1
IIT-JEE 2007 Paper 1 Offline
MCQ (Single Correct Answer)
+3
-1
$$\mathop {\lim }\limits_{x \to {\pi \over 4}} {{\int\limits_2^{{{\sec }^2}x} {f(t)\,dt} } \over {{x^2} - {{{\pi ^2}} \over {16}}}}$$ equal
2
IIT-JEE 2007 Paper 1 Offline
MCQ (Single Correct Answer)
+3
-1
Match the integrals in Column I with the values in Column II.
| Column I | Column II | ||
|---|---|---|---|
| (A) | $$\int\limits_{ - 1}^1 {{{dx} \over {1 + {x^2}}}} $$ | (P) | $${1 \over 2}\log \left( {{2 \over 3}} \right)$$ |
| (B) | $$\int\limits_0^1 {{{dx} \over {\sqrt {1 + {x^2}} }}} $$ | (Q) | $$2\log \left( {{2 \over 3}} \right)$$ |
| (C) | $$\int\limits_2^3 {{{dx} \over {1 + {x^2}}}} $$ | (R) | $${\pi \over 3}$$ |
| (D) | $$\int\limits_1^2 {{{dx} \over {x\sqrt {{x^2} - 1} }}} $$ | (S) | $${\pi \over 2}$$ |
3
IIT-JEE 2005 Screening
MCQ (Single Correct Answer)
+3
-0.75
$$\int\limits_{ - 2}^0 {\left\{ {{x^3} + 3{x^2} + 3x + 3 + \left( {x + 1} \right)\cos \left( {x + 1} \right)} \right\}\,\,dx} $$ is equal to
4
IIT-JEE 2005 Mains
MCQ (Single Correct Answer)
+3
-1
Evatuate:
$$\int_\limits{0}^{\pi} e^{|\cos x|}\left[2 \sin \left(\frac{1}{2} \cos x\right)+3 \cos \left(\frac{1}{2} \cos x\right)\right] \sin x ~d x$$
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