Subject

Mathematics

Class

CBSE Class 12

Pre Boards

Practice to excel and get familiar with the paper pattern and the type of questions. Check you answers with answer keys provided.

Sample Papers

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 Multiple Choice QuestionsShort Answer Type

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1.

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


straight A to the power of negative 1 end exponent space equals space fraction numerator Adj space straight A over denominator vertical line straight A vertical line end fraction
therefore space vertical line straight A to the power of negative 1 end exponent vertical line space equals space fraction numerator vertical line Adj space straight A vertical line over denominator vertical line straight A vertical line end fraction
equals space fraction numerator vertical line straight A vertical line to the power of 3 minus 1 end exponent over denominator vertical line straight A vertical line end fraction
left square bracket because space If space straight A space is space straight a space non space singular space matrix space of space order space straight n comma space then space vertical line adj space left parenthesis straight A right parenthesis space equals space vertical line straight A vertical line to the power of straight n minus 1 end exponent right square bracket

equals space fraction numerator vertical line straight A vertical line squared over denominator vertical line straight A vertical line end fraction
As space we space are space given space that space vertical line straight A to the power of negative 1 end exponent vertical line space equals space vertical line straight A vertical line to the power of straight k
therefore space straight k space equals negative 1
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2.

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

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3.

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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4.

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

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5.
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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.

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7.

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

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8.

Prove that 

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9.

Using properties of determinants, prove that 

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10.

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

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