter two miles at 3m.p.h. and the last two miles at 2m.p.h. The average speed for the entire journey is : (in m.p.h)

Find the coordinates of the mid-point of the following pairs of points .(-7,3), (8,-4) .

If cos x=|sinx| then, the general solution is

Find the derivative of x^(3) from the first principle.

Let [ x ] denote the largest integer le x. If the number of solutions of cos^(2)theta is k, then for x in [pi/4,pi/3] the value of k^(tan^(2)x)

If a function f is defined by : f(x) = 0, when x = 1, = x^(3) - 1, when 1 lt x lt oo, = x - 1, when -oo lt x lt 1, then at x = 1, f is

int(sin 2x)/(sin5x*sin3x)dx=.....+c

For any two statements p and q, the statement ~(p ^^ q) vee (~p ^^ q) is equivalent to

Find the number of ways to arrange 5 boys and 5 girl in a row such that no two girls sit together

Let a_n = int_(0)^(pi//2) (1-cos2npi)/(1-cos2pi)dx The value of |{:(pi//2 , a_2 , a_3),(a_4 ,a_5, a_6),(a_7 , a_8 , a_9):}|=

State which of the following are positive ? cot 375^@

int_(0)^(1) sin (2 tan^(-1) sqrt((1+x)/(1-x))) dx is equal to

Consider an ellipse (x^(2))/(13)+(y^(2))/(4)=1 and a variaote point P(1-,2t) is takne in such a way that angle S_(1)PS_(2) is maximum where S_(1) and S_(2) are the foci of the given ellipse then the value of (S_(1)P)/(S_(2)P) is

When a pair of six faced fair dice are thrown, the probability that the sum of the numbers on the two dice is greater that 7, is

Length of median from A to BC of triangle﻿ ABC where A (2,5) B (7,-1) and C (3,5) is

The two geometric means between the numbers 1 and 64 are

A fair die is rolled . Consider events E = {1, 3, 5} F = {2, 3} and G = {2, 3, 4, 5} . FindP(E//F) and P(F//E)

Integrate the following functions x^2/sqrt(x^6+a^6)

The points in the set {zinC: Arg " ((z-2)/(Z-6i))=pi/2}lie on the curve which is a (where C denotes the sets of all complex number )

The solution of (dy)/(dx) = (x + 2y -3)/(2x + y -3) is

Find (dy)/(dx): x= te^(t),y=1 + log t

Prove theA nn B = B nn A results of the sections 1.13 and 1.14 that are stated with our proof.

Evaluate : (i) int_(0)^(pi//2)xcosxdx (ii) int_(0)^(pi)cos2xlog sinx dx (iii) int_(1)^(2)(logx)/(x^(2))dx (iv) int_(0)^(pi//6)(2+3x^(2))cos3x dx

The vertices of a triangle are (6, 0), (0, 6) and (6, 6). Then distance between its circumcentre and centroid, is

Origin is the orthocentre of DeltaABC where A = (5, -1), B = (-2, 3) then the orthocentre of DeltaOAC is

I.F. Of the differential equation dy/dx+2y=e^(2x) is :

Find the probability of getting sum 7 when two dice are rolled

If the points (1, 1, lambda) and (-3, 0, 1) be equidistant from the plane vecr.(3hati+4hatj-12hatk)+13=0 find the value of lambda.

Four bad apples are mixed with 20 good apples. If 2 apples are drawn at random at a time then find mean of number of bad apples

Consider the inequalities x_(1)+x_(2)le3,2x_(1)+5x_(2)ge10x_(1),x_(2)ge0 which of the following point does not lie in the feasible region ?

Determine the intervals of concavity of the curve f(x)=(x-1)^(3)(x-5),x in Rand , points of inflection if any

Evaluate the following integrals (iii) int_(0)^(pi/2) (1)/(4 +5 cos x) dx

Evaluate the definite integral in exercise overset(1)underst(0) int (dx)/(1+x^(2))

If n= (sqrt2 +1)^6. Then the integer just greater than n is

Evaluate the following integrals. intcosxcos2x cos3xdx

Solve graphically x le 0

To prove geometrical properties of an ellipse, we may take its standard equation as (x^2)/(a^2)+(y^2)/(b^2)=1 we will assume that a gt bgt0and foci S,S' lie on positive and negative side of X-axis, respectively. If P is any point on the ellipse and G is same as above, then S'G"/"SG must be:

If the vertices of a Delta ABC are A = (2, 3, 5), B = (-1, 3, 2), C = (3,5, -2) then the area of the DeltaABC (in sq. units) is

Number of points lying on the line 7x+4y+2=0 which is equidistant from the lines 15x^2+56xy+48y^2=0 is

For x,y in R define a relation R by x R y if and only if x-y +sqrt(2) is an irrational number .Then R is

Write the differential equation of parabolas y^2=8x+c

A relation R={(x,y):x,y in A and x lt y} is defined on set A={1,2,3,4,5}. The relation R is :

Length of median from A to BC of triangle ABC where A (2,5) B (7,-1) and C (3,5) is