1
IIT-JEE 2010 Paper 1 Offline
MCQ (Single Correct Answer)
+3
-1

Let $p$ be an odd prime number and $T_p$ be the following set of $2 \times 2$ matrices :

$$ \mathrm{T}_{\mathrm{p}}=\left\{\mathrm{A}=\left[\begin{array}{ll} a & b \\ c & a \end{array}\right]: a, b, c \in\{0,1,2, \ldots, p-1\}\right\} $$

The number of A in $\mathrm{T}_p$ such that the trace of A is not divisible by $p$ but $\operatorname{det}(\mathrm{A})$ is divisible by $p$ is

[Note : The trace of a matrix is the sum of its diagonal entries.]

A
$(p-1)\left(p^2-p+1\right)$
B
$p^3-(p-1)^2$
C
$(p-1)^2$
D
$(p-1)\left(p^2-2\right)$
2
IIT-JEE 2010 Paper 1 Offline
MCQ (Single Correct Answer)
+3
-1

Let $p$ be an odd prime number and $T_p$ be the following set of $2 \times 2$ matrices :

$$ \mathrm{T}_{\mathrm{p}}=\left\{\mathrm{A}=\left[\begin{array}{ll} a & b \\ c & a \end{array}\right]: a, b, c \in\{0,1,2, \ldots, p-1\}\right\} $$

The number of A in $\mathrm{T}_p$ such that $\operatorname{det}(\mathrm{A})$ is not divisible by $p$ is :
A
$2 p^2$
B
$p^3-5 p$
C
$p^3-3 p$
D
$p^3-p^2$
3
IIT-JEE 2010 Paper 1 Offline
Numerical
+3
-0
A 0.1 kg mass is suspended from a wire of negligible mass. The length of the wire is 1 m and its crosssectional area is 4.9 $$ \times $$ 10-7 m2. If the mass is pulled a little in the vertically downward direction and released, it performs simple harmonic motion of angular frequency 140 rad s−1. If the Young’s modulus of the material of the wire is n $$ \times $$ 109 Nm-2, the value of n is
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4
IIT-JEE 2010 Paper 1 Offline
MCQ (Single Correct Answer)
+3
-0.75

A block of mass m is on an inclined plane of angle θ. The coefficient of friction between the block and the plane is μ and tan θ > μ. The block is held stationary by applying a force P parallel to the plane. The direction of force pointing up the plane is taken to be positive. As P is varied from P1 = mg(sinθ − μ cosθ) to P2 = mg(sinθ + μ cosθ), the frictional force f versus P graph will look like

IIT-JEE 2010 Paper 1 Offline Physics - Laws of Motion Question 25 English
A
IIT-JEE 2010 Paper 1 Offline Physics - Laws of Motion Question 25 English Option 1
B
IIT-JEE 2010 Paper 1 Offline Physics - Laws of Motion Question 25 English Option 2
C
IIT-JEE 2010 Paper 1 Offline Physics - Laws of Motion Question 25 English Option 3
D
IIT-JEE 2010 Paper 1 Offline Physics - Laws of Motion Question 25 English Option 4
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