If (4, 0) and (–4, 0) are foci of an ellipse and semiminor axis is 3, then the ellipse passes through which one of the following points?
Under what condition do the planes bx – ay = n, cy – bz = 1, az – cx = m intersect in a line?
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What is the equation of the plane through z-axis and parallel to the line
If the lines 3y + 4x = 1, y = x + 5 and 5y + bx = 3 are concurrent, then what is the value of b?
What is the least value of f (x) = 2x3 – 3x2 – 12x + 1 on [–2, 2.5]?
If (–5, 4) divides the line segment between the coordinate axes in the ratio 1 : 2, then what is its equation?
Out of 32 persons, 30 invest in National Savings Certificates and 17 invest in shares. What is the number of persons who invest in both?
What are the equations of the directives of the ellipse 25x2 + 16y2 = 400?
Let A be an n x n matrix. If det (λA) = λs det (A), what is the value of s?
Let E be the ellipse and C be the circle x2 + y2 = 9. Let P = (1, 2) and Q = (2, 1). Which one of the following is correct?
What is the geometric interpretation of the identity ?
1. If the diagonals of a given parallelogram are used as sides of a second parallelogram, then the area of the second parallelogram is twice that of the given parallelogram.
2. If the semi-diagonals of a given parallelogram are used as sides of a second parallelogram, then the area of the second parallelogram is half that of the given parallelogram.
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If A be a real skew-symmetric matrix of order n such that A2 + I = 0, I being the identity matrix of the same order as that of A, then what is the order of A?
If sin x + cosec x = 2, then what is the value of sin4x + cosec4x?
If A + B + C = π/2, then what is the value of tan A tan B + tan B tan C + tan C tan A?
If angles of a triangle are in the ratio 1 : 2 : 3, then what is the ratio of its corresponding sides?
If x = (1 1 0 1)2 and y = (1 1 0)2, then what is the value of x2 – y2?
If (1 0 x 0 1 0)2 (1 1 y 1)2 = (1 0 z 1 1)2, then what are the possible values of the binary digits x, y, z respectively?