A to Z Exams

If α,β,γ are the roots of x3-px2+qx-r=0 then α4+β4+γ4=

If the diagonals of a parallelogram are given by 3i+j-2k and i-3j+4k, then the lengths of its sides are

If it rains, a dealer in rain coats can earn Rs.500/- a day, If it is fair, he can lose Rs.40/- per day. If the probability of affair day is 0.6, his mean profit is

The equation of the sphere on the join of 2i+2j-3k, 5i-j+2k as a diameter is

If (1,2), (4, 3) are the limiting points of a coaxal system , then the equation of the circle in its conjugate system having minimum area is

If x2+ky2+x-y is resolvable into two linear factors then k=

If A,B,C are the remainders of x3-3x2-x+5,3x4-x3+2x2-2x-4,2x5-3x4+5x3-7x2+3x-4 when divided by x+1,x+2,x-2 respectively then the ascending order of A,B,C is

The equation of the circle passing through the points (4, 1), (6, 5) and having the centre on line 4x+y-16=0 is

If the circle x2+y2+2x-2y+4=0 cuts the circle x2+y2+4x+2fy+2=0 orthogonally,then f=

If PM is that perpendicular from P(2, 3) onto the line x+y=3,then the coordinates of  M are

If the sum of the roots of the equation 5x2-4x+2+k(4x2-2x-1)=0 is 6,then k=

If the equation of the circle cutting orthogonally the circles x2+y2-6x=0, x2+y2+4x+3y+1=0 and which has its centre on the line x+2y=5 is x2+y2-2ax-2by+c=0 then the descending order of a, b, c is

If 1,2,3,4 are the roots of the equation x4+ax3+bx2+cx+d=0 then a+2b+c=

The period of cos x cos(π/3+x) sin(π/3-x)is

The solution of dy/dx +1  = e x+y 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

If α,β are solutions of a cos 2θ+b sin 2θ=c, then tan α tan β=

The centres of the circles are (a, c) and (b, c) and their radical axis is the y-axis. The radius of one of the circle is r. The radius of the other circle is

If , in a right triangle ABC, the hypotenuse AB=p, then AB.AC+BC.BA+CA.CB=

If the line hx+ky=1/a touches the circle x2+y2=a2 then the locus of (h,k) is a circle of radius

The number of real solutions of Tan1 x+Tan 1 (1/y) = Tan1 3 is

3[sin4(3π/2-α)+ sin4(3π+α)]-2[sin6(π/2+α)+ sin6(5π-α)]=

If cos θ=cos 5π/4, then θ=

The area bounded by y = 3x and y = x2 is (in sq units)

If the equation k(6x2+3)+rx+2x2-1=0 and 6k(2x2+1)+px+4x2-2=0 have both the roots common,then the value of 2r-p is

If A(1, 1), B(√3+1, 2) and C(√3, √3+2) be three vertices of a square, then the diagonal through B is

If x2+p1x+q1=0,x2+p2x+q2=0,x2+p3x+q3=0 has a common root,then p12+p22+p32+4(q1+q2+q3)=

A and B are two independent events. If the probability that both A and B occur is 1/20 and the probability that neither of them occurs is 3/5, then P(A),P(B)=

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

A set contains (2n+1) elements. The number of subsets of the set which contain more than n elements is

The equation of the line passing through the point (5, -4), with slope -7/2 is

The inverse point of (1, -1) with resapect to the circle x2+y2=4 is

If sin θ=-7/25 and  is not in the first quadrant, then (7cot θ -24 tan θ) / (7cot θ+24 tan θ) =

The radius of the sphere (r-2i+3j-k).(r+3i-j+2k)=0 is

If √(x2+4ax+5)+√(x2+4bx+5)=2(a-b) then x=

The equation of the line passing through the point of intersection of the lines 2x+3y-4=0, 3x-y+5=0 and the origin is

If the circles x2+y2=4 and x2+y2-6x-8y+K=0 touch internally then K=

The circumfence of a circle measured as 14cm with   an error of 0.01 cm. the approximate percentage error in the area of the circle is

The derivative of Tan-1√(1+x2)-1/x w.r.to Tan-12x√(1-x2)/(1-2x2) at x=0 is

If a=i+4j, b=2i-3j and c=5i+9j then c=

If one root of the quadratic equation ax2+bx+c=0 is 3-4i, then a+b+c is :

If the difference of the roots of x2-bx+c=0 is equal to the difference of the roots of x2-cx+b=0 and b≠c,then b+c=

The minimum value of cos3 x+ cos3 (1200+x)+ cos3 (1200-x) is

A curve passes through the point (2, 0) and the slope of the tangent at any point is x2-2x for all values of x. The point of maximum or donation the curve is

If α,β,γ are the roots of x3-7x+6=0 then the equation whose roots are (α–β)2,(β–γ)2,(γ–α)2 is

There are 5 letters and 5 addressed envelopes. If the letters are put at random in the envelopes, the probability that at least one letter may be placed in wrongly addressed envelope is

If a denotes the number of permutations of x+2 things taken all at a time, b the number of permutations of x-11 things taken all at a time such that a=182bc, then the value of x is

If 9x2-24xy+ky2-12x+16y-12=0 represents a pair of parallel lines, then k=

The pair of straight lines x2-3xy+2y2 = 0 and x2-3xy+2y2+ x -2 =0 form a

The domain of sin-1(2x-7) is

The locus of midpoints of chords of the circle x2+y2=2r2 subtending a right angle at the centre of the circle is

Observe the following statements A: f'(x) = 2x3 - 9x2  + 12x - 3 is increasing outside the interval (1, 2)R: f'(x) < 0 for x belongs to (1,2).Then which of the following is true

The tangents at (at12, 2at1) and (at22, 2at2) on the parabola y2=4ax are at right angles then

The equation of the circle passing the origin having its centre on the line x+y=4 and cutting the circle x2+y2-4x+2y+4=0  orthogonally is

If y=(x+√x2-1)m then (x2-1)y2+xy1=

If the points (0, 0), (2, 0), (0, 4), (1, k) are concyclic then k2-4k =

If 1,-2,3 are roots of x3-2x2+ax+6=0 then a=

There are 25 st5amps numbered from 1 to 25 in a box. If a stamp is drawn at random from the box, the probability that the number on the stamp will be a prime number is

E1: a + b + c = 0 if 1 is a root of ax2 + bx + c = 0E2: b2 - a2 = 2ac if sinθ, cosθ are the roots of ax2 + bx + c = 0Which of the following is true

Mr. A is called for 3 interviews .There are 5 candidates at the first interview, 4 at the second and 6 at the third .If the selection of each candidates is equally likely then the probability that A will be selected for at least  one post is

Express 4+3i/(2+3i)(4-3i) in the form of x+iy

The solution of x2dy-y2dx=0 is

The points (2a,4a), (2a,6a) and  ((2+√3)a,5a are the vertices of an

If x is so small that x2 and higher powers of x may be neglected then (1-x)1/2(1+x)2/3/(1-x)1/2

sin4 θ+2 sin2 θ(1- 1/cosec2θ)+ cos4θ=

The value of tan 150+ tan 300+ tan 150 tan 300 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

The equation of the tangent to the curve  (x/a)2/3+(y/b)2/3 =1 at (a cos3θ, b sin3θ ) is

If ax2+2bx+c=0 and px2+2qx+r=0 have one and only one root in common and a,b,c being rational,then

If (2i+4j+2k)x(2i-xj+5k)=16i-6j+2xk then the value of x is

If x= a(cos θ+θ sin θ), y=a(sin θ-θ cos θ)then dy/dx=

If f(x)=cos2x+cos2(600+x) + cos2(600-x) and g(3/2)=5 then gof(x)=

A straight line through  the origin O meets the parallel lines 4x+2y=9 and 2x+y+6=0 at points P and Q respectively.Then the point  O divides the segment  PQ in the ratio

The equation whose roots are multiplied by 3 of those of 2x2+3x-1=0 is

The value if b such that x4-3x3+5x2-33x+b is divisible by x2-5x+6 is

If cos200=K and cosx = 2k2-1,then the possible values of x between 00 and 3600 are

The equation whose roots are 2,-3,5 is

If the equation of the pair of tangents drawn from (1, 2) on the ellipse x2+2y2=2 is 3x2-4xy-y2+ax+by+c=0 then the ascending order of a, b, c is

The latusrectum of a hyperbola is 9/2 and eccentricity is 5/4.Its standard equation in standard form is

If the number of common tangents of the circles x2+y2+8x+6y+21=0, x2+y2+2y-15=0 are 2,then the point of their intersection is

If (sin x+ cos x)/(cos3 x)= a tan3 x+ b tan2 x+c tan x+d then a+b+c+d=

The point (3, -4) lies on both the circles x2+y2-2x+8y+13=0 and x2+y2-4x+6+11=0. Then the angle between the circles is

In ΔABC, if cos2 A+cos2B+ cos2C=3/4, then the triangle is

If cos(x-y), cos x, cos(x+y) are three distinct numbers which are in harmonic progress and cos x≠cos y, then 1+ cos y=

If the line y=x touches the circle x2+y2+2gx+2fy+c=0 at P, OP=4√2, then c=

3.C0+7.C1+11.C2+……..+(4n+3).Cn =

x2-y2+5x+8y-4=0 represents

The parabola with directrix x + 2y - 1 = 0 and focus (1, 0) is

The point P in the first quadrant of the ellipse x2/8+y2/18=1 so that the area of the triangle formed by the tangent at P and the coordinate axes is least

If cos 2θ+cos 8θ= cos 5θ then θ=

If α, β, γ are the roots of x3+px2+qx+r=0 then (β+γ-3α)(γ+α-3β)(α+β-3γ) =

The equation of the circle which cuts orthogonally the  three circles x2+y2+4x+2y+1=0, 2x2+2y2+8x+6y-3=0 , x2+y2+6x-2y-3=0 is

The equation of the sphere one of whose diameter has end points (1, 2, 4) and (3, 0, 2)

x-axis divides the line segment joining (2,-3), (5,7) in the ratio

Cos (sin-13/5+Sin-1 5/13)=

(cos 2α /cos4α- sin4 α)- (cos4 α+ sin4 α/ 2- sin22α)=

2.4+4.7+6.10+….(n-1) terms=

If ax2+2hxy+by2+2gx+2fy+c=0 represents a pair of straight lines , then the square of the distance to their point of intersection from the origin is

If (cos3 200 +cos3400)/ cos 200+cos 400=k, then the value of k is

If  O(0,0), A(3,4), B(4,3) are the vertices of a triangle then the length of the altitude from O is