Let A be a 3 x 4 matrix of rank 2. Then the rank of ATA, where AT denotes the transpose of A. is,
Let f : R2 --> R be a function defined by
Then, the value of fx(0, 0) and, fy(0, 0) are
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Let [x] denote the greatest integer function of x. The value of a for which the function
is continuous at x = 0 is
Let f : R --> R be given by f(x) = [x] the greatest integer less than or equal to x. Then
Suppose f : R —> R and g : R --> R are uniformly continuous functions with g(x) > 0, V x. Then which of the following is true?
The equation of the curve for which the square of the ordinate is twice the rectangle contained by the abscissa and the intercept of the normal on x-axis and passing through (2, 1) is
At what point will be function f (x) = be continuous ?
Suppose that the dependent variables z and w are functions of the independent variables x and y, defined by the equations f(x, y, z, w) = 0 and g(x, y, z, w) = 0, where fz gw – fw gz = 1. Which one of the following is correct?
Which of the following statement(s) is/are correct?
If is α repeated root of the polynomial equation f(x) = 0, then
Consider the function f(x) = , then which one of the following is correct?
If f(x) = x5 - 20x3 + 240 x, then f(x) is
The value of ‘C’ in Rolle’s theorem, where -π/2 < C < π/2 and f(x) = cos x is equal to
Let f(x) = xn | x | for real x. Then f(x) is differentiable at origin, if n is equal to which one of the following ?
Let
Then, the value of k for which f(x, y) is continuous at (0, 0) is
If f(x, y) is differentiable at (a, b), then the partial derivatives fx and fy at (a, b)
Let f(x ,y ) =, then the value of fx(0, 0) and fy(0, 0) is
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