A to Z Exams

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

sin2200+ sin21000 +sin2 1400=

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

If n is even then C02-C12+C22-……….+(-1)n Cn2 =

If the orthocenter of the angle formed by the lines 2x+3y-1=0, x+2y-1=0, ax+by-1=0  is at the origin, then (a, b) is given by

A question paper contains 5 questions each having an alternative. The number of ways that a student can answer one or more questions is

Two angles ofa triangle are Cot-1 2 and Cot-1 3.Then the third angle is

(cos 3θ - sin 3θ)/ (cos θ+ sin θ)=

The length of the intercept made by the normal at (1,6) of the circle x2+y2-4x-6y+3=0 between the coordinate axes is

If α, β, γ are the angles made by a line with x, y, z axes in positive directions then the range of cos α cos β+ cos β cos γ+cos γ cos α is

If 3x-2y+4=0 and 2x+5y+k=0 are conjugate lines w.r to the ellipse 9x2+16y2=144 then the value of k is

The vertices of a hyperbola (2,0),(-2,0) and the foci are (3,0),(-3,0).The equation of the hyperbola is

For all values of λ, the polar of the point (2λ, λ-4) with respect to the circle x2+y2-4x-6y+1=0 passes through the fixed point

If u=(x-y) (y-z) (z-x) then ux+uy+uz=

The term independent of x in (√(x/3)+√3/(2x2 ))10is:

(a-b).(b-c)x(c-a)=

The solution of (x2y3+x2)+(y2x3+y2)dy=0 is

If x

In ΔABC , cos(A+2B+3C/2)+cos(A-C/2) =

The equation of the circle passing through the points of intersection of the circlesx2+y2=5, x2+y2+12x+8y-33=0 and touching x-axis is

Equation of the latusrectum of the parabola x2+8x+12y+4=0 is

If the slope of one line of 8x2+2hxy+by2=0 is double the other, then h2=

A line which makes an acute  angle ? with the possitve direction f x-axis is drawn through the point P(3, 4) and cuts the curve =4x at Qand R . The lengths of the segments  PQ and PR  are numerical values of the roots of the equation

 If α is a non real root number of x6 = 1 then  (α5 + α3 +α +1 ) / (α2 +1) is equal to

The equation of the tangent to the  curve y2=4x+5 and which is parallel to0 y=2x+7 is

If the lines x2 + 2xy – 35y2 - 4x + 44y -12=0 and 5x +λy -8 = 0 are concurrent, then the value of λ is

d/dx{cos-1√(1+x)/2}=

If the area of the triangle formed by the points (t,2t), (-2,6), (3,1) is 5sq.unit, then t is

If the straight line a(x+y-1)+b(2x-3y+1)=0 for different values of a and b are parallel to y- axis then the realization ship between  a& b is

If a,b,c are distinct then (b-c)x+(c-a)y +(a-b)=0 and (b3-c3)x + (c3-a3)y+(a3-b3)=0 represent the same line when

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

The normal of the circle(x-2)2+(y-1)2=16 which bisects the chord cut off by the line x-2y-3=0 is

If α,β,γ are the roots of x3+2x2-5x+2=0 then the equation whose roots α-1/βγ,β-1/γα,γ–1/αβ is

If the pair of straight lines xy - x - y + l = 0 and the line ax + 2y - 3a = 0 are concurrent, then a is equal to

The roots of x3-6x2+7x+2=0, one root being 2+√5 are

The vectors a+2b+3c, 2a+b-2c, 3a-7c are

If α,β,γ are the roots of x3+3px2+3qx+r=0 then the equation whose roots α-1/βγ,β-1/γα,γ–1/αβ is

If cos 5θ=a cos θ+bcos3 θ+c cos5 θ+d, then

The volume of the parallelepiped whose conterminal edges are 2i-3j+4k, i+2j-2k, 3i-j+k is

The lines x-y—2=0, x+y-4=0 and x+3y=6 meet in the common point

The locus of the middle point of chords of the ellipse x2/a2+y2/b2=1   which are at a constant distance d from the centre of the ellipse is

If y2=(x-a)(x-b) then d3/dx3[(d2y/dx2)-2/3]=

If an error of 0.02cm is made while   measuring the radius 10cm of a sphere, then the error in the volume is

The additive inverse of (1+2i)(3-4i) is

The angle between the lines x cos α + y sin α = p1 and x cos β +y sin β =p2 where α

d/dx{Sin-12x/1+x2}=

If cot θ+ cosec θ= √3 then θ=

The inverse point of (1, 2) w.r.t the circle x2+y2=25 is (5, k), then k=

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

If x= 2 cos t- cos 2t, y= 2 sin t- sin 2t then dy/dx=

The point diametrically opposite to the point P(1, 0) on the circle x2+y2+2x+4y-3=0 is

A:The area of the triangle formed by the two rays whose combined equation is y=|x| and the line x+2y=2 is 3/4 R: The area of the triangle formed by the lines ax2+2hxy+by2=0,lx+my+n=0 is (n√h2-ab)/(|am2-2nlm+bl2|)

A family of curves has the differential equation (xy)dy/dx = 2y2 - x2. Then the family of curves is

The lines joining the origin to the points of intersection of the line x-y=2 with the curve 5x2+12xy-8y2+8x-4y+12=0 are equally inclined to

If the roots of 2x3-3x2+kx+6=0 are in A.P then k=

The equation of the line passing through the point (-2, 1) and having intercepts whose product is 1 is

The equation of the normal at the positive end of the latus rectum of the hyperbola x2-3y2=144 is

d/dx{Tanxn+Tannx+Tan-1(a+xn/1-axn)}=

Cos-1(63/65) + 2 Tan-1(1/5) =

If y= ax+b/(x-1)(x-4) has a maximum value at the point (2, -1) then

If in a binomial distribution n=20 and q=0.75,then its mean is

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

cos 200+cos 1000+cos 1400 =

The harmonic mean of the roots of the equation (5+√2)x2-(4+√5)x+8+2√5)=0 is

"The points (0,"  8/3   )," (1, 3), (82, 30) are"

A tower 51 m high has a mark at a height of 25m from the ground. If the two parts subtend equal angles to an eye at the height of 15 m from the ground, the distance of the tower from the observe is

If f : R → R is defined by f(x) = [2x] - 2[x] for x ε R, where [x] is the greatest integer not exceeding x, then the range of f is :

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

If θ= Sin-1 x+ Cos-1 x+ Tan-1 x, 0≤x≤1, then the smallest interval in which θ lies is given by

If two angles of ∆ ABC are 45o and 60o, then the ratio of the smallest and the greatest sides are

If cot θ=-3/4 and θ is not in the second quadrant then 5 sin θ+10 cos θ+9 sec θ-16 cosecθ- 4cot θ=

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

If fg=ch, the lines represented by hxy+gx+fy+c=0 fprm a quadrilateral with coordinate axes which is

In a ?ABC , orthocentre is H(2354,981), A(2,1), B (-10,6) then the distance between the orthocentres of ?HBC, ?HAC is

cos(n+1)α cos(n-1)α+ sin(n+1)α.sin(n+1)α

The transformed equation of x3-(5/2)x2-(7/18)x+(1/108)=0 by removing fractional coefficients is

The sum of the distances of any point on the ellipse 3x2+4y2=24 from its foci is

The product of the slopes of the tangents to the ellipse 2x2+3y2=6 draw from the point (1, 2) is

tan 200+ tan 400+√3 tan 200. tan 400=

The points on the ellipse x2/25+y2/9=1 whose angles differ by a right angle are

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

The sides of triangle are 3x+2y-6=0, 2x-3y+6=0, x+2y+2=0. P(0, b) is a point on y-axis. If P lies on the triangle or inside the triangle then the range of b is

A man is known to speak the truth 2 out of 3 times. He throws a die and reports that it is a six. The probability that it is actually a five is

If α,β are acute angles, sin α=4/5, tan β=5/12 then the descending order of A=sin(α+β) ,B= cos(α+β), C= tan(α+β) is

x+(x2/3!)+(x3/5!)+....∞=

The period of cos (5x/2) is

Statement I: The points 4i+5i+k, -j-k, 3i+9j+ 4k and -4i+4j+4k are coplanar Statement II  : The given points from  the  vertices of a parallelogram. Which of the following is true? a)  Both statements  are  true and statement II is correct explanation of statement I b)  Both  statements  are true  and statement II is not correct explanation of statement I cv) Statement I is true and statement II is false d)  Statement I is false and  Statement II is true

In a ∆ABC ,  ∑(b+c) tan a/2 tan(b-c)/2  is equal to

C2+C4+C6+……….. =

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 equation of the circle cutting orthogonally circles x2+y2-4x+3y-1=0 and passing through the points (-2, 5), (0, 0) is

If α,β,γ are the roots of 4x3-6x2+7x+3=0 then αβ+βγ+αγ=

The shortest distance between the straight line passing through the point A=(6, 2, 2) and parallel to the vector(1, -2, 2) and the straight line passing through A’=(-4, 0, 1) and parallel to the vector (3, -2, -2) is

If x= a(2 cos θ+cos 2θ), y= a(2 sin θ+sin 2θ)then dy/dx=

The number of numbers greater than 1000 but not greater than 4000 that can be formed with the digits 0,1,2,3,4 repetition of digits being allowed is

If f(x) =2x2+3x-5, x=3, δx=0.02, then  δf=

The solution of x2dy-y2dx=0 is

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

(i): If 12Cr+1=12C3r-5, then r=3 or 4 (ii): 9C3+9C5=10Cr, then r=4 or 6

The value of ‘a’ such that the sum of cubes of the roots of the equation x2 – ax + (2a – 3)=0 assumes the minimum value is