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If f(y)=e^(y),g(y)=y:ygt0andF(t)=int_(0)^(t)f(t-y)g(y)dy, then

If ax + by^(2) = cos y find (dy)/(dx).

Solve: 1(1/ysinx/y-y/x^(2)cosy/x+1)dx+(1/xcosy/x-x/y^(2)sin y/x+1/y^(2))dy=0

The point which divides the line joining the points (1,3,4) and (4,3,1) internally in the ratio 2:1, is

Find the variance of the number obtained on a throw of an unbiased die.

If the foot of the perpendicularfrom (0,0,0) to the plane is (1,2,2) then the equation of the plane is

The mean and standard deviation of 10 observations x_(1), x_(2), x_(3)…….x_(10) are barx and sigmarespectively. Let 10 is added to x_(1),x_(2)…..x_(9) and 90 is substracted from x_(10). If still, the standard deviation is the same, then x_(10)-barx is equal to

Find the number of 4 digited numbers that can be formed by using the digits 0, 2, 3, 5, 7, 8 which are divisible by i) 2 ii) 3 iii) 4 i)

Find the vertex and focus of 4y^(2)+12x-20y+67=0

Consider a binary operation ** on N defined as a"*"b=a^(3)+b^3. Choose the correct answer.

Find the projectionof thevector veca= 2 hati+ 3hatj+ 2hatkon the vectorvecb = hati +2hatj +hatk

If x_(1),x_(2),x(3)as well as y_(1),y_(2),y_(3) are in geometric progression with the same common ratio,then the points (x_(1),y_(1)),(x_(2),y_(2)),(x_(3),y_(3))

Evaluate the following:lim_(xtoinfty)(2x+1)/(3x-2)

Select the CORRECT order of E.A. ?

Differentiate the following w.r.t. x: log (cos e^(x))

A box contains 100 bulbs, out of which 10 are defective. A sample of 5 bulbs is drawn. The probability that none is defective is

Negation of the proposition : If we control population growth, we prosper

Find three distinct positive integers with the least possible sum such that the sum of the reciprocals of any two integers among them is an integral multiple of the reciprocal of the third integer.

If A and B are symmetric matrices of the same order with AB!= BA, final whether AB-BA is symmetric or skew symmetric.

The plane y-z+1=0 is_____

If p and q are chosen randomly from the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} with replacement. Find the probability that the roots of the equation x^(2) + px + q = 0 are real.

Resolve (3x^(3)-8x^(2)+10)/((x-1)^(4)) into partial fractions.

If a leap year is selected at random, what is the chance that it will contain 53﻿ tuesdays?﻿

Find the approximate change in the volume V of a cube of side x metre caused by increasing the side by 1%.

Check the injectivity and surjectivity of the following function . f:R rarrR , f(x) = {{:(2x+1,xge0),(x^2,x lt0):}

Let alpha^(k) when k=0, 1, 2, 3, 4….253 are 254^(th) roots of unity then the unity digit of sum_(k=0)^(253)|z+alpha^(k)z^(2)|^(2) is ________ (where z=e^(i((2pi)/7)))

Find the equation of tangents of the following curves at the given points: (i) Curvex^(2) = 25 at point (3, 4) (ii) Curve y = 2x^(3) + 2x^(2) - 8x+7 at point (1, 3) (iii) Curve y = x + 2/x at point (2, 3) (iv) Curve y^(2)(x-1) = 4x^(2) at point (5, 5)

Let f: R to R be a differentiable function, such that f(0) = 0, f((pi)/(3)) = 3.53. If G(x)= int_(x)^(pi/3) (f'(t) sec t+ sec t tan t f(t)) dt, x in (0, (pi)/(2) ], then lim_(x to oo)G(x) is equal to

If all the letters of the word ARRANGE are arranged in all possible ways, in how many of words we will have the A's not together and also the R's not together?

(1) /( cos 80^@) - (sqrt(3))/( sin 80 ^@) =

Three dice, red, blue and green in colour arerolled together. Let B be the event that sum of the numbers shown up is 7. Let A be the event that the red die shows 1. The conditional probability of the events A given B, P (A|B) is

If the function d^(-x) f(X) assumes its minimum in the interval [0,1] at x = 1//4 which of the following is true ?

Anintegeris chosenfrom{2K//-9le K le 10}.the probabilitythat itisdivisibleby both4and6is

IF theequationax^2 + 2bx + 3c =0and3x^(2)+8x+15=0 havea commonroot, wherea,b,care thelengthof the sidesof aDeltaABC, thensin ^2A + sin^2 B+ sin^(2)C=

At a point P on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2)) =1 tangents PQ is drawn. If the point Q be at a distance (1)/(p) from the point P, where 'p' is distance of the tangent from the origin, then the locus of the point Q is

What is the maximum number of 3 x 3 square that can be formed from the square in the 6 x 6 checkerboard shown?

If x =sin t,y = sin 2t then prove that (1-x^2)(d^2y)/(dx^2)- x dy/dx + 4y = 0

Length of the principal axis of the hyperbola xy= 32is

Let y=f(x) ={{:(e^((1)/(x^(2))), if x ne 0),( 0, ifx=0):} thenwhichof thefollowing can best represent the graph of y=f(x)?

The value of lim_(xrarroo)[(1^((1)/(x))+2^((1)/(x))+3^((1)/(x))+…+10^((1)/(x)))/(10)]^(10x) is

A child atttempts to open a five disc-lock.He takes 5 seconds time to dial a particular number on the disc.If he does so for 5 hrs .Every day,then the numbers of days he would be sure to open the lock is

The solution of the differential equation (dy)/(dx) - 2y tan 2x = e^(x) sec 2x is

Find the radical centre of the circles x^(2)+y^(2)+4x=7=0, 2x^(2)+2y^(2)+3x+5y-9=0 and x^(2)+y^(2)+y=0.

Find the area enclosed between y= sqrt(5-x^(2)) and the lines y= |x-1|

The sum of the series 1 + 1/(4.2!) + 1/(16.4!) + 1/(64.6!) + ....infty is

1+(2)/(6)+(2.5)/(6.12)+(2.5.8)/(6.12.18)+….....=

If a lne makes angles. 90^@, 135^@, 45^@with the x,y and Z−axes respectively, find its direction cosines.

If a leap year is selected at random, what is the chance that it will contain 53 tuesdays?