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tan 100. tan 200. tan 300. tan 400. tan 500. tan 600. tan 700. tan 800 =

If tan θ + tan 2θ+ √3 tan θ tan 2θ=√3 then θ=

Let a, b, c be the distinct non-negative numbers. If the vectors ai+aj+ck, i+k and ci+cj+bk lie in a plane then c is

If the third term in the expansion of (1/x+ xlog10 x)5 is 1, then x=

The equations of the tangents to the hyperbola 9x2-16y2 =144 at the ends of latus recta are

AB is a focal chord of the parabola y2=4ax.If A=(4a,4a)then B=

The cartesian equation of the plane passing through the points (1, 2, 3), (2, -3, 1), (3, 1, -2) is

If the circles (x+a)2+(y+b)2=a2, (x+α)2+(y+β)2=β2 cut orthogonally then α2+b2

Sum of the last 20 coefficients in the expansion of (1+x)39, when expanded in ascending powers of x, is

Express (a+ib/ a-ib)+(a-ib/ a+ib) in the form of a+ib

The angle between the normals at (1, 3),(-3,1) to the circle x2 + y2=10 is

The vector equation of the plane passing through the points -2i+6j-6k, -3i+10j-9k, -5i-6k is

If aZ and the equation (x-a)(x-10)+1=0 has integral roots,then the values of a are

If A,B,C,D are angles of a cyclic quadrilateral,then cosA+cosB +cosC +cosD is equal to:

If α,β,γ are the roots of x3-x2+33x+5=0 and A=s1,B=s2,C=s3 then the descending order of A,B,C is

The portion of the tangent drawn at any point on x2/3+y2/3=a2/3 (a>0), except the points on the coordinate axes, included between the coordinate axes is

The roots of the equation x3 - 3x - 2 = 0 are

The equation of the common tangent at the point contact of the circles x2+y2-10x+2y+10=0, x2+y2-4x-6y+12=0 is

The vertex and focus of a parabola are (-2,2),(-6,6).Then its length of latus rectum is

The difference of the slopes of the lines 3x2-8xy-3y2=0 is

The centre and radius of the sphere 2x2+ 2y2 + 2z2 – 2x +4y + 2z + 1=0

If (3,2 )is limiting point of the coaxal system of circles whose common radical axis is 4x+2y=11, then the other limiting point is

cos (θ + α).cos (θ - α)+ sin (θ + α). sin(θ - α)=

The acute angle between the lines x2-2xycotθ+ y2=0 is

C1/1 – C2/2 + C3/3 – C4/4 +………. +(-1)n-1 Cn/n =

The ends of the base of an isosceles triangle are at (2a, 0) and at (0, a). the equation of one side is x=2a. The equation of the other side is

The circumfernce of a circle is measured as 56 cm with error 0.02 cm. the percentage error in its area is

If α,β are the roots of ax2+bx+c=0 then αβ2+α2β+αβ=

The curve described parametrically by x=t2+t+1, y= t2-t+1 represents

k.C0+k2.C1/2+K2. C2/3+.…………+kn+1.Cn/n+1 =

In ΔABC, cot A/2+ cot B/2+ cot C/2=

If the equation of the circle cutting the circle x2+y2+2x-4y+8=0 orthogonally and coaxal with the circles x2+y2+6x+4y-12=0, x2+y2-4x-6y-12=0 is x2+y2+2ax+2by+c=0 then the ascending order of a, b, c is

The number of ways in which 5 red balls and 4 black balls of different sizes can be arranged in a row so that two balls of the same colour come together is

If the acute angle between the lines 2x+3y-5=0, 5x+ky-6=0 is then the value of k is

The centroid of the triangle formed by the points (2,3,-1), (5,6,3),(2,-3,1) is

The transformed equation of x3-4x2+1/4x-1/9=0,by eliminating fractional coefficients is

The vertex and focus of a parabola are (2, 1), (1, -1). Then the equation of the tangent at the vertex is

The solution of (12x+5y-9)dx+(5x+2y-4)dy=0 is

tan x + tan(x + π/3)+tan(x+2π/3)=3⇒tan3x=

18 guests have to be seated half on each side of a long table. 4 particular guests desire to sit on one particular side and 3 others on the other side. Determine the number of ways in which the sitting arrangements cn be made

If z=1/3+1.3/2.6+1.3.5/1.2.3+..........∞,then

The centre of the circle passing through the points (0, 0), (1, 0) and touching the circle x2+y2=9 is

sin 200.sin 400.sin 600 sin800=

The locus of the centre of the circles which touché both the circles x2+y2=a2 and x2+y2=4ax externally has the equation

If the roots of the equation ax2+bx+c=0 is of the form k+1/k and k+2/k+1(k≠0),then (a+b+c)2 is equal to

The condition that the three different lines ax+by+c=0, bx+cy+a=0, cx+ay+b=0 to be concurrent is

The roots of the equation a(b-c) x2+b(c-a)x +c(a-b) =0 are

The angle between the line joining the points (1, -2), (3, 2) and the line x+2y-7=0 is

The length of the subtangent at (2, 2) to the curve x5 = 2y4 is

If the polars of points on the circle x2+y2= a2 w.r.t the circle x2+y2= b2 touch the circle x2+y2= c2, then a, b, c are in

If the slope of the tangent to the curve xy+ax=by at (1, 1) is 2, then (a, b)

If tan θ=-4/3 and θ is not in the fourth quadrant , then the value of 5 sin θ+10cos θ+ 9 secθ+16 cosec θ – 4 cot θ=

The period of cot(5x+3)+sin(3x+4)/ sec(3-4x)-cos(4-6x) is

If a random variable X take values 0 and 1 with respective probabilities 2/3 and 1/3 then the expected value of X is:

The number of 6 digited numbers which are not divisible by 5 that can be formed with the digits 4,5,6,7,8,9 is

There are 3 routes from Tenali to Vijaywada and 4 routes from Vijaywada to Hyderabad,in how many different ways a person can travel from Tenali to Hyderabad via Vijaywada?

In a binomial distribution n = 400, p = 1/5, its standard deviation is

Bag A contains 8 black and 5 white balls. Bag B contain 6 black and 7 white balls. A die is rolled. If 2 or 5 turns up, then choose bag A otherwise choosen B. If one ball is drawn from the selected bag, the probability that it is black is

The coefficient of x5 in the expression of (1+x)21+(1+x)22+……+(1+x)30 is

The quadratic equation for which the sum of the roots is 12 and the sum of the cubes of the roots is 468 is

f(x)= x-1/x is

The equation of the line having inclination 1200 and y-intercepts -3 is

The equation of the tangent to the parabola y2 = 8x and which is parallel to the line x – y + 3 = 0

3√1003 -3√997

The locus of the point of intersection of perpendicular tangents drawn to each of circles x2+y2=16 and x2+y2=9 is a circle whose diameter is

The approximate percentage reduction in the volume of a cube of ice, if each side of the ice cube to reduced by 0.7% due to melting to:

A, B,C are aiming to shot a balloon. A will succeed 4 times out of 5 attempts. The chance of B to shoot the balloon is 3out of 4 and that of C is 2out of 3. If the three aim the balloon simultaneously, then the probability that at least two of them hit the balloon is

Tan (π/4+1/2cos-1a/b) +tan (π/4-1/2cos-1a/b) =

If (2,1,1) is the centroid of the triangle for which (3,2,-1), (2,-2,5) are two vertices then the third vertex is

If one root of the equation ix2-2(1+i)x+(2-i)=0 is 2-I,then the other root is

The number of 5digit numbers that can be formed with 0,1,2,3,5 so that no digit being repeated in any number is

If (0, 0) is one limiting point of the coaxial system radical axis x + y=1, then the other limiting point is:

The equation of the circle whose centre lies in the first quadrant and which touches the coordinate axes and the line (x/3)+(y/4)=1 is x2+y2-2cx-2cy+c2=0, then c=

The point of intersection of the tangents to the circle passing through (4, 7), (5, 6). (1, 8) at the points where it is cut by the line 5x+y+17=0 is

Tan-1 1/3+ Tan-1 1/5+ Tan-1 1/7+ Tan-1 1/8 =

The roots of x5-5x4+9x3-9x2+5x-1=0 are

A and B throw a pair of dice. A wins if he throw 6 before B throws 7 and B wins if he throws 7 before A throws 6. If A begins, his chance of winning is

The equation of the parabola with latusrectum joining the points (6,7) and (6,-1) is

If α,β,γ are the roots of x3+x2+x+1=0 then α3+β3+γ3=

The length of the chord of the circle x2+y2+4x-7y+12=0 along the y-axis is

The locus of the poles of chords of the parabola y2 = 4ax, which subtend a right angle at the vertex is

The number of tangents that can be drawn from (6, 0) to the circle x2+y2-4x-6y-12=0 are

P, Q, R are the midpoints of the sides AB, BC and CA of the triangle ABC and O is the point with the triangle , tehn OA+OB+OC=

The function f(x) = tan x has

The equation of the circle cutting orthogonally the circles x2+y2-8x-2y+16=0, x2+y2-4x-4y-1=0 and passing through the point (1, 1) is

The length of the line segment joining the points 2i-2j+3k, 5i+2j+3k is

P(θ) and D(θ+π/2) are two points on the ellipse x2/a2+y2/b2=1. The locus of point of intersection of tangents at P and D to the ellipse is

The distance between the limiting points of the coaxial system x2 + y2 – 4x – 2y – 4 + 2λ(3x + 4y + 10)=0

The equations whose roots are diminish by 3 than those of x4-5x3-20x2+3x+17=0 is

The quadratic equation x2 + ax + bc = 0, x2 + bx + ca = 0 have a common root, then the quadratic equations whose roots are the remaining roots in the given equations is (where, a ≠ b)

The locus of the midpoints of chords of the circle x2+y2=25 which touch the circle (x-2)2+(y-5)2=289 is

The length of the sub normal to the curve y2=4ax at any point

In a business venture a man can make a profit of Rs.2000/- with probability of 0.4 or have a loss of Rs.1000/- with probability 0.6his expected profit is

AB is a chord of the parabola y2 = 4ax with vertex at A. BC is drawn perpendicular to AB meeting the axis at C.The projection of BC on the axis of the parabola is

The ratio in which the line joining the points A(-1, -1) and B(2, 1) divides the line joining C(3, 4) and D(1, 2) is

sin 100 sin 500 sin 700 sin 900 =

If z = log (tan x + tan y), then (sin 2x)∂z /∂x+(sin 2y) ∂z /∂y is equal to

If sinA + sinB = l, cosA - cosB = m, then the value of cos(A - B) =

If f(x)= (a-xn)1/n, where a>0 and n?N, then (fof)(x)=

The vectors i-2j+3k, 2i-3j+4k, i-3j+5k are

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