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If y = mx + 6 is a tangent to the hyperbola he parabola y^(2) = 4ax, then the length ofthe latus rectum of the parabola is

The slopes of the lines which make an angle﻿ 45^(@) with the line 3x - y = -5 are

Solve (x^(3) - 3xy^(2)) dx + 2x^(2)ydy= 0

Find the sum upto n termsofthe series 1*4*7*10*13*16+"....".

A beg contains 4 red and 4 black , another bag contains 2 red and 6 black balls. One of the two bags is selected at random and a ball is drawn from the bag which is found to be red. Find the probability that the ball is drawn from the first bag.

Solution of differential equation f^(')(x)f^(''')(x)=3(f^('')(x))^(2),(y=f(x)) is:

If b be the p^(th)term of G.P. where (p+q)^(th)and (p - )^(th)terms are a and c respectively and if f(x)=ax^(2)+2bx+c,then for all x in R

Check the injective and surjective of the following functions : f : Z rarr Z given by f(x) = x^2

Find the parametric form of vector equation, and Cartesian equations of the plane containing the line vecr=(hati-hatj+3hatk)+t(2hati-hatj+4hatk) and perpendicular to plane vecr*(hati+2hatj+hatk)=8.

Let S={(x,y):abs(abs(absx-2)-1)+abs(abs(absy-2)-1)=1). If S is made out of wire, then the length of wire required is

Translate "Chinu and Minu went to Calcutta, but Minu came back earlier since she lost all her money" propositions into symbolic form, stating the prime components

The vector equation of the line, whose cartesian equation is (x-3)/(2)=(y+4)/(5)=(z-6)/(3) is

(0,-1) and (0, 3) are two opposite vertices of a square. The other two vertices are...

Find the value of k, so that the length of the subnormal at any point on the curve xy^(k)=a^(k+1) is a constant.

Integrate the function in Exercise. e^(x)((1)/(x)-(1)/(x^(2)))

Let V_(r) denotes the sum of the first r terms of A.P. whose first term is r and the common difference is (2r-1). Let T_(r)=V_(r+1)-V_(r)-2 and Q_(r)=T_(r+1)-T_(r) for r = 1, 2 ………… Which one of the following is a correct statement

Value of [1^(-i)] is [.] G.I.F.

Differentiate tan^2x+a^x

Evaluate the determinants below in examples number 1 and 2 |{:(costheta,-sintheta),(sintheta,costheta):}|

Let f(x)=[x] where [x] be the greatest integer less than or equal to x. g(x)={{:(0,","x inZ),(x^2,"," x in R-Z):} z is the set of integers , phi(x)=fog(x) and Psi(x)=gof(x). Then on the set R-Z .

Find the area of the triangular region boundedby the sides y = 2x + 1, y = 3x + 1 andx = 4

A bag contains 5 balls of unknown colours. A ball is drawn at random from it and is found to be red. Then the probability that all tha balls in the bag are red, is

The normals at three points P,Q,R of the parabola y^(2)=4axmeet in (h.k) . The centroid of triangle PQR lies on

Let **' be the binary operation on N given by a**'b= L.c.m. of a and b. Find 5**7, 20**16

If f(x)={:(,(sin (1+[x]))/(x),"for "[x] ne 0),(,0,"for [x]=0"):} where [x] denotes the greatest integer not exceeding x then underset(x to0-)"Lt" f(x)=

Bag I contains 3 red and 4 black balls. While Bag II contains 5 red and 6 black balls. One ball is drawn at random from one of the bags and it is found to be red. Find the probability that it was drawn from Bag II.

If sinA+sinB=a and cosA+cosB=b, show that sin(A+B) = (2ab)/(b^2+a^2)

Find the mean deviation from the mean for the set of obervations 1,2,3.

Express tan^(-1)((cosx)/(1-sinx)),-(3pi)/2ltxltpi/2 in the simplest form.

Let X and Y be the sets of all positive divisors of 400 and 1000 respectively ( including 1 and the number). Then n(XcapY)=

The values of a for which the function f(x)=sin x - ax + b increases on R are …………..

Amy drove the 200 miles to New Orleans at at average speed 10 miles per hour faster than her usual average speed. If the complwrws the trip in 1 hour less than usual, what is her usual driving speed, in miles per hour?

If a.hati=4 then (axx hatj).(2hatj-3hatk) is equal to

Find the number of ways to arrange 8 persons around circular table if never sit together

If (d)/(dx)((1+x^2+x^4)/(1+x+x^2)) = a+bx, find the values of a and b .

One atom of an element x weigh 6.643 xx 10^(-23) g. Number of moles of atom in 20 kg is :-

Find int(xsin^(-1)x)/(sqrt(1-x^(2)))dx

The smallest natural number 'n' for which n!lt((n+1)/2)^(n) holds is

If r^(3)+|r|=0, what are the possible values of r?

Solve 4-x^(2) lt 0 by algebric method and graphical method.

Five cities A,B,C,D,E are connected to each other by straight roads. What is the total number of such roads?

If Integration using trigonometric identities : int(cos 8x+1)/(tan2x-cot 2x)dx=acos 8 x+c then a=..........

Equation of the tangent at a point P on the parabola y^(2)=4ax, the normal at which is at a distance a sqrt5//4 from the focus of the parabola is

Let f(X)=In (2x -x^2)+ sin (pix)/(2). Then which one of the following options is not correct?

Find the second order derivatives of the functions given in Exercises 1 to 10. x^(2)+3x+2

Prove that if to each element of any row or column of a determinant, the equimultiples of corresponding elements of other row (or column) are added, then value of determinant remains the same.

Find the Quantifiers There exists an even prime number other than 2.

Which of the following is true Statement-I : int_(0)^(2pi) sqrt((1-cos2x)/(2)) dx=4 Statement-II : int_(-1)^(1) log((1+x)/(1-x))dx= 2 int_(0)^(1) log (1+ x)/(1-x)dx

The slopes of the lines which make an angle 45^(@) with the line 3x - y = -5 are

Find the sum upto n termsofthe series 147*101316+"....".

Let ' be the binary operation on N given by a'b= L.c.m. of a and b. Find 57, 2016