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If angles A,B,Care in A.P . , then2cos (( A-C)/( 2))=

1+ ((1)/(3) + (1)/(3^2) ) + (( 1)/( 3^3) + (1)/( 3^4)+ (1)/( 3^5) ) + .... sum of the termsin the n^( th) bracket=

Let f be differentiable for all x. Iff(1) = -2and f'(x)ge2 for all x in [1,6], then

Find the value of a and b: (a-3,b+7)= (3,7)

If a, b and c are in AP then the straight lines ax+by+ c =0 will always pass through. …..... .

Find the value of f(0) so thatf(x) = (log (1 + (x)/(a))- log (1 - (x)/(b)))/(x)is continuous x = 0

If tan^(-1)x,tan^(-1)y,tan^(-1)z are in A.P then (2y)/(1-y^(2))=

Find points on line x + y + 3 = 0 whose distance from line x+2y+2=0 is sqrt(5) unit.

If x=-2-sqrt(3)i then find the value of 2x^(4)+5x^(3)+7x^(2)-x+41

How many elements has P(A), if A = φ?

If U= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A= {1, 2, 3, 5},B= {2, 4, 6, 7} and C= {2, 3, 4, 8}. Then, (B cup C)'="………"

If 0 lt alpha lt beta lt ( pi )/( 2), and if ( tan beta)/( tan alpha) gt k, then k is

Find the value of k such that the line (k-2)x+(k+3)y-5=0 isparallel to the line 2x-y+7=0

A = tan 1,B = tan2, C = tan3, then the desending order of A,B,C is

Evaluate the following limits : Lim _(x to 0) (tan 3x - 2x)/(3x - sin^(2)x)

Integrate the following with respect to x. cos^(2)5x.sin2x

Solve the equation: 5^(x+1)+5^(2-x)=5^(3)+1

Write the first four terms of the sequence whose nth term is given (-1)^(n) sin"" (npi)/(2)

Assertion (A) : The normals to the planes x-lambday+z=1, 3x+2y-lambdaz+1=0 are perpendicular to each other if lambda+1=0. Reason (R ) : If the planes a_(1)x+b_(1)y+c_(1)z+d_(1)=0,a_(2)x+b_(2)y+c_(2)z+d_(2)=0 are perpendicular to each other then a_(1)a_(2)+b_(1)b_(2)+c_(1)c_(2)=0

Two pillars of equal height stand at a distance of 100 metres. At a point between them the elevation of their tops are found to be 30^(@) and 60^(@). Then height of the each pillar in metres is

If phi(x) is polynomial function and phi(x)gtphi(x)AAxge1andphi(1)=0,then

Find the derivative of the function wrt x. sin (tan ^(-1) (e ^(-x)))

The orthocentre of triangle formed by (a cos alpha, a sin alpha),(a cos beta, a sin beta),(a cos gamma, a sin gamma) is

Find the component statements of the following and check whether they are true or not: All prime numbers are either even or odd.

Identify the figure in which the line has a positive slope.

If 4x + i(3x-y) + i(-6), where x and y are real numbers, then find the values of x and y.

If S= {x |x is a positive multiple of 3 less than 100} and P= {x | x is a prime number less than 20} then n(S)+n(P) is equal to

Number of solutions of the equation cos^(-1)(1-x)-2cos^(-1)x=pi/2 is

lim_(hto0)(4sqrt(x+h)-4sqrt(x))/(h)=………...

In which ratio the plane x + y + z = 5 divides line segment joining points (2, -1, 3) and (-1, 2, 1) ?

Let a=cos^(-1)cos20, b=cos^(-1)cos30, c=sin^(-1)sin(a+b) then If 5sec^(-1)x+10sin^(-1)y=10(a+b+c) then the value of tan^(-1)x+cos^(-1)(y-1) is

Equation of pair of lines passing through origin and making an angle Tan^(-1)2 with the line 4x-3y+7=0

A circular hole of 4 mm in diameter and 12 mm deep in a metal block is rebored to increase the diameter to 4.12 mm, then the amount of metal removed is approximately

From a class of 25 students, 10 are to be chosen for an excursion party. There are 3 students who decide that either all of them will join or none of them will join. In how many ways can the excursion party be chosen ?

If cot alpha=1/2, alpha in (pi,(3pi)/2) and sec beta=(-5)/3, beta in ((pi)/2, pi) find tan (alpha+beta)

Find a positive value of m for which the coefficient of x^2 in the expansion (1+x)^m is 6.

If cos^(-1)sqrt(p)+cos^(-1)sqrt(1-p)+cos^(-1)sqrt(1-q)=(3pi)/4, then the value of q is

In triangle ABC are in A.P and b:c= sqrt(3): sqrt(2), then

Find mean deviation about the mean for the following data : {:("x"_(i),2,5,6,8,10,12),("f"_(i),2,8,10,7,8,5):}

The locus of the point which is equidistant from the point A(0, 2, 3) and B(2, -2, 1) is

A coin is tossed and a die is thrown.

2sin((5pi)/12) sin(pi/12)=.........

Find the value of a if the distances of the points (2,3) and (-4,a) from the straight line 3x+4y-8=0 are equal.

The set (A cap B')' cup (B cap C) is equal to

Find a positive number smaller than(1)/(2^(1000)) Justify

Observe the following lists. Let (sinx)/(a)=(cosx)/(b)=(tanx)/(c)=k. The correct match for List-I form List-II is

vec(a)= 3vec(i)- vec(j) + 2vec(k), vec(b)= -vec(i) + 3vec(j) + 2vec(k), vec(c )= 4vec(i)+ 5vec(j)- 2vec(k) and vec(d)= vec(i)+ 3vec(j) + 5vec(k), then compute (vec(a) xx vec(b)).vec( c) - (vec(a) xx vec(d)).vec(b)

Write the following as intervals : {x : x ∈ R, – 4 < x ≤ 6}