1
IIT-JEE 2009 Paper 1 Offline
MCQ (Single Correct Answer)
+3
-1

Let A be the set of all 3 $$\times$$ 3 symmetric matrices all of whose entries are either 0 or 1. Five of these entries are 1 and four of them are 0.

The number of matrices A in A for which the system of linear equations $$A\left[ {\matrix{ x \cr y \cr z \cr } } \right] = \left[ {\matrix{ 1 \cr 0 \cr 0 \cr } } \right]$$ has a unique solution, is

A
less than 4
B
at least 4 but less than 7
C
at least 7 but less than 10
D
at least 10
2
IIT-JEE 2009 Paper 1 Offline
MCQ (Single Correct Answer)
+3
-1

Let A be the set of all 3 $$\times$$ 3 symmetric matrices all of whose entries are either 0 or 1. Five of these entries are 1 and four of them are 0.

The number of matrices A in A for which the system of linear equations $$A\left[ {\matrix{ x \cr y \cr z \cr } } \right] = \left[ {\matrix{ 1 \cr 0 \cr 0 \cr } } \right]$$ is inconsistent, is

A
0
B
more than 2
C
2
D
1
3
IIT-JEE 2009 Paper 1 Offline
MCQ (Single Correct Answer)
+3
-1
A block of base 10 cm × 10 cm and height 15 cm is kept on an inclined plane. The coefficient of friction between them is $$\sqrt 3 $$. The inclination θ of this inclined plane from the horizontal plane is gradually increased from $$0^\circ $$. Then
A
at θ = $$60^\circ $$, the block will start sliding down the plane
B
the block will remain at rest on the plane up to certain θ and then it will topple
C
at θ = $$60^\circ $$, the block will start sliding down the plane and continue to do so at higher angles
D
at θ = $$60^\circ $$, the block will start sliding down the plane and on further increasing θ, it will topple at certain θ
4
IIT-JEE 2009 Paper 1 Offline
MCQ (Single Correct Answer)
+3
-1

Look at the drawing given in the figure below which has been drawn with ink of uniform line-thickness. The mass of ink used to draw each of the two inner circles, and each of the two line segments is $$m$$. the mass of the ink used to draw the outer circle is $$6m$$. The coordinates of the centres of the different parts are: outer circle (0, 0), left inner circle ($$-a,a$$), right inner circle ($$a,a$$), vertical line (0, 0) and horizontal line ($$0,-a$$). The y-coordinate of the centre of mass of the ink in this drawing is

IIT-JEE 2009 Paper 1 Offline Physics - Impulse & Momentum Question 3 English

A
$$\frac{a}{10}$$
B
$$\frac{a}{8}$$
C
$$\frac{a}{12}$$
D
$$\frac{a}{3}$$
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