A to Z Exams

The points (2,5), (0,3), (2,1), (4,3) taken in order, form

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

The number of terms in the expansion of (a+b+c+d)5 is

In ΔABC,tan A+tan B+tan C =

If f(x)=x3-2x2+7x+5 then f(x-2)=

The equation of the sphere on the join of (3, 4, -1), (-2, -1, 0) as diameter is

If  ((1+i)x-2i)/(3+i)+((2-3i)y+i/3-i)=I, then (x,y)=

If 4y=x+7 is diameter of the circumscribing circle of the rectangle ABCD and A(-3, 4), B(5, 4), then the area of the rectangle is

The lines acosθ+2sinθ+(1/r)=0, bcosθ+3sinθ+(1/r)=0 and ccosθ+4sinθ+(1/r)=0 are concurrent then a,b,c are in

I: In a ΔABC, if 4s(s-a) (s-b) (s-c) =a2b2 then it is right angled triangle II: In a ΔABC, if sin A+ sin B +sin C maximum then triangle is equilateral

A lot consists of 12 good pencils, 6 with minor defects and 2 with major defects. A pencil is drawn at random. The probability that this pencil is not defective is

The ascending order of A= Sin-1(log32),B= Cos-1(log3(1/2)), C=Tan-1(log1/3 2) is

If cos 2θ+cos 8θ= cos 5θ then θ=

Three groups of children contain 3girls and one boy;2 boys; 2 girls and 2 boys. One girl and 3 boys. One child is is selected at random from each group. The probability that three selected consists of 1 girl and 2 boys is

If A,B,C,D are the sum of the squares of the roots of 2x2+x-3=0,x2-x+2=0,3x2-2x+1=0,x2-x+1=0 then the ascending order of A,B,C,D is

sin A+sin 5A+sin 9A)/(cos A+ cos 5A+ cos 9A)=

The lines 2x+3y = 6,2x+3y = 8 cut the x-axis at A,B respectively.A line L=0 drawn,through the point(2,2) meets the x-axis at C in such a way that abscissa of A,B and C are in the arithmetic progression.Then the equation of L=0 is

For the curve y2=(x+a)3, the square of the sub tangent is……. Subnormal

If A= Tanh-1 (1/2)+ Coth-1(2), B= sinh(Cosh-1 9), C= sech2(Tanh-1 1/2)+cosech2(Coth-1 3) then

(2-)5 + (2+)5 =

Tan (tan-1 1/2+ tan-11/3) =

Two tangents are drawn from the point (-2, -1) to the parabola y2 = 4x. If α is the angle between those tangents then tan α =

Let n = 1! +4! +7!+................ +400! Then ten's digit of n is

The angle at which the circles x2+y2+8x-2y-9=0 and x2+y2-2x+8y-7=0 intersects is

(cosh x+ sinh x)n=

1.nC0+41.nC1+42.nC2+43.nC3+……..+4n.nCn =

If m and M respectively denote the minimum and maximum of f(x) = (x - 1)2+ 3 for x ε [ -3, 1], then the ordered pair (m, M) is equal to

If f(x)=x2sin(1/x) for x≠0, f(0)=0 then

The point of contact of  2x – y + 2 = 0 to the parabolay2 = 16x is

13+23+ 33+….+1003=k2, then k=

In order to eliminate the first degree terms from the equation 2x2 + 4xy + 5y2 - 4x - 22y + 7 = 0, the pointto which origin is to be shifted, is

The distance of the point (4, 1) measured along a line making an angle 1350 with the x-axis is

For the parabola y2 +6y-2x+5 = 0(I) The vertex is (-2 , -3)(II) The directrix is y+3 = 0

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

The condition that the lines joining the origin to the points of intersection of x/a+y/b=1, 5(x2+y2+bx+ay)=9ab are at a right angles is

sin 480.sin 120=

Domain of log(x-2)/√3-x is

The locus of a point P such that the distances from P to the points (2,3,5) ,( 1,2,-1)  are in the ratio 5:2 is

The ascending order of A= Sin-1(sin 8π/7),B= Cos-1(cos 8π/7), ), C=Tan-1(tan 8π/7) is

The equation of the hyperbola with its transverse axis is parallel to y-axis, and its centre is (2,-3), the length of transverse axis is 12 and eccentricity 7/6 is

The length of latus rectum of parabola y2+8x-2y+17 = 0 is:

The coefficient of x6 in (1+x+x2+x3+x4+x5)6 is

If the focus and directrix of a parabola are (3,-4) and x+y+7=0 then its length of latusrectum is

The sub-tangent, ordinate and sub-normal to the parabola y2 = 4ax at a point ( diffferent from the origin ) are in

The radius and height of a cylinder are measured as 5cm and 10 cm respectively and there is an error of 0.02 cm in both the measurements. The approximate error in the volume is

The equation Sin-1 x- Cos-1 x=Cos-1 (√3/2) has

The equation of the normal to the curve y=3x2+4x-6 at (1, 1) is

If the variable line l1(x-a)+y=0 and l2(x+a)+y=0 are conjugate lines w. r. to the ellipse x2/a2+y2/b2=1. Then the locus of their point of intersection is

7 Coupons are numbered 1 to 7. Four are drawn one by one with replacement. The probability that the least number appearing on any selected coupon is greater then or equal to 5 is

If three points A, B and C have position vectors (1, x, 3), (3, 4, 7) and (y, -2, -5) respectively and if they are collinear then (x, y) is equal to

The perpendicular distance of radical axis determined by the circles x2+y2+2x+4y-7=0 and x2+y2-6x+2y-5=0 from the origin is

If ( x - 2 ) is a common factor of the expressions x2 + ax + b and x2 +cx+ d, then b-d/c-a is equal to :

(cos A+ cos 3A+cos 5A+cos 7A)/ (sin A+sin 3A+sin 5A+sin 7A)=

The sum of the coefficients of even powers of x in the expansion of (1+x+x2)15 is

The angles of the triangle formed by the lines 5x+3y-15=0, x+y-4=0, 2x+y-6=0 is

The two curves 2x2+y2=20, x2-4y2+8=0

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 locus of a point P for which the chord of contact of  x2/a2+y2/b2=1 touch the circle x2+y2=r2

The orthocentre of the triangle formed by the points(2,-1,1), (1,-3,-5), (3,-4,-4) is

The number of possitive odd divisors of 216 is

If x2-cx+d=0, x2-ax+b=0 have one common root and second has equal roots then 2(b+d)= .If x2-cx+d=0, x2-ax+b=0 have one common root and second has equal roots then 2(b+d)= 1)0 2)ac 3)a+c 4)a-c

The quadrilateral formed by the lines x-y+2=0, x+y=0, x-y-4=0, x+y-12=0 is

cos3200+ cos31000 +cos3 1400=

Minimum value of 25 cos2 x +16 sec2 x is

A particle is moving along a line according to the law s=t3-3t2+5. The acceleration of the particle at the instant where the velocity is zero is

If θ lies in the first quadrant and 5 tan θ = 4 then (5 sin θ  -  3 cos θ) / (sin θ + 2 cos θ) is equal to

The value of k for which the points A(1, 0, 3), B(-1, 3, 4), C(1, 2, 1) and D(k, 2, 5) are coplanar is

The point on the curve x2=2y which is closest to the point (0, 5) is

If the tangent at θ=π/4 to the curve x=a cos3θ, y= a sin3θ meets the x and y axis in A and B, then the length of AB is

The radius of the base and depth of a conical funnel are 20 cm and 40 cm respectively. Water flows from the funnel at the rate 2.25 cc/sec. the rate at which the water level decreases when altitude is 30 cm is

Four tickets marked 00,01,11 respectively are placed in a bag. A ticket is drawn at random 5 times being replaced each time. The probability that the sum of the numbers on the tickets is 22 is

The equation to the circle touching the y-axis at the origin and passing through(b, c) is

If α,β,γ,δ are the roots of 3x4-8x3+x2-10x+5=0 then the equation whose roots are –α,-β,-γ,-δ is

The equation of the circle passing through the point of intersection of the circles x2+y2-3x-6y+8=0, x2+y2-2x-4y+4=0 and touching the line x+2v=5 is

Tan [cos-1 4/5+tan-1 2/3] =

(1.03)19 =

8 cos3 100 -6cos100=

If y2=4ax then 4a(1+y12)3/2+(y2+4a2)3/2y2=

The equation of the normal to the curve y2=x3/2a-x at (a, a) is

The vector of magnitude √51 which makes equal angles with the vector a=1/3(i-2j+2k), b=1/5(-4i-3k), c=j is

The circumcentre of the triangle formed by(0,0), (2, -1) and ( -1, 3) is (5/2,5/2). Then the orthocentre is

At a selection, the probability of selection of A is 1/7 and that of B is 1/5.The probability that both of them would not be selected is

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

sin 780 -sin 180 +cos 1320=

For a binomial variate X with n = 6, if P(X = 2) = 9P(X = 4), then its variance is

(x+y+z)(x+yω+zω2)(x+yω2+zω)=

cos2(450- α)+ cos2(150+ α)- cos2(150- α)=

The circle x2+y2-4x+4y-1=0 cuts the positive coordinate axes in A and B respectively. The equation to the diameter of the circle perpendicular to the chord AB is

Tangents OA and OB are drawn to the circle x2+y2+gx+fy+c=0 from O(0,0). The equation of the circum circle of the ?OAB is

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

cot 160 cot 440+cot 440cot 760- cot 760cot 160=

If [(x2+x+1)/(x2+2x+1)]=A+[B/(x+1)]+[C/(x+1)2] then A-B=

If the expression x2-(5m-2)x+(4m2+10m+25)=0 can be expressed as a perfect square,then m=

If b2-4ac>0,then the graph of y= ax2+bx+c

If 10 balls are to be distributed among 4 boxes, that the probability for the first box always to contain 4 ball is

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

The straight line x + y = k touches the parabola y = x-x2, if  k =

sin2200+ sin21000 +sin2 1400=

If radii of two circles are 4 and 3 and distance between centres is √37 then the angle between the circles is

If α,β are the roots of 6x2-6x+1=0 then 1/2(a+bα+cα2+dα3)+1/2(a+bβ+cβ2+dβ3)=