WBJEE 2014 | Mathematics

If x = 2 + 2^2/3 + 2^1/3 , then the value of x³ - 6x² + 6x is :

If x, y, z are in AP as well as in GP and x+3, y+3, z+3 are in HP, then :

The locus of point z satisfying Re(1/z) = k, where k is a non-zero real number, is :

The locus of the point z satisfying Re(1/z) = k, where k is a non-zero real number, is :

The eqn of the tangents to 2x² - 3y² = 36 which are parallel to the straight line x + 2y - 10 = 0 are :

If sin A + cos A = m and sin³ A + cos³ A = n, then

The principle value of sin^-1 (sin 2pi/3) is:

The eccentricity of the hyperbola 3x² - 4y² = -12 is equal to :

the common tangents to the circle x² + y² + 2x = 0 and x² + y² - 6x = 0 form a triangle which is

The plane 2x - (1+ρ)y + 3ρz = 0 passes through the intersection of the planes :

The side of a triangle are 3x+4y, 4x+3y and 5x+5y unit where x,y>0. The triangle is :

The ordr of the differentiable wqn associated with the primitive y = c₁ + c₂ e^x + c₃ e^{-2x + c₄} , where c₁, c₂, c₃, c₄ are arbitery constants,

If f(x) = ax + b and g(x) = cx + d, then f(g(x)) = g(f(x))↔

x₁, x₂, x₃, x₄ are the root pf the eqn x⁴ - x³ sin 2β + x² cos 2β - x cosβ - sinβ = 0 then tan^-1 x₁ + tan^-1 x₂ + tan^-1 x₃ + tan^-1 x₄ is equal to :

AB is a chord of the parabola y² = 4ax with vertex at ABC is drawn perpendicular to AB meeting the axes at C, the projection of BC on the axis of the parabola is :

The two parts of 100 for which the sum double of first and square of second part is minimum, are :

The curve for which the normal at any point (x,y) and line joining origin to the points from the isosceles triangle with x axis as base is :

The value of (0.16) ^{log₂₅[1/3 + 1/32 + 1/33 ... + ∞]} is :

If a circle of radius 3k passes through the origin and meet the axes at A and B, the locus of the centroid of ΔOAB is :

If the complex numbers z₁, z₂, z₃ are in AP. Then they lie on a

If cos α + cos β + cos γ = sin α + sin β + sin γ = 0, then the value of cos 3α + cos 3β + cos 3γ  is

If the function f : R → A given by x²/(x² + 1) is surjection, then A is equal to ;

An ellipse slide between two perpendicular straight lines. Then the locus of the centre is a/an :

If M is the foot of the perpendicular from a point P on a parabola to its directrix and SPM is an equilateral triangle, where S is the locus, then SP is equal to ;

The smallest angle of the triangle whose sides are 6 + √12, √48, √24 is :

Let a = cos 2pi/7 + i sin 2pi/7, α= a + a² +a⁴ and β= a³ + a⁵ + a⁶.Then the eqn whose roots are α,β is :

The function f(x) = max {(1 - x), (1 + x), 2}, x belongs to (-∞, ∞ ) is :

A farmer has to go 500 m due north, 400 m dues east and 200 m due south to reach his field. If he takes 20 m to reach the feild, then a average speed of farmer during the walk is:

The set of points where the function f(x) = x|x| is differentiable is :

If the parametric eqn of a curve is given x = e^t cos t, y = e^t sin t, then the tangent to curve at the point t = pi/4 makes with the x axis of the angle :

If  [x] denotes the greatest integer less than or equal to x, then lim_x→∞  [1²x] + [2²x] + [3²x] + ... + [n²x] equal :

Let a, b, c be real numbers, a ≠ 0, If α is a root of a²x²  + bx + c = 0, β is the root of a²x² - bx - c = 0 and 0<α<β, then the eqn a²x² + 2bx + 2c = 0 has root γ that always satisfies :

A perticle is moving with a velocity of v = (3+6t+9t²) cm/s. The displacement of the perticle in the interval t=5s to t=8s is:

The point of intersection of the curve whose parametric eqn are x = t² + 1, y = 2t and x = 2s, y = 2/s is given by :

In a triangle ABC sin A - cos B = cos C, then angle B is :

The eqn asin x + bcos x + c, where |c|>√(a² + b²) has :

The no of natural nos smaller than 10⁴ in the decimal notation of which all the digit are different, is :

If tan θ = - 4/3, then sin θ is :

For the curve x = t² - 1, y = t² - t, the tangent line is perpendicular to x-axis where :

If two circles a(x² + y²) +bx +cy = 0 and A(x²) + y²) +Bx +Cy = 0 touch each other then :

If a,b,c are in GP, then the eqn ax² + 2bx + c = 0 and dx² + 2ex + f = 0 have a common root, if d/a,e/b,f/c are in :

If y^1/m = [x + √(1+x²)], then (1+x²)y₂ + xy₁ is equal to :

If f(x) = |log|x||, then

The image of the point (3,8) in the line x + 3y = 7 is :

An equilateral triangle is inscribed in the parabola y² = 4ax whose one vertex is at the vertex of the parabola, the length of its side is :

Ten different letters of an alphabet are given, words with five letters are formed from these given letters. Then the number of words which have at least one letter repeated, is :

The eccentricity of the hyperbola with latus rectum 12 and semi-conjugate axis 2√3 is

AB is a diameter of x² + 9y² = 25. The eccentric angle of A is pi/6, then the eccentric angle of B is :

In a triangle ABC, the value of 1 - tan B/2 tan C/2 = 2a/(a + b + c) is equal to :

If the normal at the one end of the latus rectum of an ellipse x²/a² + y²/b² = 1 passes through the one end of the minor axis, then :