WBJEE Maths Test - 2

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

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

How many words are formed from the letters of the word EAMCET so that two vowels are never together?

The probability of getting a total of 10 in a single throw of two dice is

A fair dice is tossed repeatedly until six shows up 3 times. The probability that exactly 5 tosses are needed is

The probability that a radar will detect an object is p. The probability that it will be detected in n cycles is

In an equilateral triangle, (circumradius) : (inradius) : (exradius) is equal to

If the side of a triangle are 13, 14, 15, then the radius of the incircle is

Let α, β be the roots of the quadratic equation x² + px + p³ = 0. If (α, β) is a pt. on the parabola y² = x, then the roots of the qudratic equation are

The absiccae of the points of the curve y = x³ in the interval [-2, 2], when the slope of the tangent can be obtained by mean value theorem for the interval [-2, 2] are

If a, b, c are distinct +ve real numbers and a² + b² + c² = 1 then ab + bc + ca is

If the roots of the equation x³ - 12x² + 39x - 28 = 0 are in A.P., then their common difference will be

The function f (x) = log ((1 + x)/(1 - x)) satisfies the equation

If A = [(x,y) : x² + y² = 25] and B = [(x,y) : x² + 9y² = 144] and A ∩ B contains

The equation of bisectors between the lines 3x+4y-7=0 and 12x+5y+17=0 are

The roots of the equation x⁴ - 4x³ + 9x² − 12x + 18 = 0 are____

The sides AB, BC and CA of a triangle ABC have 3, 4 and 5 interior points respectively on them. The number of triangles that can be constructed using these interior points as vertices is

If the curves intersect each other at right angles, then

Let the algebraic sum of the perpendicular distances from (3, 0), (0, 3) and (2, 2) to a variable line is zero, then the line passes through a fixed point whose co-ordinates are

Let d₁ , d₂ , d₃ , … …, d_k be all the divisors of a positive integer n including 1 and n.
Suppose d₁ , d₂ , d₃ + … … + d_k = 72 , then the
value of is

The equation f(x) = 0 has eight distinct real solution f also satisfy f(4+x) = f(4-x). The sum of all the eight solution of f(x) = 0 is

In a triangle X Y Z , ∠ Z = are the roots of the equation ax² + bx + c = 0, a ≠ 0 then

If , then

In triangle ABC, line joining circumcentre and incentre is parallel to side AC, then cos A + cos C is equal to

The system of confocal conics
being an arbitary constant

Two mutually perpendicular tangents of the parabola y² = 4ax meet the axis in P₁ and P₂. If S is the focus then equals

If a line segment AM = 'a' moves in the plane XOY remaining parallel to OX so that the left end point A slides along the circle x² + y² = a², the locus of M is

Let P (a secθ , b tan θ)    and Q (a sec φ , b tan φ)  where θ + φ = π/2 , be two points on the hyperbola x² ∕ a² − y² ∕ b² = 1 . If (h, k) is the point of intersection of normals at P and Q, then k is equal to

Let g x = ;0 < x < 2, m and n are integers, m ≠0, n > 0 and let p be the left hand derivative of | x - 1 | at x = 1. then

The locus of the orthocentre of the triangle formed by the lines
(1 + p)x - py + p(1 + p) = 0,
(1 + q)x - qy + q(1 + q) = 0,
and y = 0, where p ≠ q , is

Let x be a positive real number not equal to 1. In each of the following diagrams, the shaded region does not include its boundary. Which of these regions represents the set {x,y| log_x log_xy² > 0} ?

The set of discontinuities of the function f (x) = ( 1/2 − cos2x) contains the set

The value of   is

In a triangle ABC, tan C < 0. Then

Two functions f and g have first and second derivatives at x = 0 and satisfy the relations,

The differential equation

Let x₀ = 2007 and let Then

If z₁ = a + ib and z₂ = c + id are complex number such that |z₁| = |z₂| = 1 and Re = 0, then the pair of complex numbers w₁ = a + ic and w₂ = b + id satisfies :

Let A and B be two square matrices of same order that satisfy A + B = 2B^⊤ and 3A + 2B = l then which of the following statements is true?

There exist a triangle ABC satisfying the conditions,

If P is any point lying on the ellipse  whose foci are S and S'. Let ∠ PSS ′ = α and ∠ PS′S = β , then: