1
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) $${\pi \over 2}$$

A
A - s, B - s, C - r, D - p
B
A - s, B - q, C - p, D - r
C
A - s, B - s, C - p, D - r
D
A - s, B - q, C - s, D - r
2
IIT-JEE 2007 Paper 1 Offline
MCQ (Single Correct Answer)
+3
-1

A resistance of 2 $$\Omega$$ is connected across one gap of a metre-bridge (the length of the wire is 100 cm) and an unknown resistance, greater than 2 $$\Omega$$, is connected across the other gap. When these resistance are interchanged, the balance point shifts by 20 cm. Neglecting any corrections, the unknown resistance is

A
3 $$\Omega$$
B
4 $$\Omega$$
C
5 $$\Omega$$
D
6 $$\Omega$$
3
IIT-JEE 2007 Paper 1 Offline
MCQ (Single Correct Answer)
+3
-1

In an experiment to determine the focal length (f) of a concave mirror by the u-v method, a student places the object pin A on the principal axis at a distance x form the pole P. The student looks at the pin and its inverted image form a distance keeping his/her eye in line with PA. When the student shifts his/her eye towards left, the image appears to the right, oh the object pin. Then,

A
$$x < f$$
B
$$f < x < 2f$$
C
$$x = 2f$$
D
$$x > 2f$$
4
IIT-JEE 2007 Paper 1 Offline
MCQ (Single Correct Answer)
+3
-1

Two particles of mass m each are tied at the ends of a light string of length 2a. The whole system is kept on a frictionless horizontal surface with the string held tight so that each mass is at a distance 'a' form the centre P (as shown in the figure). Now, the mid-point of the string is pulled vertically upwards with a small but constant force F. As a result, the particles move towards each other on the surface. The magnitude of acceleration, with the separation between them becomes 2x, is

IIT-JEE 2007 Paper 1 Offline Physics - Laws of Motion Question 9 English

A
$${F \over {2m}}{a \over {\sqrt {{a^2} - {x^2}} }}$$
B
$${F \over {2m}}{x \over {\sqrt {{a^2} - {x^2}} }}$$
C
$${F \over {2m}}{x \over a}$$
D
$${F \over {2m}}{{\sqrt {{a^2} - {x^2}} } \over x}$$

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