﻿ If A is a 3 × 3 invertible matrix, then what will be the value of k if det(A–1) = (det A)k. from Class 12 CBSE Previous Year Board Papers | Mathematics 2017 Solved Board Papers

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# CBSE Class 12 Mathematics Solved Question Paper 2017

#### Short Answer Type

1.

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

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2.

Prove that

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# 3.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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4.

Let find a matrix D such that CD – AB = O.

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5.

Using properties of determinants, prove that

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6.

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

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7.

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.

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8.
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9.

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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10.

Show that the function f(x) = 4x3 – 18x2 + 27x – 7 is always increasing on R.

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