BITSAT Maths Test - 3 - JEE MCQ

The equation of the line parallel to the tangent to the circle x² + y² = r² at the point (x₁, y₁) and passing thro' origin is

The lines 2x-3y=5 and 3x-4y=7 are diameters of a circle of area 154 sq. units. Then the equation of this circle is :

The solution of the equation cosx cosy (dy/dx)=-sinx siny is

The differential equation with respect to the curve y=e^mx is

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

The sum of the series 2/3! + 4/5! + 6/7! + ......∞ is

At a point a metres high above a lake the angle of elevation of a cloud is α and the angle of depression of its image is β, the height of the cloud is

The differential equation (d²y/dx²)^2/3 = (y + (dy/dx))^1/2 is of

The tangents to the hyperbola x² - y² = 3 are parallel to the st. line 2x + y + 8 = 0 at the following points

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

The domain of sin^⁻1 x is

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

 For a skew symmetric odd ordered matrix A of integers, which of the following will hold true:

The sum of the products of the elements of any row of a determinant A with the same row is always equal to

The point on the curve y = x² + 4x + 3 which is closest to the line y = 3x + 2 is

Which of the following statements are true ?
(1) The amplitude of the product of complex numbers is equal to the product of their amplitudes.
(2) For any polynomial f(x) =0 with real co-efficients, imaginary roots occurs in conjugate paris.
(3) Order relation exists in complex numbers whereas it does not exist in real numbers.
(4) The value of ω used as a cube root of unity and as a fourth root of unity are different.

The acute angle between the lines joining origin to the intersection points of the curve x²+y²-2x-1=0 and line x+y=1 is

The focus of the parabola x² − 2 x − 8 y − 23 = 0 is

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

The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is :

A group of 7 is to be formed from 6 boys and 4 girls. In many ways can this be done if the boys are in majority?

In eight throws of 1 die or 3 is considered a success. Then the standard deviation of the success is

In a competitions A, B and C are participating. The probability that A wins is twice that of B, the probability that B wins is twice that of C. The probability that A loses is

In a triangle ABC, A = 30^o, b = 8, a = 6, then B = sin^⁻1 x where x =