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Find |veca-vecb|, if two vectors veca and vecb are such that |veca|=2,|vecb|=3 and veca*vecb=4.

Given the following frequency distribution with some missing frequencies {:(Class , "Frequency") , (10-20 ,, 180), (20-30 ,, --), (30-40 ,, 34) , (40-50 ,, 180) , (50-60 ,, 136) , (60-70 ,, --) , (70-80 ,, 50):} If the total frequency is 685 and median is 42.6 then the missing frequencies are

On a multiple choice examination with three possible answers for each of the five questions. Then what is the probabilitythat a candidate would get four or more correct answer is

Find the inverse of the following A=[[2,1,3],[4,-1,0],[-7,2,1]]

If A=[{:(1,2,1),(2,1,3),(1,1,0):}] then prove that A^3-2A^2-7A-4I_3=0. Hence find A^(-1)

Trachea is supported by :-

A vertical lamp-post, 6 m high stands at a distance of 2 m from a wall, 4 m high. A 105 m tall man starts to walk away from the wall on the other side of the wall, in line with the lamp-post. The maximum distance to which the man can walk remaining in the shadow is :

Determine whether the solution set is finite or infinite or empty: x lt 1, x in Z (set of integers)

intdx/((2x+5)sqrt(x+2))

The number of whole number solutions of x + y + z = 20 is

If y=e^(x)(log x), " then " xy_(2)+(x-1)y=

If alpha, beta are roots of equation x^(2)-4x-3=0 and s_(n)=alpha^(n)+beta^(n), n in N then the value of (s_(7)-4s_(6))/s_(5) is

(dy)/(dx) + 2x tan (x-y) = 1 rArr sin (x-y) =

The shortest distance between the lines r = (3t-4) hati -2thatj -(1+ 2t) hatkand r ( 6 + s) hati + (2- 2s) hatj + 2 (1 + s) hatk is

int (dt)/((e^(t) + e^(-t))^(2)) =

Evalute the following integrals int e^(-1"log(cosecx)")dx

If A = [( 1, cos theta , 1),( - cos theta ,1,cos theta ),( -1 , - cos theta ,1)] where0 lethetale2 pithen …..

Three normals from a point to the parabola y^(2)=4ax meet the axis of the parabola in points whose abscissa are in A.P. Find the locus of the point.

sec^(2)xtan y dx + sec^(2) y tan x dy = 0

If 2a + 3b + 6c = 0, then atleast one root of the equation ax^(2) + bx + c = 0 lies in the interval

The points O, A, B, X and Y are such that bar(OA)=bar(a), bar(OB)=bar(b), bar(OX)=3bar(a) and bar(OY)=3bar(b)," find "bar(BX) and bar(AY) in terms of bar(a) and bar(b). Further if the point p divides bar(AY) in the ratio 1 : 3 then express bar(BP) interms of bar(a) and bar(b).

From the following frequency distribution (i)Find mean. (ii)Calculate variance and standard deviation.

Fromthe polynomial equation whose roots are 3,2,1+I,,1-I

If f(x)={((sqrt(1+kx)-sqrt(1-kx))/x),((2x+1)/(x-1)):} if -1lexlt0 is continuous at x=0, then the value of

Find the area enclosed between y=x^(2)-5x and y=4-2x

I: In a Delta ABC, if a=3,b=4, angle A=30^@ the number of possible triangles is 2 II. In a Delta ABC, ((a+b)cosC+(b+c)cosA+(c+a)cosB)/(sinA+sinB+sinC)=R

1+(log_(e)5)/(1!) +(log_e5)^2/(2!)+(log_e5)^3/(3!)+ .......oo =

A : (3^(2))/(2!)+(3^(4))/(4!)+(3^(6))/(6!)+...=cosh3-1.""R:coshx=1+(x^(2))/(2!)+(x^(4))/(4!)+....

If x+y ge 6, 2x+y ge 8, x ge 0, y ge 0 then the minimum value of f=x+y is

int_(1)^(32) (dx)/(x^(1//5)sqrt(1+x^(4//5)))=

Find the second order derivatives of the functions given in Exercises 1 to 10. e^(x) cos 3x.

Let I_(1) and I be two lines intersecting at P. If A_(1), B_(1), C_(1) are points on hi and A_(2), B_(2), C_(2),D_(2), E_(2) are points on l_(2) and if none of these coincides with P, then the number of triangles formed by these eight points, is

If x=phi(t) is a differentiable function of 't', then prove thatintf(x)dx=intf[phi(t)]phi'(t)dt.

Consider thepolynomial fucntion f(x) = |{:((1+x)^(2),,(1+2x)^(b),,1),(1,,(1+x)^(a),,(1+2x)^(b)),((1+2x)^(b),,1,,(1+x)^(a)):}| a,b beingpositiveintegers. Whichof the followingis true ?

If y= f(x) be an invertible function with inverseg and h(x) = x f(x), then int_(f(a))^(f(b)) g(x) dx+ int_(a)^(b) f(x) dx is equal to

If the straight lines 2x+3y-3=0 and x+ky+7=0 are perpendicular, then the value of k is

If A and B are any two events such that P(A) + P(B) -P(A and B) = P(A), then

Solve the equation 6x^6-25x^5+31x^4-31x^2+25x-6=0

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

Find square root of a^2-1+2asqrt(-1)

Let f(x) = sin a x^(- +) cos bx be a periodic function, then

Prove that two parabolas y_(2)=4ax "and" x^(2)=4by intersect (other than the origin ) at an angle ofTan^(-1)[(3a^(1//3)b^(1//3))/(2(a^(2//3)+b^(2//3)))] .

Find the asymptotes of the following curves : y=x/(x^(2)+1)

A department store escalator is 25 feet long and forms an angle of 43^@ with the floor , with is horizontal . What of the follow is an expression for the horizontal distance of the escalator from beginning to end ?

If M is the midpoint of the side vec(BC) of a triangle ABC, prove that vec(AB)+vec(AC) = 2vec(AM)

The value of int_(- pi//2)^(pi//2) ((2- sin theta)/( 2+ sin theta)) d theta is

For what values of x in R, the following expressions are negative i) -6x^(2)+2x -3 ii) 15+4x-3x^(2) iii) 2x^(2)+5x -3 iv) x^(2)-7x+10 v) x^(2)-5x-6

Let A_1,A_2,A_3,….,A_m be the arithmetic means between -2 and 1027 and G_1,G_2,G_3,…., G_n be the gemetric means between 1 and 1024 .The product of gerometric means is 2^(45) and sum of arithmetic means is 1024 xx 171 The number 2 A_(171,G_5^2+1,2A_(121)