BITSAT Maths Test - 2

If the two circles 2x² + 2y² -3x + 6y + k = 0 and x² + y² - 4x + 10y + 16 = 0 cut orthogonally, then the value of k is

If then a and b are

The order and degree of differential equation √(dy/dx) - 4 (dy/ dx) - 7x = 0 are

If x dy = y(dx + y dy), y > 0 and y (1) = 1, then y (-3) is equal to

Solution of the differential equation 

If x=a[(cost)+(log tan(t/2))], y=a sint, (dy/dx)=

then  = f '(1)

1/2! - 1/3! + 1/4! - 1/5! + ....... equals

The length of the shadow of a rod inclined at 10^o to the vertical towards the sun is 2.05 metres when the elevation of the sun is 38^o.The length of the rod is

The area of the region bounded by the curve y = x - x² between x = 0 and x = 1 is

The product of the perpendicular, drawn from any point on a hyperbola to its asymptotes is

The sum of first 50 terms of the series cot^⁻13 + cot^⁻1 7 + cot^⁻1 13 + cot^⁻1 21 + ... is

The area bounded by the curve x = at², y = 2at and the X-axis is 1 ≤ t ≤ 3 is

The domain of the function f(x) = √(2 - 2x - x²) is

The difference of an integer and its cube is divisible by

If A and B are two matrices such that AB = B and BA = A, then A² + B² is equal to

if A is a 3 x 3 matrix and B is its adjoint matrix. If ∣B∣ = 64, then ∣A∣ =

The strength of a beam varies as the product of its breadth b and square of its depth d. A beam cut out of a circular log of radius r would be strong when

Which of the following is correct

The pole of the line lx+my+n=0 w.r.t. the parabloa y² =4ax

Equation x²+7xy+3y²+8x+14y+λ=0 represents a pair of straight lines, value of λ is

The latus rectum of the parabola y² = 5x + 4y + 1 is

How many total words can be formed from the letters of the word INSURANCE in which vowels are always together?

A polygon has 44 diagonals. The number of its sides is

A committee consists of 9 experts from three institutions A, B and C, of which 2 are from A, 3 from B and 4 from C. If three experts resign, then the probability that they belong to different institutions is

A single letter is selected at random from the word "PROBABILITY". The probability that it is a vowel is

If the area of a Δ A B C be λ then a² sin 2B + b² sin 2A is equal to

In a Δ A B C , a = 1 and the perimeter is six times the AM of the sines of the angles. The measure of ∠ A is

If α, β are the roots of the equation x²- 2x + 2 = 0, then the value of α² + β² is

The sum of an infinite G.P. is 3. The sum of the series formed by squaring its terms is also 3. The series is

The 5th term of a G.P. is 2, then the product of its first 9 term is

If f : R → R is given as f (x) = |x| and A = {x ∈ R : x > o}, then f^⁻1(A) =

If f (x) = {2x - 3, x ≤ 2} {x, x > 2} then f (1) is equal to

The equation line passing through the point P(1,2) whose portion cut by axes is bisected at P, is

The equation of the common tangent to the curves y²=8x and xy=-1 is :

The radius of the circle in which the sphere x² + y² + z² + 2x - 2y - 4z - 19 = 0 is cut by the plane x + 2y + 2z + 7 = 0, is

The acute angle between the planes 2x-y+z=6 and x+y+2z=3 is

If 0≤x≤π and 81^sin2x + 81 ^cos2x = 30, then x is equal to

If 1 + sin x + sin ² x + … ∞ = 4 + 2 √ 3 , 0 < x < π , x ≠ π/2 then x =

(secA+tanA-1)(secA-tanA+1)-2 tanA=

The value of b such that the scalar product of the vector î+ĵ+k̂ with the unit vector parallel to the sum of the vectors 2î + 4ĵ - 5k̂ and bî+ 2ĵ + 3k̂ is one is

The angle between the vectors 3i+j+2k and 2i-2j+4k is