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If p=Xcostheta-Ysintheta,q=Xsintheta+Ycosthetaandp^(2)+4pq+q^(2)=AX^(2)+BY^(2),0le0le(pi)/(2).What is the value of B ?

[[7,1,2],[9,2,1]][[3],[4],[5]] + 2[[4],[5]] is equal toa) [[43],[50]]b) [[43],[45]]c) [[45],[44]]d) [[44],[45]]

Incircle of Delta ABC touches the sides BC, CA and AB at D, E and F, respectively. Let r_(1) be the radius of incircle of DeltaBDF. Then prove that r_(1) = (1)/(2) ((s-b) sin B)/((1+ sin.(B)/(2)))

(C_0)/(2)+(C_1)/(3)+(C_2)/(4)+…...+(C_n)/(n+2)=

Write the following function in the simplest form : "tan"^(-1)x/(sqrt(a^(2)-x^(2))),|x|lta

Let A be a square matrix of order 3xx3" then "|5A|=

Sovle tan^(-1)2x+tan^(-1)3x=(pi)/4

If S_(n)=1^(3)+2^(3)+…+n^(3) and T_(n)=1+2+….+n, then

If continued product of three number in G.P. is 216 and sum of there product in pairs is 156. Find the numbers.

Let A be a 2 xx2 matrix such that 3A^(2) + 6A - l_(2)= O_(2) . Then a value of det (A+l) is :

Differentiate the following functions with respect to x. y= cos (x^(x)) + sin (x^(x))

If f(x) = int cosec^(2) x dx, then f ((pi)/(4)) =

Consider P,Q,R to be vertices with integral coordinates and (|PR|+|RQ|)^(2)lt8. Area (/_\PQR)+1 then

If xsqrt(1+y+)ysqrt(1+x)=0 then (dy)/(dx) equals.

If one quarter of all three element subsets of the set A={a_(1), a_(2), a_(3), ......., a_(n)} is equal to the three element subsets which contains the element az, then n is

Find the number of distinct terms in the following expansions. (x^(2)+1+(1)/(x^(2)))^(40)

If bara,barb" and "barc represent the vertices A,B and C respectively of triangleABC, then prove that |(bara xx barb)+(barb xx barc)+(barc xx bara)| is twice the area of triangle ABC.

Discuss the applicability of Rolle's theorem on the function given by f(x) = {(x^(2) + 1",","if" 0 le x lt 1),(3-x",","if" 1 le x le 2):}

If int(f(x))/(x^(2)-x+1)dx=(3)/(2)log(x^(2)-x+1)+(1)/(sqrt(3))tan^(-1)(2x-1)/(sqrt(3))+C then f(x) is equal to

Prove that the image of point P(costheta, sin theta) in the line having slope tan(alpha//2) and passing through origin is Q(cos(alpha-theta),sin(alpha-theta)).

If three lettersare placed in three addressed envelopesthen the mean and variance of X where X denotes the number of correct despatches.

For X ~ B (n = 8, p = 0.5), P (|X-2| le 2) =

If a,b,c, are the radii of the circles x^(2)+y^(2)-6x-8y=0, x^(2)+y^(2)+4x-6y-3=0, x^(2)+y^(2)+6x+8y-11=0 then the ascending order of a,b,c is

The primitive of (1)/((x-a)^(3//2)(b-x)^(1//2)) is

Integrate the functions ((logx)^(2))/x

Evaluate the following :[[a,h,g],[h,b,f],[g,f,c]]

(i) Find the equations of the tangents to 9x^(2)+16y^(2)=144, which makes equal inter­cepts on the coordinate axes.(ii) Find the value of k if 4x + y + k = 0 is a tangent to the ellipse x^(2) + 3y^(2) = 3

The range of function f(x)= abs(x-1)/(x-1)

Consider the system of equations x cos^(3) y+3x cos y sin^(2) y=14 x sin^(3) y+3x cos^(2) y sin y=13 The value/values of x is/are

Consider differential equation (x^(2)+1).(d^(2)y)/(dx^(2))=2x.(dy)/(dx) Statement I For many member of this family ytooo as xtooo. Statement II Any solution of this differential equation is a polynomial of odd paralled to y-axis with and latusrectum is fixed is 2.

A student read common difference of are A.P. as -3 instead of 3 and obtained the sum of first 10 terms as -30. Then the actual sum of first 10 terms is equal to

Integration of some particular functions : int(x-2)/(x^(2)-4x+3)dx=....+c

The maximum area of a rectangle inscribed in the circle (x+1)^(2)+(y-3)^(2)=64 is

Solve system of linear equations , using matrix method if exists x-2y=10 2x+y+3z=8 -2y+z=7

A line has slope m and y-intercept 4. The﻿ distance between the origin and the line is﻿ equal to

Let A ={x in R : x is not an integer} Define f : A to R as f(x) = (2x)/(x-1) AA x in A, then f is

Examine the following functions for continuity. f(x)= x-5

Consider a plane P-=2x+y-z-=0 a line (x-3)/2=(y+1)/(-3)=(z-2)/(-1) and a point A(3,-4,1). L_(2) is a line passing through A intersecting L_(1) an parallel to the plane P Plane containing L_(1) and L_(2) is

If (x^(4)+24x^(2)+28)/((x^(2)+1)^(3))=A/((x^(2)+1))+B/((x^(2)+1)^(2))+C/((x^(2)+1)^(3)), then A + C =

Examine the following functions for continuity. f(x) = |x-5|

Let f:R to R and g:R to R is define by f(x)=2x-1 and g(x)=5x+2, then find (g circ f)^(-1)(x)

Equation of the circle of radius sqrt(2), and touching the line |x-1| =|y-1| ,is :

Letf'(sin x)lt0 and f''(sin x) gt0 forall x in (0,(pi)/(2)) and g(x) =f(sinx)+f(cosx) which of the following is true?

If the line, y=mx bisects the area of the region {(x,y):0 le x le (3)/(2), 0 le y le 1+4x-x^(2)}, then m equals:

Assertion (A) : If z = ilog (2 - sqrt3) then cos z= 2 Reason (R) : cos h theta = (e^(itheta ) + e^(itheta))/(2)

Each of the following defines a relation of N : x is greater than y,x, y inN. Determine which of the above relations are reflexive , symmetric and transitive .

E and F are independent 'such that P(E) = 0.35 and P(E cup F)=0.6 then find P(F).

The product of n positive numbers is 1, then their sum is a positive integer, that is

(i) Find the equations of the tangents to 9x^(2)+16y^(2)=144, which makes equal intercepts on the coordinate axes.(ii) Find the value of k if 4x + y + k = 0 is a tangent to the ellipse x^(2) + 3y^(2) = 3

A line has slope m and y-intercept 4. The distance between the origin and the line is equal to