A to Z Exams

The area (in sq unit ) of the region bounded by the curves 2x = y2-1 and x = 0 is

cos2 720- sin2 540=

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 product of the perpendicular distances from the origin on the pair of straight lines12x2 + 25xy + 12y2 + 10x + 11y + 2 = 0, is

The fourth vertex of the parallelogram whose consecutive vertices are (2,4,-1), (3,6,-1),(4,5,1) is

tan 2A- sec Asin A=

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

The modules of (3+2i)(2-i)/ (1+i) is

The functions y=x4-6x2+8x+15 has minimum at x=A, y=x(x-1)(x-2) has maximum at x=B, y=2x3-3x2-12x+5 has minimum at x=C. The ascending order of A, B, C is

6 boys and 4 girls sit around a round table at random. The probability that the no two girls sit together is

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

If C0, C1, C2,...... are binomial coefficients , then C1+C2+C3+C4+....+Cr+....+Cn is equal to :

A man 6 feet height walks at a uniform of 20 above the floor. An object falls freely under gravity, starting from rest at the same height as the lamp, put at a horizontal distance of 5 ft from it. The speed of the shadow of the object on the floor when it has fallen through 15 ft is

The equations whose roots are exceed by 1 than those of x3-5x2+6x-3=0 is

The locus of the point of intersection of two perpendicular tangents to the circle x2+y2=a2, x2+y2=b2 is

Bag A contains4 white, 3black balls.Bag B contains 3 white and 5 black balls.One ball is drawn from each bag .The probability that both are black is

If n ≥ 2, then 3.C0 – 5.C1 + 7.C2 – ……+(-1)n(2n +3).Cn=

Equation of the circle touching the y-axis at (0, √3) and cuts the x-axis in the points (- 1, 0) and (-3, 0) is

(1.03)19 =

The equations to the common tangents to the two hyperbolas x2/a2-y2/b2=1 and y2/a2-x2/b2=1Are

The function f(x)=cot-1 x+x increases in the interval

If tan θ=-4/3 and θ is not in the fourth quadrant , then the value of 5 sin θ+10cos θ+ 9 secθ+16 cosec θ – 4 cot θ=

The locus of midpoints of the chord of the circle x2+y2 = 25 which pass through a fixed point (4, 6) is a circle. The radius of that circle is

Sum of the product of the binomial coefficients C0,C1,C2,…….Cn taken two at a time is

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

The domain of √3+x + √3-x/x is

If a is small in comparision with x, then (x/x+a)1/2+( x/x-a)1/2

The locus of poles of tangents to the hyperbola x2-y2=a2 w. r. t the parabola y2=4ax is

If f(x)= (a-xn)1/n, where a>0 and n?N, then (fof)(x)=

The equation whose roots are diminished by 1 than those of 4x3-x2+2x-3=0 is

Equation of the directrix of the parabola y2=5x – 4y – 9 is

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

The two circles (x-a)2+(y-b)2=c and (y-b)2+x2=4c have only one real common tangent then

The slopes of the lines passing through A(2,0) and making an angle of 450 with the tangent at A to the circle x2+y2+4x-6y-12=0 is

(sin(n+1)α- sin(n-1)α)/ (cos(n+1)α+ 2 cos nα+ cos(n-1)α)=

The points (1, 1, 1), (1, 2, 3), (2, -1, 1) form

The equation ax2+8xy+2y2+2gx+13y+c=0 represents a pair of parallel straight lines then ascending order a,g,c is

The transformed equation of x3-4x2+1/4x-1/9=0,by eliminating fractional coefficients is

If s=cot θ+cos θ,y= cot θ- cos θ, then (x2-y2)2=

The equation of the plane passing through the points (3, -5, -1), (-1, 5, 7) and parallel to the vector (3, -1, 7) is

The foot of the perpendicular from the point (3, 4) on the line 3x-4y+5=0 is:

If x4-6x3+3x2+26x-24 is divided by x-4 then the quotient is

The tangent to y2 = ax makes an angle 450 with x- axis. Then its point of contact is

The number of four digited numbers that can be formed from using the digits 2,4,5, 7,8 that are divisible by 4 is

cos (θ + α).cos (θ - α)+ sin (θ + α). sin(θ - α)=

The points (2, -1, 3), (-1, 2, -4), (-12, -1, -3), (6, 2, -1) are

The number of possitive odd divisors of 216 is

If the pairs of lines x2+2axy-y2=0, x2+2bxy-y2=0 are such that each pair bisects the angles between the other pair then ab=

The line y = m(x + a)+a/m touch the parabola y2= 4a(x+ a) form

The roots of x4-12x3+34x2-12x+1=0 are

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

2 cos 540. Sin 660=

The line y =2x + k is a normal to the parabola y2= 4x,then=

{n (n+1) (2n+1) : n Є Z }  is subset of

Let the base of the triangle lie along the line x=a and be of the length a. The area of the triangle id a2 if the vertex lies on

The area of the parallelogram whose diagonals are i-3j+2k, -i+2j is

If a circle passes through the point (a, b) and cuts the circle x2+y2=k2 orthogonally, the equation of the locus of its centre is

If [x3/(2x-1)(x+2)(x-3)]=A+(B/[2x-1])+(C/[x+2])+(D/[x-3]) then A is equal to

The tangent and normal to the ellipse 4x2+9y2 =36 at a point P on it meets the major axis in Q nd R respectively. If QR=4, then the eccentric angle of P is

If pr=2(q+s) then among the equations x2+px+q=0 and x2+rx+s=0 have

The slopes of the lines passing through A(2, 0) and making an angle of 450 with the tangent at A to the circle x2 + y2 +4x-6y-12=0 is

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

If x / cos θ= y / cos(θ- 2π/3)= z / cos(θ+2π/3), then x+y+z=

sin5θ/sinθ is equal to

The centroid of the tetrahedron formed by the points(3,2,5), (-3,8,-5), (-3,2,1),(-1,4,-3) is

Express (a+ib/ a-ib)+(a-ib/ a+ib) in the form of a+ib

The equation whose roots are 2√3-5 and -2√3-5 is

If the 3rd, 4th and 5th terms of (x+a)n are 720, 1080 and 810 respectively then (x,a,n)=

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

(1)+(1+2)+(1+2+3)+…. n brackets=

ABC is an isosceles triangle and B= 900. If B and the midpoint P of AC are represented by 3+2i and 1-i then the other vertices are

The least interval value of x such that (x-5)/(x2+5x-14)>0 is

The equations of the tangents to the hyperbola 4x2-5y2 =20 which make an angle 900 with the transverse axis are

A unit vector perpendicular to the plane of a=2i-6j-3k, b=4i+3j-k is

sin θ+ sin (θ + 1200)- sin (1200- θ)=

The pair of lines 6x2+xy-12y2-14x+47y-40=0, 14x2+xy-4y2-30x+15y=0

d/dx{x1/x}=

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 sum of three numbers is 30. The first plus three times the second plus four times the third add on to 80. The numbers so that the product of all three is as large as possible are

The value of a such that x3+3ax2+3a2x+b is increasing on R-{-a} are

If 2,3 are the roots of the equation 2x3+px2-13x+q=0,then (p,q)=

d/dx{√(1+cos x)/sin x}=

A box contains 40 balls of the same shape and weight. Among the balls 10 are white, 16 are red and the rest are black, the probability that a ball drawn from the box is not a black is

The equation of the circle passing through (-7, 1) and having centre at (-4, -3) is

From a point on the level ground, the angle of elevation of the top of a pole is 300 on moving 20 metres nearer, the angle of elevation is 450. Then the height of the pole (in metres), is:

The Cartesian form of the polar equation θ = tan -1 2 is

If Sn = 13 + 23 + .......... + n3  and Tn = 1+2+..................n then

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

The locus of the point of intersection of two tangents to the parabola y2 = 4ax which intercept a constant length d on the directrix is

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

If there is an error of 0.02 cm in the measurement of the side 10 cm of a cube, then error in the surface area is

If 20Pr : 20Pr-1 = 15 : 1 then r =

Consider the circle x2+y2-4x-2y+c=0 whose centre is A(2, 1). If the point P(10, 7) is such that the line segment PA meets the circle in Q with PQ=5, then c=

Three numbers are selected at random without replacement from the set of numbers {1,2,...,n}. The conditional probability that the third number lies between the first two, if the first number is known to be smaller than the second, is

x2 +4ax+3 =0 and 2x2+3ax-9 =0 have a common root, then a =

d/dx{√(1+sin x/1-sin x)}=

If y= a cos x+(b+2x)sinx then y2+y=

If a chord of the circle x2+y2=8 makes equal intercepts of length a on the coordinate axes, then |a|

The extremities of a diagonal of a parallelogram are the points (3, -4) and(-6, 5). If the third vertex is (-2, 1) then the fourth vertex is

The equation of lines passing through the intersection of  lines x-2y+5=0 and 3x+2y+7=0 and perpendicular to x-y=0 is