WBJEE Maths Test - 2 - JEE MCQ

If in the expansion of ((x⁴) - (1/x³))¹⁵, x^-17 occurs in the rth term, then

x² + y² + 2(2K+3)x - 2Ky +(2K+3)² + K² - r² = 0 represents the family of circles with centres on the line

The solution of the equation (1+x²)(1+y)dy+(1+x)(1+y²)dx=0 is

The differential equation of family of curves y=a cos(x+b) is

If z 1 and z 2 are two non-zero complex numbers such that |z₁ + z₂| = |z₁| + |z₂| , then Arg z₁ − Arg z₂ is

The differential of sin⁻¹[(1-x)/(1+x)] w.r.t. √x is equal to

The function f(x)=|x| is defined on [-1,1]. It does not satisfy the Rolle's theorem because

In an ellipse the distance between the foci is 6 and it's minor axis is 8. Then its eccentricity is

If S′ and S are the foci of the ellipse (x²/a²)+(y²/b²)=1 and P(x,y) be a point on it, then the value of SP + S′P is

If e and e ′ are the eccentricities of the hyperbola x² ∕ a² − y² ∕ b² = 1 and its conjugate hyperbola, the value of 1 ∕ e² + 1 ∕ e′² is

Sin (sin⁻¹1/2 + cos⁻¹1/2) equals

The equation of circle which passes through (4,5) and whose centre is (2,2) is

If the function f (x)   = increases for all x, then

If A is a square matrix such that A² = I, then A⁻¹ is equal to

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

If the parabola y²=4ax passes thro' the point (1,-2), then the tangent at this point is

The line x-y+2=0 touches the parabola y²=8x at the point

The number of 7 digit numbers which can be formed using the digits 1, 2, 3, 2, 3, 3, 4 is