1
IIT-JEE 2011 Paper 1 Offline
MCQ (Single Correct Answer)
+3
-1

Let a, b and c be three real numbers satisfying

$$[\matrix{ a & b & c \cr } ]\left[ {\matrix{ 1 & 9 & 7 \cr 8 & 2 & 7 \cr 7 & 3 & 7 \cr } } \right] = [\matrix{ 0 & 0 & 0 \cr } ]$$ ........ (E)

Let b = 6, with a and c satisfying (E). If $$\alpha$$ and $$\beta$$ are the roots of the quadratic equation ax2 + bx + c = 0, then $$\sum\limits_{n = 0}^\infty {{{\left( {{1 \over \alpha } + {1 \over \beta }} \right)}^n}} $$ is

A
6
B
7
C
$${6 \over 7}$$
D
$$\infty$$
2
IIT-JEE 2011 Paper 2 Offline
MCQ (Single Correct Answer)
+3
-1

Let $$\omega$$ $$\ne$$ 1 be a cube root of unity and S be the set of all non-singular matrices of the form $$\left[ {\matrix{ 1 & a & b \cr \omega & 1 & c \cr {{\omega ^2}} & \omega & 1 \cr } } \right]$$, where each of a, b, and c is either $$\omega$$ or $$\omega$$2. Then the number of distinct matrices in the set S is

A
2
B
6
C
4
D
8
3
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 in A is

A
12
B
6
C
9
D
3
4
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
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