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CBSE Class 12 Mathematics Solved Question Paper 2017

Short Answer Type

If A is a 3 × 3 invertible matrix, then what will be the value of k if det(A^–1) = (det A)^k.

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Determine the value of the constant ‘k’ so that the function is continuous at x = 0.

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If a line makes angles 90° and 60° respectively with the positive directions of x and y axes, find the angle which it makes with the positive direction of the z-axis.

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Show that all the diagonal elements of a skew symmetric matrix are zero.

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6.
The volume of a sphere is increasing at the rate of 3 cubic centimetres per second. Find the rate of increase of its surface area, when the radius is 2 cm.

straight V space equals 4 over 3 πr cubed rightwards double arrow space dV over dt space equals space 4 over 3 straight pi.3 straight r squared dr over dt rightwards double arrow space dV over dt space equals space 4 πr squared dr over dt rightwards double arrow dr over dt space equals space fraction numerator 1 over denominator 4 πr squared end fraction dV over dt rightwards double arrow dr over dt space equals space fraction numerator 3 over denominator 4 straight pi left parenthesis 2 right parenthesis squared end fraction open square brackets straight r equals space 2 space cm space and space dV over dt space equals space 3 space cm squared divided by sec close square brackets rightwards double arrow dr over dt space space equals fraction numerator 3 over denominator 16 space straight pi end fraction cm divided by sec

Now, let S be the surface area of the sphere at any time t. then,
S = 4πr²
$rightwards double arrow space dS over dt space equals space 8 πr dr over dt rightwards double arrow space dS over dt space equals space 8 straight pi space left parenthesis 2 right parenthesis space straight x fraction numerator 3 over denominator 16 straight pi end fraction open square brackets straight r space equals 2 space cm space and space dr over dt space equals space fraction numerator 3 over denominator 16 straight pi end fraction space cm divided by sec close square brackets rightwards double arrow space dS over dt space equals space 3 space cm squared divided by sec$