SSC CPO SI and ASI 2011 Paper

© examsiri.com

Question : 140 of 200

Marks: +1, -0

If

a^{2}+b^{2}=2

and

c^{2}+d^{2}=1

, then the value of

(a d-

bc)

^{2}+(a c+b d)^{2}

is

$4/9$
$1/2$
1
2

Solution:

(4)

(a d-b c)^{2}+(a c+b d)^{2}

=a^{2} d^{2}+b^{2} c^{2}-2 a b c d+a^{2} c^{2}+b^{2} d^{2}+2 a b c d

=a^{2} d^{2}+b^{2} c^{2}+a^{2} c^{2}+b^{2} d^{2}

= {d}^{2} ( {a}^{2}+ {b}^{2}\ )+ {c}^{2}\ (\ { a}^{2}+\ {b}^{2} )

= (a^{2}+b^{2} ) (d^{2}+c^{2} )=2 × 1=2

© examsiri.com

Go to Question:

Prev Question

Next Question