NARAYANA IIT ACADEMY JEE MAIN â 2013 - Narayana Group
NARAYANA IIT ACADEMY JEE MAIN â 2013 - Narayana Group
NARAYANA IIT ACADEMY JEE MAIN â 2013 - Narayana Group
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(1) Statement-I is true; Statement – II is true; Statement – II is a correct explanation for<br />
Statement – I.<br />
(2) Statement-I is true; Statement – II is true; Statement – II is not a correct explanation for<br />
Statement – I.<br />
(3) Statement – I is true; Statement – II is false.<br />
(4) Statement – I is false; Statement – II is true.<br />
Ans. (2)<br />
Sol.<br />
p q<br />
74. If<br />
~ ~ (p ~ q) (~ p q) (p ~ q) <br />
(~ p q)<br />
T T F F F F F<br />
T F F T T F F<br />
F T T F F T F<br />
F F T T F F F<br />
(p q) (~ q ~ p)<br />
T T T<br />
F F T<br />
T T T<br />
T T T<br />
(p q) <br />
(~ q ~ p)<br />
f (x)dx (x), then x 5 f (x 3<br />
)dx is equal to :<br />
1 x x 3 x x dx C<br />
3 <br />
<br />
1 x 3 x 3 x 2 x 3<br />
dx C<br />
3<br />
Ans. (3)<br />
1 x x 3 x x dx C<br />
3<br />
1 x 3 x 3 x 3 x 3 dx C<br />
3 <br />
<br />
<br />
3<br />
(1) 3<br />
2 3<br />
<br />
3 3 3 3<br />
(2) <br />
(3) <br />
(4) <br />
Sol. Let I =<br />
<br />
5 3<br />
x f (x )dx<br />
1 2 3 3<br />
I = 3x .x f (x )dx<br />
3 <br />
put x 3 = t<br />
1<br />
I t.f (t)dt<br />
3<br />
<br />
1<br />
I t f (t)dt f (t)dt<br />
dt<br />
3 <br />
1 3 3<br />
I x . (x ) (t)dt<br />
3 <br />
<br />
<br />
1 3 3 3 2<br />
I x . (x ) (x ).3x dx<br />
3 <br />
<br />
<strong>NARAYANA</strong> <strong>IIT</strong> <strong>ACADEMY</strong> <strong>JEE</strong> <strong>MAIN</strong> – <strong>2013</strong>
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