BITSAT Maths Test - JEE

The equation of a circle which is ortho gonal to circles x²+y²+3x-5y+6=0 and 4x²+4y²-28x+29=0 and whose centre lies on the line 3x+4y+1=0 is

The least positive integral value of n for which

The differential equation for the family of curves x² + y² - 2ay = 0, where a is an arbitrary constant is

The solution of differential equation

Differential of sin^⁻1[(1-x)/(1+x)] w.r. to √x is equal to

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

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

From the top of a building of height h metres, the angle of depression of an object on the ground is α. The distance (in metres) of the object from the foot of the building is

The area of the region bounded by the curves y = |x-2|, x = 1, x = 3 and the x-axis is

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

The solution of the equation x(dy/dx)=y-xtan(y/x) is

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

The sum of first 50 terms of the series cot^⁻1 3 + cot^⁻1 7 + cot^⁻1 13 + cot^⁻1 21 + ... is

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

(1/1)+(1/(1+2))+(1/(1+2+3))+...up to (n+1) terms is equal to

If B is a non-singular matrix and A is a square matrix, then det (B^⁻1 AB) is equal to

If in a square matrix A=[a_ij], we find that
a_ij = a_ji ∀ i,j, then A is a

If the function f(x) = 2x³ - 9ax² + 12a²x + 1, where a > 0, attains its max. and min. at p and q respectively such that p² = q then a equals

The complex numbers 1,-1, i √3 from a triangle which is

If the normal at the point t on a parabola y = 4ax meet it again at t₁, then t₁ =

The locus of the point of intersection of two normals to the parabola x²=8y, which are at right angles to each other,is

Each line represented by equation (x₁y-xy₁)²=a²(x²+y²) is at a distance from (x₁,y₁)

The number of words formed from the letters of the word INDEPENDENCE when vowels are together is

A problem in mathematics is given to 3 students whose chances of solving individually are 1/2, 1/3, and 1/4. The probability that the problem will be solved atleast by one is

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

The mean and variance of a Binomial distribution are 6 and 4. The parameter n is

In a ΔABC , A : B : C = 3 : 5 : 4 . Then a + b + c √2 is equal to

If the product of the roots of the equation mx² + 6x + 2m - 1 = 0 is -1, then the value of m is

If the sum of n terms of the series 2³ + 4³ + 6³ + ... ∞ is 3528, then n equals

 to n terms is S, then S is equal to

If f (x) = (1)/(1 - x), then f[f{f (x)}] =

4 [cot^⁻13 + cosec^⁻1 (√5)] is equal to

If the parametric equation of a curve is given by x=e^t cos t, y=e^t sin t, then tangent to the curve at the point t=(π/4) makes the angle with the axis of x

The equidistance point from lines 4x+3y+10=0, 5x-12y+26=0 and 7x+24y-50=0 is

The entercepts of the plane 2x-3y+4z=12 on the co-ordinate axes are given by

The plane which passes through the point (3, 2, 0) and the line (x - 3)/1 = (y - 6)/5 = (z - 4)/4 is

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

In a triangle A B C , s − a Δ = 1 8 , s − b Δ = 1 12 , s − c Δ = 1 24 , then b =

If tan (cotx) = cot(tanx), then sin2x is equal to

If x tan 45^o cos 60^o= sin 60^o cot 60^o, then x is equal to

If a is any vector then |axi|²+|axj|²+|axk|²=

If a+b+c=0, |a|=3, |b|=5, |c|=7, then the angle between a and b is