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[b xx c c xx a a xx b] =

The number of vectors of units length perpendicular to both the vectors hati +2hatj - hatkand2hati + 4hatj -2hatkis

Evaluate the integerals.int e ^(x) ((1+ x log x)/(x)) dx on (0,oo).

Find the number of 9 digit natural numbers in which each digit appears at least thrice.

Find the volume of the parallelopiped whose edges are represented by vec(a) = 2 hat(i) - 3 hat(j) + 4 hat(k) , vec(b) = hat(i) + 2 hat(j) - hat(k), vec(c) = 3 hat(i) - hat(j) + 2 hat(k)

Form the differential equation from y = Ae^(3x) +Be^(-2x).

Draw the graph of y = cos pix.

If the area of the region bounded by the curves y=x =x^(2)and x = y^(2)is k then the area of the region bounded by the curves (x+sqrt(3y))/(2)=(sqrt(3x)-y^(2))/(2) and (sqrt(3x)-y)/(2)=(x+sqrt(3y))^(2)/(2) is

If (sinalpha)x^(2)-2x+bge2 for all real values of x le 1 andalpha in(0,(pi)/(2))cup((pi)/(2),pi), then the possible real values of b is/are

If int(x^(3))/(4+x^(16))dx=(A)/(8)tan^(-1)(z)/(sqrt(2))-(1)/(64)log |(u-sqrt(2))/(u+sqrt(2))|+C , where u = y + 1/y and z = y - 1/y = x^(4) // sqrt(2) then A is equal to.

Find the equation of the circle which touches the circle x^(2) + y^(2) - 2x - 4y - 20 = 0 externally at (5, 5) with radius 5.

If |bar(a)|=10,|bar(b)|=2 and bar(a).bar(b)=12 then the value of |bar(a)xx bar(b)| is …………

Find the equation of the circle passing through the point (4,1) and (6,5) and whose centre is on the line 4x + y = 16.

A particle moves so that the distance moved is according to the law s(t)=(t^(3))/(3)-t^(2)+3. At what time the velocity and acceleration are zero respectively ?

Find the 2xx2 mtrix X Given [x y z ]-[-4 3 1] =[-5 1 0] derermine x,y,z.

Let p:7 is not greater than 4 and q: Paris is in France be two statements. The ~(pvvq) is the statement

Discuss the applicability of Rolle's theorem for the function f(x)={{:(x^(2)-4",",x le1),(5x-8"," , x gt1):}

Find the area bounded by the curves 4 y = |4-x^(2)|, y = 7 - |x|

Show that int_(0)^(n pi + alpha) |sin x|dx = (2n+1) - cos alpha where n in N and 0 le alpha le pi

If (2i + 4j + 2k) xx (2i - xj + 5k) = 16i - 6j + 2xk, then the value of x is

The solution of (dy)/(dx) = (4x+9y+1)^(2) is

Integrate the function is Exercise. (1)/(x-x^(3))

If omega is a complex cube root of unity, then the value of sin{(omega^(10)+omega^(23))pi- (pi)/(6)} is

Find the number of ways of arranging the letters of the word a^(4)b^(3)c^(5) in its expanded form.

If int(log(x+sqrt(1+x^(2))))/(sqrt(1+x^(2)))dx =(gof)(x)+c then

if A[{:(2,-3,-5),(-1,4,5),(1,-3,-4):}]and B=[{:(2,-2,-4),(-1,3,4),(1,-2,-3):}],thenshowthat (i) AB=A and BA=B.

Find the vector equation of the line passing through the point (1, 2, -4) and perpendicular to the two lines : (x-8)/(3)=(y+19)/(-16)=(z-10)/(7) and (x-15)/(3)=(y-29)/(8)=(z-5)/(-5).

MaximizeZ=8x+9y, subject to the contraints given below: 2x+3y le 6, 3x-2y le 6, y le 1, x,y ge 0

If the sum of two unit vectors is a unit vector, then the magnitude of their diffierence is

Evaluate int_(-1)^(1) f(x)dx, where f(x) = {:(1,2x, x le 0),(1+2x, x ge 0):}

If (i^(4)+i^(9)+i^(16))/(2-i^(8)+i^(10)+i^(3))=a +ib, then (a,b) is

Evaluate the following integrals int(x^(2)-1)/(x^(4)+1)dx

Differentiate the functions given in Exercises 1 to 11 w.r.t. x. x^(x)-2^(sin x).

Find the number of integral solutions of x+y+z+t=29 where xge1,yge1,zge3 and tge0

let k gt 0 , s_alpha -= x^2 + y^2 + 2alpha x + k= 0 " and "s_beta -= x^2 + y^2 + 2 beta y - k= 0 . Then match the items of List -I with those of List - II The correct match is

Let P be a poointon the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1(agtb) in the first or second quadrants whowse foci are S_(1)and S_(2). Then the least possible value of circumradius of DeltaPS_(1)S_(2) will be

If the point whose position vectors are 2hati+hatj+hatk,6hati-hatj+2hatk and 12hati-5hatj+phatk are collinear, then the value of p is

If bar(a)=hati+hatj+2hatk and bar(b)=2hati+hatj-2hatk, find the unit vector in the direction of (i) 6bar(b)"" (ii) 2bar(a)-bar(b)

Evaluate (i) int_(0)^(pi//2) sin^(2) x dx

With usaual notation in a triangle ABC, prove that r^2+s^2+4Rr= ab+bc+ca.

Obtain the following integrals : int (2x+3)/(x^(2)+3x)dx

Let setA = { 1, 2, 3, ….., 22}. Set B is a subset of AandB has exactly 11 elements, find the sum of elements of all possible subsets B .

If is given the sigma_(x)^(2)=9,r=0.6 and regression equation of Y on X is 4x-5y+33=0 find Var (Y).

The roots of the equation x^(3)-14x^(2)+56x-64=0 are in

Consider the following If vec(a) and vec(b) are the vectors forming consecutive sides of a regular hexagon ABCDEF, then 1. vec(CE)=vec(b)-2vec(a) " " 2. vec(AE)=2vec(b)-vec(a) 3. vec(FA)=vec(a)-vec(b) Which of the above are correct?

If 1,2,3 and 4 are the roots of the eqaution x^(4) + ax^(3) + b x^(2) + cx + d = 0,thena + 2b + c =

A bag containsn white and n black balls. Pairs of balls are drawn until the bag is empty. The probability that each pair consists of one white and one black ball is

The vertices of the feasible region determined by some linear constraints are (0, 2), (1, 1), (3, 3), (1, 5). Let Z = px + qy where p, q gt 0. The condition on p and q so that the maximum of Z occurs at both the points (3, 3) and (1, 5) is ……..

Consider the straight line 3x + 4y + 8 = 0 ﻿ i. What is the slope of the line which is perpendicular to the given line?﻿ ii. If the perpendicular line passes through (2,3), form its equation, ﻿ iii. Find the foot of the perpendicular drawn from (2,3) to the given line.﻿

Consider the straight line 3x + 4y + 8 = 0 i. What is the slope of the line which is perpendicular to the given line? ii. If the perpendicular line passes through (2,3), form its equation, iii. Find the foot of the perpendicular drawn from (2,3) to the given line.