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The area common to the parabola y = 2x^{2} and y = x^{2} + 4 is
The equation of the line parallel to the tangent to the circle x^{2} + y^{2} = r^{2} at the point (x₁, y₁) and passing thro' origin is
The lines 2x3y=5 and 3x4y=7 are diameters of a circle of area 154 sq. units. Then the equation of this circle is :
The solution of the equation cosx cosy (dy/dx)=sinx siny is
The differential equation with respect to the curve y=e^{mx} is
At a point a metres high above a lake the angle of elevation of a cloud is α and the angle of depression of its image is β, the height of the cloud is
The differential equation (d^{2}y/dx^{2})^{2/3} = (y + (dy/dx))^{1/2} is of
The tangents to the hyperbola x^{2}  y^{2} = 3 are parallel to the st. line 2x + y + 8 = 0 at the following points
The solution of the differential equation (dy/dx) = (y/x) + (φ (y/x)/φ' (y/x)) is
The function f(x) = cot^{⁻1} x + x increases in the interval
For a skew symmetric odd ordered matrix A of integers, which of the following will hold true:
The sum of the products of the elements of any row of a determinant A with the same row is always equal to
The point on the curve y = x^{2} + 4x + 3 which is closest to the line y = 3x + 2 is
Which of the following statements are true ?
(1) The amplitude of the product of complex numbers is equal to the product of their amplitudes.
(2) For any polynomial f(x) =0 with real coefficients, imaginary roots occurs in conjugate paris.
(3) Order relation exists in complex numbers whereas it does not exist in real numbers.
(4) The value of ω used as a cube root of unity and as a fourth root of unity are different.
The acute angle between the lines joining origin to the intersection points of the curve x^{2}+y^{2}2x1=0 and line x+y=1 is
The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of there parallel lines is :
A group of 7 is to be formed from 6 boys and 4 girls. In many ways can this be done if the boys are in majority?
In eight throws of 1 die or 3 is considered a success. Then the standard deviation of the success is
In a competitions A, B and C are participating. The probability that A wins is twice that of B, the probability that B wins is twice that of C. The probability that A loses is
In a triangle ABC, A = 30^{o}, b = 8, a = 6, then B = sin^{⁻1} x where x =
x^{2}+x+1+2k(x^{2}x1)=0 is a perfect square for how many values of k?
If the arithmetic and geometric means of two distinct, positive numbers are A and G respectively, then their harmonic mean is
a, b, c are three unequal numbers such that a, b, c are in A.P. ; b  a, c  b, a are in G.P., then a : b : c : :
If A and B are two sets such that n(A) = 70, n(B) = 60 and n(A ∪ B)= 110, then n (A ∩ B) is equal to
If y = 4x  5 is a tangent to the curve y^{2} = ax^{3} + b at (2, 3), then
The equation of a line passing through the intersection of lines 3x2y1=0 and x4y+3=0 and point (π,0) is
The smallest radius of the sphere passing thro'(1,0,0),(0,1,0) and (0,0,1) is
The equation of the sphere concentric with the sphere x^{2}+y^{2}+z^{2}4x6y8z=0 and which passes thro' (0.1,0) is
If α is a root of 25cos^{2}θ + 5cosθ  12 = 0, (π/2)<α<π, then sin2α is equal to
If 0≤x≤π and 81^{sin2x} + 81 ^{cos2x} = 30, then x is equal to
Given that θ is a acute and that sin θ =3/5. Let x,y be positive real numbers such that 3(xy) =1, then one set of solutions for x and y expressed in terms of θ is given by
The number of vectors of unit length perpendicular to vectors and is
A force acts at a point A whose position vector is If point of application of moves from A to the point B with position vector then work done by is
2 videos16 docs143 tests

2 videos16 docs143 tests
