IIT-JEE 2007 Paper 1 Offline | JEE Advanced Year Wise Previous Years Questions

IIT-JEE 2007 Paper 1 Offline

MCQ (Single Correct Answer)

-1

Consider the following linear equations

$$ax + by + cz = 0$$

$$bx + cy + az = 0$$

$$cx + ay + bz = 0$$

Match the conditions/expressions in Column I with statements in Column II.

	Column I		Column II
(A)	$$a + b + c \ne 0$$ and $${a^2} + {b^2} + {c^2} = ab + bc + ca$$	(P)	the equations represent planes meeting only at a single point.
(B)	$$a + b + c = 0$$ and $${a^2} + {b^2} + {c^2} \ne ab + bc + ca$$	(Q)	the equations represent the line $$x=y=z$$.
(C)	$$a + b + c \ne 0$$ and $${a^2} + {b^2} + {c^2} \ne ab + bc + ca$$	(R)	the equations represent identical planes.
(D)	$$a + b + c = 0$$ and $${a^2} + {b^2} + {c^2} = ab + bc + ca$$	(S)	the equations represent the whole of the three dimensional space.

A - (q), B - (r), C - (p), D - (s)

A - (r), B - (q), C - (s), D - (p)

A - (r), B - (p), C - (q), D - (s)

A - (r), B - (q), C - (p), D - (s)

IIT-JEE 2007 Paper 1 Offline

MCQ (Single Correct Answer)

-1

In the following [x] denotes the greatest integer less than or equal to x.

Match the functions in Column I with the properties Column II.

	Column I		Column II
(A)	$$x\|x\|$$	(P)	continuous in ($$-1,1$$).
(B)	$$\sqrt{\|x\|}$$	(Q)	differentiable in ($$-1,1$$)
(C)	$$x+[x]$$	(R)	strictly increasing in ($$-1,1$$)
(D)	$$\|x-1\|+\|x+1\|$$	(S)	not differentiable at least at one point in ($$-1,1$$)

A - (p), (q), (r), B - (p), (s), C - (r), (s), D - (p), (q)

A - (p), (q), B - (p), (s), C - (r), (s), D - (p)

A - (p), (q), (r), B - (p), C - (r), D - (p), (q)

A - (p), (r), B - (p), (s), C - (r), D - (p), (q)

IIT-JEE 2007 Paper 1 Offline

MCQ (Single Correct Answer)

-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 - s, B - s, C - r, D - p

A - s, B - q, C - p, D - r

A - s, B - s, C - p, D - r

A - s, B - q, C - s, D - r

IIT-JEE 2007 Paper 1 Offline

MCQ (Single Correct Answer)

-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

3 $$\Omega$$

4 $$\Omega$$

5 $$\Omega$$

6 $$\Omega$$

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