BITSAT Maths Test - 4

Let z₁ and z₂ be two roots of the equation z² + az + b = 0,z being complex . Further ,assume that the origin ,z₁ and z₂ form an equilateral triangle .Then

The solution of the equation (dy/dx)=cotx coty is

AOB is the positive quadrant of the ellipse , where OA = a, OB = b. The area between the arc AB and the chord AB of the ellipse is

If y=a cos (log x) + b sin (log x) where a,b are parametres, then x²y+xy'

The general solution of the equation x²dy=-2xydx is

If f(x)=log_x²log(x), then at x=e, f'(x)=

The function f(x)=x³-3x²-24x+5 is increasing in the interval

1/(1.2.3.4) + 4/(3.4.5.6) + 9/(5.6.7.8) + 16/(7.8.9.10) + ....... ∞ =

The angle of elevation of the top of a tower from the top and bottom of a building of height 'a' are 30^o and 45^o respectively. If the tower and the building stand at the same level, the height of the tower is

The curve represented by x = a (cosh θ + sinh θ), y = b (cosh θ − sinh θ)    is

The parabolas y² = 4x and x² = 4y divide the square region bounded by the lines x = 4, y = 4 and the coordinate axes. If S₁, S₂, S₃ are respectively the areas of these parts numbered from top to bottom; then S₁ : S₂ : S₃ is

The area of the region bounded by the curves y = |x-1| and y = 3-|x| is

If cos^-1p + cos^-1q+cos^-1r = π, then p² + q² + r² + 2pqr is equal to

The value of α for which the function f(x)=1+αx, α≠0 is the inverse of itself, is

The difference of an integer and its cube is divisible by

x₁+2x₂+3x₃ = 2x₁+3x₂+x₃ = 3x₁+x₂+2x₃ = 0. This system of equation has

If the traces of the matrices A and B are 20 and -8, then the trace of (A + B)=

A cylindrical gas container is closed at the top and open at the bottom. If the iron plate of the top is 5/4 times as thick as the plate forming the cylindrical sides, the ratio of the radius to the height of the cylinder using minimum material for the same capacity is

(sin θ + i cos θ) ⁴

Lines x²+4xy+y²=0 and x-y=4 form the figure

Equation of the tangent at (-4,-4) on x²=-4y is

On the parabola y² = 8 x if one extremity of a focal chord is (1 ∕ 2, − 2) then its other extremity is

How many words can be formed from the letters of the word COMMITTEE?

The numbers of all words formed from the letters of the word CALCUTTA is

Out of 30 consecutive integers, 2 are chosen at random. The probability that their sum is odd, is

Three identical dice are rolled. The probability that the same number will appear on each of them is

If two angles of a Δ A B C are 45^o and 60⁰then the ratio of the smallest and the greatest sides are

In a triangle the line joining circum-centre and in-centre is parallel to BC, then cosB+cosC=

The value of p for which the difference between the roots of the equation x²+px+8 = 0 is 2, are

If a, b, c be in G.P. and p, q be respectively A.M., between a, b and b, c then

The sum of first n terms of the series (3/1²) + (5/(1² + 2²)) + (7/(1² + 2² + 3²)) + ... is

If f (x) = (x)/(x - 1) = 1/y, then f (y) =

If f (x) = x/logx then 2f(x - 2) > f(x) if

If lines 3y+4x=1, y=x+5 and 5y+bx=3 are concurrent, then the value of b is

The length of the sub normal to the parabola y²=4ax at any point is equal to

The smallest radius of the sphere passing thro'(1,0,0),(0,1,0) and (0,0,1) is

The d.r. of normal to the plane through (1,0,0), (0,1,0) which makes an angle π/4 with plane x + y = 3 are

The general solution of the equation tan2θ.tanθ=1 for n∈I is, θ is equal to

If sinθ=√3cosθ, -π<θ<0, θ=

cos 255^o + sin 165^o=

If p=7i-2j+3k and q=3i+j+5k, then the modulus of p-2q is

The position vector of a point which divides the segment joining 2a-3b and 3a-2b in the ratio 2:3 internally is