WBJEE 2014 | Mathematics

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

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

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 :

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

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

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 :

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

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

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

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

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:

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

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 :

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

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

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:

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 :

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

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

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

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

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

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 :

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

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 :

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

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

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

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

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

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 :

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

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

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

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

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

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

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

If tan θ = - 4/3, then sin θ 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  [x] denotes the greatest integer less than or equal to x, then lim_x→∞  [1²x] + [2²x] + [3²x] + ... + [n²x] equal :

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

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 :

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 :