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Find the sum of the following C_1 - 2C_2 + 3C_3 - ..... + n(-1)^(n-1) C_n

The point of intersection of the direct common tangents drawn to the circles (x+11)^(2)+(y-2)^(2)=225 and (x-11)^(2)+(y+2)^(2)=25 is

Find dy/dxifxy=e^((x-y))

Statement-I : If (x^(2)+3x+1)/(x^(2)+2x+1)=A+(B)/(x+1)+(C)/((x+1)^(2)), then A+B+C=0 Statement-II: If (x^(2)+2x+3)/(x^(3))=A/x + (B)/(x^(2))+(C)/(x^(3)), then A+B-C=0 Which of the above statements is true

Let a gt 0, b gt 0, c gt 0. Then both the roots of the equation ax^2+ bx + c = 0 are

If 2x=y^(1//m)," then: "(dy)/(dx)=

"y is "50%" of "x%" of "x. {:("Quantity A","Quantity B"),(y,x):}

If x= t^(2) and y= t^(3), then (d^(2)y)/(dx^(2)) is equal to

There are 5 like objects of first kind, 6 like objects of second kind, 4 like objects of third kind. Find the number of linear arrangements of these objects so that at least one object from like

Evalute the following integrals int (1)/((x -a)(x -b)(x-c))dx

sin12+sin48+sin54=?

Show that f(x) = |x| is not differentiableat x =0

The population of a village increases continuously at the rate proportional to the number of its inhabitants present at any time. If the population of the village was 0,000 in 1999 and 25000 in the year 2004, what will be the population of the village in 2009 ?

A Bag I contain 3 red and 4 black balls. White bag II contains 5 red 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.

The number of ways in which a team of eleven players can be selected from 22 players always including 2 of them and excluding 4 of them is

A staight line passing through O (0,0) intersect the curve (x-1)^2+(y-1)^2=1 at 'A' and 'B' and (x-2)^2+y^2=1 at C and D . If OA,OC , OD and OB form an A.P. , then the equation of the line is …………… .

If {:(f(x),=(10^x + 7^x - 14^x- 5^x)/(1-cos x),",","for"x != 0),(,=10/7, ",","for"x = 0):}, then f(x) is

The tangent at any point to the circle x^(2)+y^(2)=r^(2) meets the coordinate axes at A and B. If the lines drawn parallel to axes through A and B meet at P then locus of P is

(i) Twelve balls are distributed at random among three boxes what is the probability that the first box will contain 3 balls ? (ii) If 'n' different biscuits are distributed amoong N beggers, find the chance that a particular begger receives exactly r ( lt n) biscuits.

If 3x+2y=3 and 2x+5y=1 are conjugate lines w.r.t the circle x^(2)+y^(2)=r^(2) then r^(2)=

Definebinary operation.

Ifx=h+asecthetaandy= k + b "cosec" thetathen

If A={:[(3,2,6),(1,1,2),(2,2,5)]:},B={:[(1,2,-2),(-1,2,-2),(-,-2,1)]:}, then

Let f(x) = (x-3) ^(2018) (2-x)^(2019) , x in R . If (alpha) is a relative maximum of f at alpha, then 2alpha _3 f(alpha)=

If a , b , c in Rsuch that a + b + c= 0 and az_(1) + bz_(2) + cz_(3) = 0 then z_(1) , z_(2) , z_(3) are

If A, B, c are three square matrices such that AB=AC implies B=C, then the matrix is always a/an

Assertion(A) : The locus of the point of intersection of perpendicular tangents to y^(2)= 4ax is its directrix.Reason (R) : If theta is acute angle between the pair of tangents drawn from (x_(1),y_(2)) to parabola S =0 then tan theta= (sqrt(S_(11)))/(|x_(1)+a|) The correctanswer is

a = I + j - 2k implies sum {(a xx i) xx j }^(2)

Let A_(alpha)=[(cosalpha, -sinalpha,0),(sinalpha, cosalpha, 0),(0,0,1)], then :

If int (dx)/(x^(2) + 2x+ 2)= f(x) + c then f(x) =

Two perpendicular tangents to the ellipse (x^2)/(16)+(y^2)/(9)=1 are such that the auxiliary circle intercepts chord of length l_1" and "l_2 on these tangents, then :

If P (A) =6/11,P(B)=5/11and P(AnnB)=7/11,find P(A/B)

DeltaABC is an equilateral triangle. Its side is l. Any point P lies on the circum centre of DeltaABC. Then |bar(PA)|^(2)+|bar(PB)|^(2)+|bar(PC)|^(2) = …………….

int(2-sin 2x)/(1-cos2x)e^(x) dx is equal to

int_(2)^(3)1/x dx

int_0^1(x^5(4-x^2))/sqrt(1-x^2)dx

Usingintegration, findthe areaoftheregionboundedby theline2y = 5x+ 7, x axisandthe linesx=2andx=8.

Consider the quadrationax^(2) - bx + c =0,a,b,c in N whichhas two distinct real roots belonging to theinterval (1,2). The least value of a is

Consider the quadrationax^(2) - bx + c =0,a,b,c in N whichhas two distinct real roots belonging to theinterval (1,2). Theleastvalue of c is

Consider the quadrationax^(2) - bx + c =0,a,b,c in N whichhas two distinct real roots belonging to theinterval (1,2). The least value of b is

A plane has intercepts p-1,1 and p+1 on the coordinate axes x, y and z respectively. If the distance of plane from the origin is 1//sqrt(3), then the largest value of p is:

I. underset(x to 0)"Lt" (log_(e)(1+x))/(3^(x)-1)=log_(3)e II. underset(x to 1)"Lt" (log_(5) 5x)^(log_(x)5)=e

The standard deviation of a,a+d,a+2d,……,a+2nd is

If 3^(rd), 7^(th) and 12^(th) terms of A.P. are three consecutive terms of a G.P., then the common ratio of G.P is

Find the derivative of (sqrt(x) - 3x) (x + 1/x)

{{:(-x^(2)+4x+a","xle3,),(ax+b","3ltxlt4,),(-(b)/(4)x+6","xge4,):}If x=3 isa point of minima and x=4 is a point of mxima then which of the following is true?

Show that the coefficient of a^m and a^n in expansion of (1+a)^(m+n) are equal.