A to Z Exams

If f(x)=√(1-√(1-x2)), then

If Cos (A-B) =  3/5 and tan A tan B  = 2 then which one of the following is true

.In ΔABC, if 2R+ r= r1, then the triangle isa

If the roots of the equation 4x3-12x2+11 x + k = 0 are in arithmetic progression, then k is equal to :

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

If y=x+1/(x+1/x+....∞) then dy/dx=

If the range of a random variable X is {0, 1, 2, 3, 4,........} with P(X = k) = (k+1)a / 3k for k ≥ 0 then a is equal to

If ak is the coefficient of xk in the expansion of  (1+x+x2)n for k = 0,1,2,..........2n then a1 + 2a2 +.....+2na2n  =

A person of height 180 cm starts from a lamp post of height 450 cm and walks at the constant rate of 4 km per hour. The rate at which his shadow increases is

The circumcentre of the triangle with vertices at A(5, 12),B(12, 5), c (2√(13 ) ,3√(13 )) is

If cos θ+ sin θ=a, then sin 2θ=

If g is the inverse of f and f1(x)=1/(1+xn),then g1(x) equals,

The circles x2+y2-4x+6y+8=0 and x2+y2-10x-6y+14=0,touch

If a=2i+3j+6k, b=3i-6j+2k, c=6i+2j-3k then axb=

If n positive integers are taken at random and multiplied together , the probability that the last digit of the product is 2,4,6 or 8 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 the distance of two points P and Q on the parabola y2 = 4ax are 4 and 9 respectively,then 9  respectively,then the distance of the point of intersection of the tangents at P and Q fro the focus is

If (3+i) is a root of the equation x2 + ax+ b=0 then a =

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 sum of divisors of 253453 is

2 cos 540. Sin 660=

∫ exloga , ex dx is equal to :

Assertion(A):x2+x+1 is greater than zero for all real x. Reason(R):when b2-4ac

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

(sin 3A+ sin A) sin A+ (cos 3A- cos A) cos A=

The number of non trivial solutions of the system x-y+z =0 ,x+2y-z=0  and 2x-y+3z=0  is

If the latusrectum of a hyperbola subtends an angle 600 at the other focus then its e=

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

The system of circle x2+y2+2λx-5=0 is

If the coefficients of (2r+1)th term and (4r+5)th term in the expansion of (1+x)10 are equal then r=

If ax+by+c=0 is the equation of the common radical axis of the coaxial system (3x2+3y2-2x-2y-1)+λ(x2+y2-x-2y-3)=0 then ab+bc+ca=

The equation of the incircle of triangle formed by x=0,y=0 and (x/3)+(y/4)=1 is

The locus of the point of intersection of two tangents drawn to the circle x2+y2=a2 which make a constant angle α to each other is

If f(x,y,z)=√(yz)+ √(zx)+ √(xy) then xfx+yfy+zfz=

If n is a positive integer, then the coefficient of xn in the expansion of (1 + x)n/(1-x) is

All the values of x satisfying sin 2x+ sin 4x= 2 sin 3x are

If (1 + x)n = C0 + C1x + C2x2 + …. + CnXn, then C0 - C2 + C4 - C6 + … is equal to:

If two roots of x4-16x3+86x2-176x+105=0 are 1,7 then the roots are

If cot θ=8/15 and θ does not lie in the first quadrant, then cos(300+ θ) +sin(450- θ)+cos(1200+ θ)=

The locus of the point of intersection of the tangents at the ends of a chord of a circle x2+y2=a2 which touches the circle x2+y2-2ax=0 is

The point equidistant from the points (-, 0, 0),(1, 0, 0),(0, 2, 0) and (0, 0, 3) is:

d/dx{Tan-1√(1-sin x/1+sin x)}=

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

If x4-16x3+86x2-176x+105=0 then s1,s2,s3,s4 are

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:

4 Tan-1 1/5- Tan-1 1/239 =

The least value of (x-a) (x-b) occurs at x=

The radius of the sphere x2+y2+z2-2x+4y-6z+7=0 is

The circumcentre of the triangle formed by the points(1,2,3), (3,-1,5), (4,0,-3) is

The solution of dy/dx = y2 / (xy - x2) is

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

If the roots of the equation x2-5x+16=0 are α,β and the roots of the eqution x2+px+q=0 are α2+β2,αβ/2,then

1.22+2.32+3.4+….+n(n+1)2=

7/5(1+1/?102 +1.3/1.2.1/104 +1.3.5/1.2.3.1/106 +...........∞)

Statement I : If f:A→B, g:B→C are such that gof is an injection, then f is an injection. Statement II : If f:A→B, g:B→C are such that gof is an injection, then g is an injection. The correct statement 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

The equation of the auxiliary circle of x2/12+y2/18=1 is

The 4th term of (1-2x)-1 when x=1/3 is

The differential equation obtained by eliminating the arbitrary constants a and b from xy=aex + be-x is

If a, b, c form a geometric progression with common ratio r,then the sum of the ordinates of the Points of intersection of the line ax + by + c = 0 and the curve x + 2y2=0

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

(2 cos θ-1) (2 cos 2θ-1) (2 cos 4θ-1) (2 cos 8θ-1)=

The ratio in which ys-plane divides the line segment joining (-3, 4, - 2) and (2,1, 3)  is

A line l meets the circle x2 + y2 = 61 in A,B and P(-5,6) is such that PA = PB= 10.  Then the equation of l is :

The common chord of x2+y2-4x-4y=0 and x2+y2=16 substends at the origin an angle equal to

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

The The limiting points of the coaxal system x2+y2+2µy+9=0 are

If 2x-y+3=0, 4x+ky+3=0 are conjugate with respect to the ellipse 5x2+6y2-15=0 then k=

If 2x+3y+4=0is perpendicular bisector of the segment joining the points A (1, 2) and B (α, β) then the value of α+β is

If the circles x2+y2-4x+6y+8=0, x2+y2-10x-6y+14=0 touch each other , then the point of contact is

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

Two cards are drawn at random from 10 cards numbered 1 to 10. The probability that their sum is odd, if the  two cards are drawn together is

A tangent to the circle x2+y2=4 meets the coordinate axes at P and Q. The locus of mindpoint of PQ is

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 locus of the midpoint of the chord of the circle x2+y2=25 which subtends a right angle at (2,-3) is

tan 2A- sec Asin A=

3 horses A, B and C run a race. If the probability of A’s win is twice that of B and the probability of B’s win is thrice that of C then the probabilities of their winning are

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

The radii of two circles are 2 units and 3 units.If the radical axis of the circles cuts one of the common tangents of the circles in P then ratio in which P divides the common tangent is

The equations of the diagonal of the square formed by the pairs of lines 12x2+7xy-12y2=0 and 12x2+7xy-12y2-x+7y=1 is

The angle A ofABC is found by measurement to be 630 an the area is calculated by the formula 1/2bc sin A. the percentage error in the calculated value of the area due to an error of 15 minutes in the measured value of A is

Three forces having magnitude 5, 4 and 3 act on a particle in the direction 2i-2j-k, i+2j+2k and -2i+2k respectively and the particle gets displacement rom the point A whose position vector is 6i-2j+3k to the point whose position vector is 9i+7j+5k. Then the work done by these forces is

The solution of (dy/dx)=ey-x is

A man throws a die until he gets a number bigger than 3. The probability that he gets a 5 in the last throw is

The length of the focal chord of the parbola y2 = 4ax which makes an angle θ with its axis is

The locus of the middle points of the chords of the circle x2+y2=8 which are at a distance of √2 units from the centre of circle is

Origin is the orthocentre  of the triangle formed by the points(5,-1), (-2,3) and (-4,-7) then its ninepoint centre is

Tan-1 3/2-Tan-11/5 =

6 sin 200- 8sin3200=

For a student the probability of getting a pass in one paper is75%and the probability of getting a pass in another paperis60%.The probability is 60% .The probability for the student to pass in one paper only is

If one end of the diameter of the circle x2+y2-6x+4y-12=0 is (7, -5),  then the other end of the diameter is

The longest distance from (-3, 2) to the circles x2+y2-2x+2y+1=0 is

If a= sin θ+ cos θ, b= sin3 θ+ cos3θ then

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

The equation x2 - 3xy + λy2 + 3x - 5y + 2 = 0, where λ is a real number, represents a pair of straight lines. If θ is the angle between these lines then cosec2 = θ

A five digit number is formed by using the digits 0, 1,2,3,4 and 5 without repetetion.The probability that the number is divisible by 6 is

 If the rate of change in y=2x3+3x2-30x+7 is 6 times the rate of change in x, then x=

The centre of the circle whose centre is on the straight line 5x – 2y +1=0 and cuts the x-axis at two points whose abscissa are -5 and 3 is

If α,β,γ are roots of x3-2x2+3x-4=0,then Σα2β2

If 3x  /(x-a) (x-b)  =  2/(x-a)  +  1/(x-b)  then a:b =