Sample BITSAT Maths Test - JEE

If the line 2x - y + k = 0 is a diameter of the circle x² + y² + 6x -6y + 5 =0, then k is equal to

If z = i log(2 - √3), then cos z =

The differential equation of the family of lines passing through the origin is

Which of the following is a solution of the differential equation

If y' = x-y/x+y, then its solution is

(d/dx)[tan⁻¹((sinx+cosx)/(cosx-sinx))]

Value of 1 + log x + (log x)²/2! + (log x)³/3! + ..... ∞ is

The angle of elevation of a cloud from a point h mt above the surface of a lake is θ and the angle of depression of its reflection in the lake is φ . The height of the cloud is

The eccentricity of the conjugate hyperbola of the hyperbola x² - 3y² = 1 is

Which of the following functions is a solution of the differential equation (dy/dx)² - x (dy/dx) + y = 0?

The solution of the differential equation (dy/dx) = (y/x) + (φ (y/x)/φ' (y/x)) is

tan⁻¹(1/4)+ tan⁻¹(2/9) is equal to

f(x) = ||x| - 1| is not differentiable at

For every n ∈ N, 2³ⁿ-7ⁿ-1 is divisible by

If A, B are two square matrices such that AB = A and BA = B, then

For a square matrix A, it is given that AA' = I, then A is a

The maximum value of xy subject to x+y=8 is

The real value of α for which the expression 1-i sin α/1+2 i sin α is purely real is

The angle between lines xy=0 is

The focus of the parabola (y-2)²=20(x+3) is

The equation of the normal to the curve x² = 4y at (1, 2) is

Two finite sets have m and n elements, the total number of subsets of the first set is 56 more than the total number of subsets of the second. The value of m and n are respectively

In how many ways can the letters of the word ARRANGE be arranged so that R's are never together?

A and B are events such that P(A ∪ B) = 3/4, P(A ∩ B) = 1/4, P(A̅)= 2/3, then P(A̅ ∩ B) is

The probability that a number selected at random from the set of numbers {1,2,3,....,100} is a cube is

In a equilateral triangle r : R : r₁ is

The perimeter of a triangle is 16cm. One of the sides is of length 6cm. If the area of the triangle is 12sq.cm, then the triangle is

The product of cube roots of -1 is equal to

The sum of all 2-digit odd numbers is

If the sum of first n terms of an A.P. be 3n² - n and its common difference is 6, then its first term is

In a town of 10,000 families it was found that 40% family buy newspaper A, 20% buy newspaper B, and 10% families buy newspaper C, 5% families buy A and B, 3% buy B and C and 4% buy A and C. If 2% families buy all the three newspapers, then number of families which buy A only is

If f : N x N → N is such that f (m,n) = m + n where N is the set of natural numbers, then which of the following is true?

The ortho centre of triangle whose vertices are (0,0), (3,0) and (0,4) is

The angle between the curves y²=x at x²=y at (1,1) is

The angle between the planes 2x-y+z=6 and x+y+2z=7 is

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

If 2cos²x+3sinx-3=0, 0≤x≤180^o, then x=

The equation sinx+cosx=2 has

Maximum value of cos²x+cos²y-cos²z is

If 3i+4j and -5i+7j represent the sides of a triangle, then its area is

If and  are mutually perpendicular, then (a+b)²=