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(i) int (sin 2x)/((1+sin x)(2-sinx))dx (ii) int (cos x)/((1+sinx) (2-sinx))dx (iii) int (cos x)/((1-sinx)^2(2+sinx)) dx (iv) int ((3sinx-2)cosx)/(13-cos^2x-7 sinx) dx (v) int (sin theta)/((4+ cos^2 theta ) (2-sin^2 theta))d theta.

Find the S.D. of the following terms: 2, 4, 5, 6, 9,10

The reflection of the point (6, 8) in the line x - y = 0 is

Find the area bounded by the following curve : (i) f(x) = sinx, g(x) = sin^(2)x, 0 le x le 2pi (ii) f(x) = sinx, g(x) = sin^(4)x, 0 le x le 2pi

The slope of the tangent to the curve x = t^2+3t-8, y = 2t^2-2t-5at the point (2,-1) is:

If therootsof32x^3- 48 x^2+22x-3=0 arein A.P thenthe middleroot is

A={(x,y):x,y in I, x ge 0, y ge 0 and 4x+5y le 40} B={(x,y):x, y in I, x gt 0, y ge 0 and 5x+4y le 40}

Let A be a non-singular matrix of order 3 xx 3. Then I adj. A I is equal to :

If A = [(1,2),(3,-5)] , B = [(1,0),(0,2)]and Xbe a matrix such that A = BX , then X is :

A box contains 6 pens,2 of which are defective. Two pens are taken randomlyfrom the box. If r.v.X, number of defectivepens obtained , then standard deviation

Solve graphically 3x + 4y ge 12

The radius of the circle having maximum size passing through (2,4) and touching both the coordinate axes is

r and n are positive integers r gt 1,n gt 2 and coefficient of (r + 2)^(th) term and 3r^(th) term in the expansion of (1 + x)^(2n) are equal, then n equals

Points L, M and N lie on the sides AB, BC and CA of the triangle ABC such that l (AL) : l (LB) = l (BM) : l (MC) = l (CN) : l (NA) = m : n, then the areas of the triangles LMN and ABC are in the ratio

Find the area bounded by the lines y=sqrt(2)x,x+sqrt(2)y=4,y=0 and y=sqrt(2).

For|x|lt1,theconstantterm intheexpansionof(1)/((x -1) ^ 2 (x - 2 ))is

The locus of the point the chord of contact of tangents from which to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1. If (1"/"2,2"/"5) be the middle-point of the chord of the ellipse (x^2)/(25)+(y^2)/(16)=1, then that its length is

Assertion (A) a, b, c, d are position vectors of 4 points such that 2a - 3b + 7c-6d = 0rArr a, b, c, d are coplanar. Reason (R) Vector equation of the plane passing through three points whose position vectors are a, b, c is r = (1-x-y) a + x + yc. Which of the following is true?

If the vector a=3 hat(j)+4 hat(k) is the sum of two vectors a_(1) and a_(2), vector a_(1) is parallel to b=hat(i)+hat(j) and vector a_(2) is perpendicular to b, then a_(1)=

Findtheareaofthe loop of thecurvey^2=x(1 - x) ^ 2 .

If the projection of a line segment on thex, yand z -axes in 3 dimensional space are 2,3 and 6 respectively, then the length of the line segment is

State which of the following are not the probability distributions of a random variable. Give reasons for your answer.

Find the number of possible common tangents that exist for the following pairs of circles. x^(2) + y^(2) + 6x + 6y + 14 = 0 x^(2) + y(2) - 2x -4y -4=0

If 2x-y+1=0 is a tangent on the parabola which intersect its directrix at (1,3) and focus is (2,1), then equation of axis of parabola is

int_(-1)^(1) (e^(|x|))/(1+a^(x))dx

Let f(x)=" max "{x^(2),(1-x)^(2),2x(1-x)} where 0le x le 1. Determine the area of the region bounded by y=f(x), x-axis, x = 0 and x = 1.

How many integers between 100 and 1000(both inclusive )consists of distinct odd digits ?

Using integration find the area of the region bounded by a triangle whose coordinates area (-2,0),(2,1),(-1,4).

Statement - I : If n = 4m + 3 , is integer then i^(n) is equal to -iStatement- II : If n in N then (1 + i)^(2n) + (1- i)^(2n) is purely real number

Write the equation of the plane parallel to x-axis having intercepts 5 and 6 on y and z-axis respectively.

If x+y=z, then cos^(2)x+cos^(2)y+cos^(2)z-2cosx.cosy.coszis equal to

For the equation of rectangular hyperbola xy = 18

Bag A contains 3 red and 2 balck balls and bag B contains 2 red and 3 black balls. One ball is drawn at random from box A and placed in B. Then again one ball is drawn at random from box B and placed in A. Find the probability that the composition of balls in the two boxes remains unaltered.

If A is a 3xx3 non-singular matrix such that "AA"'=A'A and B=A^(-1)A', then "BB"' equals:

Ify = tan^(1-) sqrt((x+1)/(x-1)) " for " |x| gt 1 " then " (dy)/(dx) =

In triangle ABC (Fig 10.18), which of the following is not true :

If a, b in {1, 2, 3} and the equation ax^(2)+bx+1=0hasreal roots, then

Integration using trigonometric identities : int (d theta)/(sin theta* cos^(3) theta)=....+c

A point on the parabola whose focus is S(1,-1) and whose vertex is A (1,1) is

If A+B+C = 2S , then P.T cos(S-A)+cos(S-B)+cos(S-C)+cosS=4cos.(A)/(2)cos.(B)/(2)cos.(C)/(2)

if (1 + C_(1)/C_(0))(1 + C_(2)/C_(1)) (1 + C_(3)/C_(2)) ...... (1 + C_(n)/C_(n - 1))is

If C_(0), C_(1), C_(2), …, C_(n) are binomial coefficients, then sum_(k=0)^(n) C_(k) sin kx cos (n-k) x equals

The sides AC and AB of a Delta ABCtouch the conjugate hyperbola of the hyperbola (x^(2))/( a^(2)) -(y^(2))/( b^(2)) =1. If the vertex A lies on the ellipse(x^(2))/( a^(2))+(y^(2))/( b^(2))= 1,then the side BC must touch

Let f:A to B f (x) = (x +a)/(bx ^(2) + cx +2), where A represent domain set and B represent range set of function f (x) a,b,c inR, f (-1)=0 and y=1 is an asymptote of y =f (x) and y=g (x) is the inverse of f (x). Area bounded between the curves y = f(x) and y=g (x) is:

Let f:A to B f (x) = (x +a)/(bx ^(2) + cx +2), where A represent domain set and B represent range set of function f (x) a,b,c inR, f (-1)=0 and y=1 is an asymptote of y =f (x) and y=g (x) is the inverse of f (x). g (0) is equal to :

Solve [[a+x,a-x,a-x],[a-x,a+x,a-x],[a-x,a-x,a+x]]=0

Let f:A to B f (x) = (x +a)/(bx ^(2) + cx +2), where A represent domain set and B represent range set of function f (x) a,b,c inR, f (-1)=0 and y=1 is an asymptote of y =f (x) and y=g (x) is the inverse of f (x). Area of region enclosed by asymptotes of curves y =f (x) and y=g (x) is: