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JEE Mathematics Solved Question Paper 2020

Short Answer Type

21.

22.

If the variance of the following frequency distribution :

Class : 10-20 20-30 30-40

Frequency : 2 x 2

is 50, then x is equal to ....

23.

A test consists of 6 multiple choice questions, each having 4 alternative answers of which only one is correct. The number of ways, in which a candidate answers all six questions such that exactly four of the answers are correct, is ......

24.

25.
$If \vec{a} = 2 \hat{i} + \hat{j} + 2 \hat{k}, then the value of {|\hat{i} \times (\vec{a} \times \hat{i})|}^{2} + {|\hat{j} (\vec{a} \times \hat{j})|}^{2} + {|\hat{k} \times (\vec{a} \times \hat{k})|}^{2} = ?$

Ans : 18

$Let \vec{a} = x \hat{i} = x \hat{i} + y \hat{j} + z \hat{k} \hat{i} \times (\vec{a} \times \hat{i}) = (\hat{i} . \hat{i}) \vec{a} - (\vec{a} . \hat{i}) \hat{i} = y \hat{j} + z \hat{k} similarly \hat{j} \times (\vec{a} \times \hat{j}) = x \hat{i} + z \hat{k} and \hat{k} \times (\hat{a} \times \hat{k}) = x \hat{i} + y \hat{k} {|\hat{i} \times (a \times i)|}^{2} + {|\hat{j} \times (\vec{a} \times \hat{j})|}^{2} + {|\hat{k} \times (\vec{a} \times \hat{k})|}^{2} {|y \hat{j} + z \hat{k}|}^{2} + {|x \hat{i} + z \hat{k}|}^{2} + {|x \hat{i} + y \hat{j}|}^{2} = 2 {|a|}^{2} = 2 (9) = 18$