A to Z Exams

The roots of the equation 2(a2+b2)x2+2(a+b)x+1=0 are

The number of moles of electrons required to deposit 36 g of Al from an aqueous solution of Al(NO3)3 is (At. wt. of Al = 27)

sin 6θ(2cos2θ-1)=

The probability that the roots of equation x2+nx+1/2+n/2=0 are real ,where n ε N such that n ≤ 5, is

If the normal at ‘θ’ on the hyperbola x2/a2-y2/b2=1 meets the tansverse axis at G, the AG, AG’=

In a thermo couple the temperature of the cold junction is 150C.If the temperature of inversion is 4850C,the neutral temperature of the thermo couple is

If tan θ+ tan 2θ+tan 3θ= 0 then θ=

The heat of formation (ΔHf) of H2O(g) is -243 KJ.ΔE of it at temperature T is

The sum of the first n terms of the series 12+2.22+32+2.42+52+2.62+…. Is n(n+1)2/2 when n is even. When n is odd the sum is

P=(-5,4) and Q=(-2,-3). If PQ is produced to R such that P divides QR externally in the ratio 1:2, then R is

If Sin-1 x+ Sin-1 y+ Sin-1 z=π then x2+y2+z2+2xyz=

P,Q,R are the midpoints of AB,BC,CA of ?ABC and the area of ?ABC is 20. The area of ?POQ is

If ax= by= cz = dw then the value of x[(1/y)+(1/z)+(1/w)]is

Which one of the following elements reduces NaOH to Na?

The locus of the middle point of chords of the ellipse x2/a2+y2/b2=1   whose pole lies on the auxiliary circle is

If tan θ+sin θ=m ,tan θ- sin θ=n then (m2-n2)2

The equation of the circle passing through (0,0) and the points of intersection of x2+y2-4x-6y+9=0 and x2+y2+4x-2y-4=

Consider the circles x2+(y-1)2=9, (x-1)2+y2=25. They are such that

75% of first order reaction is completed in 32 minutes 50% of the reaction would have been completed in

In a bag there are 6 red, 4 black balls. From it 2 balls (without replacement) are drawn. If the first drawn ball is known to be red, the probability for the second drawn ball is also red is

A stone is thrown vertically up and height s reached in time t is given by the formula s=2t2+3t+1. The stone reaches the maximum height in time t =

A molecule (X ) has (i) four sigma bonds formed by the overlap of sp2 and s orbitals (ii) one sigma bond formed by sp2 and sp2 orbitals and (iii) one π bond formed by px and pz orbitals. Which of the following is X ?

If sin A= 1/√10, sin B=1/√5 where A and B are positive and acute, then A+B=

The transition temp.at which rhombic sulphur becomes monoclinic sulphur is

The equation of the director circle of x2/12-y2/8=1 is

The equation of the line perpendicular to the line x=3 and passing through (-4, 2) is

If two of the roots of 2x3+7x2+2x-3=0 are differ by 2 then the roots are

If two of the roots of 8x4-2x3-27x2+6x+9=0 are being equal in magnitude but opposite in sign then the roots are

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

An electron remains undeflected when passing perpendicular to mutually perpendicular electric and magnetic fields. If the magnetic field is 8 Gauss and the electric field is 400 V/m, the velocity of the electron is:

Match the following Circle Radius I. x2+y2+4x-6y-12=0 a) 3 II. x2+y2-4x-2y-4=0 b) 5 III. x2+y2+6x+8y-96=0 c) 11

The condition that the slope of a line represented by ax2+2hxy+by2=0 is thrice that of the other is

If the inverse point of (1, -1) with respect to the circle x2+y2=1/4 is C then Cx+Cy=

The locus  of the  midpoint its of chords of the hyperbola x2/a2-y2/b2=1 which pass through the positive end of the transverse axis is

A person is in between two vertical mountains.The person fires a gun then hears the first echo from the nearby mountain in a time 3s and hears second echo from far mountain in a time 4s.The person hears the third echo after

Identify the correct decreasing order of the following with respect to altitude from atmosphere:I. Troposphere    II. Mesosphere  III. Thermosphere

The solution of y dx-x dy+log x dx=0 is

The Centriod of a triangle is (2,3) and two of its vertices are (5,6) and (-1,4). The third vertex of the triangle is

The quotient and the remainder when x4-11x3+44x2-76x+48 is divided by x2-7x+12 are

Let a and b be nonzero reals such that a .Then the equation of  the line passing through the origin and point of intersection  of  x/a+y/b=1 and x/b+y/a=1 is

If α , β, γ are the roots of x3 + 2x2 - 3x - 1 = 0 then α-2 + β-2 + γ-2 =

How many electrons are present in the M shell of an atom of an clement with atomicnumber 24 (Z = 24) ?

If two lines represented by ax3+bx2y+cxy2+dy3=0 are mutually perpendicular, then the slope of third line is

The area of the triangle formed by the polar of (1,2) with respect to the circle 2x2+2y2-3x=0 and the coordinate axes (in square units) is

The magnetic induction at point 1cm away from a straight long current carrying Conductor is found to be 1x10-5wb/m2.the current that is passing through the conductor is

(1-ω+ω2)(1-ω2+ω4) (1-ω4+ω8) (1-ω8+ω16)=

A uniform rod of length 8a and mass 6m lies on a smooth horizontal surface. Two point masses m and 2m moving in the same plane with speed 2 v and v repectively strike the rod perpendicularly at distances a and 2a from the mid point of the rod in the opposite directions and stick to the rod. The angular velocity of the system immediately after the collision is:

In ΔABC, 1+4 sin(π-A/4)sin(π-B/4)sin(π-C/4)=

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

The velocity v (in cm/sec) of a particle is given in terms of time t (in sec) by the equation,V = at + [b / (t+c)]. The dimensions of a,b,c are

The equation of the tangent to the curve y(x+1) =4 at the point (2, 4/3) is

A condenser of capacity 10 μF is charged to a potential of 500 V. Its terminals are then connected to those of an uncharged condenser of capacity 40 μF. The loss of energy in connecting them together is

If θ is the angle between the curves y=sin x, y =cosx at x=π/4 then tan θ=

A Tuning fork A produces 6 beats per second with another fork B.On loading B with a little wax,it produces 5 beats per second with A If the frequency of A is 256 Hz,the frequency of B is

The condition that the equation ax2+by2+c(x+y)=0 to represents a pair of straight lines is

If vibrating tuning fork of frequency 255Hz is moving with a velocity 4 ms-1 towards the wall the number of beats heard per second is (speed of found in air = 340 ms-1)

The nearest point on the line 2x-y+5=0 from the origin is

The dark lines in the solar spectrum are due to:

If, in aΔABC, r3=r1+r2+r , then ‹A+‹B is equal to

If I1,I2,I3 are excentres of the triangle with vertices (0,0), (5,12), (16,12) then the orthocentre of ?I1,I2,I3 is

A, B, C, D are four points with the position vectors a, b, c, d respectively such that (a-d). (b-c)=(b-d).(c-a)=0. The point D is the ….of ΔABC

An observer finds that the angular elevation of a tower is θ. On advancing ‘a’ metres towards the tower, the elevation is 450 and on advancing b metres the elevation is 900-θ. The height of the tower is

If y= {(3x-5)2/3(x2+1)3/2/(2x+3)5/2(3x2-1)1/3}then dy/dx=

If α,β,γ are the roots of x3+ax+b=0 then (α+β)-1+(β+γ)-1+(γ+α)-1=

x2+y2=t+(1/t),x4+y4=t2+(1/t2)⇒x3y(dy/dx)=

The heat of formation of HI from the equation H2+I2→2HI,ΔH=+52 KJ is

d/dx{cos-1√(1+x)/2}=

If A= tan 150+ cos 150, B= tan 22(1/2)0+ cot 22(1/2)0 and C=sin 540- sin 180 then the ascending order is

Sin (2Tan-13/4) =

The equation of the straight line perpendicular to the straight line 3* + 2y = 0 and passing through the point of intersection of the lines x + 3y - 1 = 0 and x - 2y + 4 = 0 is

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

An aircraft gun can take a maximum of three shots at an enemy plane moving away from it. The probabilities of hitting the plane at the first, second and third shot are 0.5,0.4,0.3 respectively. The probability that the gun hits the place is

Which of the following pairs of ions are colourless ?

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 f : R→ C is defined by f(x) = e2ix  for x є R, then f is (where C denotes the set of all complex numbers)

Liquid benzene burns in oxygen according to 2C6H6(l)+15O2 (g)→12CO2 (g)+6H2O(l) .How many litres of oxygen are required for complete combustion of 39 gms.Of liquid C6H6

If a, b c are in AP,    b- a, c - b and a are in GP, then a: b: c is

For a given reaction which one is higher than the rest among the following

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 domain of f(x)= log10(√x-4 +√6-x) is

In a triangle,if b = 20,c=21 and sinA=3/5,then 'a' is equal to

The angle between the vectors 6i+2j+k, 2i-9j+6k is

An observer is moving away from a sound source of frequency 100Hz. If the observer is moving with a velocity 49m/s and the speed of sound in air is 330m/s. The observed frequency is:

If y=2ax and (dy/dx)=log256 at x=1,then a=

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

A bullet of mass 0.02 kg travelling horizontally with velocity 250 ms_1 strikes a block of wood of mass 0.23 kg which rests on a rough horizontal surface. After the impact, the block and bullet move together and come to rest after traveling a distance of 40 m. The coefficient of sliding friction of the rough surface is

sin2 3A/ sin2A)- (cos2 3A/ cos2A)=

If α,β and γ are roots of x3+ax2+bx+c=0 then(α2+1)(β2+1)(γ2+1)

If X is a poisson variate with P(X = 0) = 0.8, then the variance of X is :

The value of c for which the area bounded by the curve y=8x2-x5,the lines x=1,x=c and x-axis is 16/3 is

If p and q are the coefficients of xn in (1+x)2n-1 and (1+x)2n respectively then 2p=

If u=3(lx+my+nz)2-(x2+y2+z2) and l2+m2+n2=1 then uxx+uyy+uzz=

The function f(x) = xe-x (x ∈R) attains a maximum value at x = …….

cos 250 - cos650=

If |x|

If x is very small and neglecting x3 and higher powers of x then the expansion of log(1+x2)-log(1+x)-log(1-x) as ascending powers of x is

If nPr =30240 and nCr=252then the ordered pair (n, r) is equal to

C2+C4+C6+……….. =

If A+B+C = 7200 then tan A+ tan B+tan C=

The length of the common chord of the circles x2+y2+2hx=0, x2+y2-2ky=0 is