1
IIT-JEE 2011 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1

Let f : R $$\to$$ R be a function such that $$f(x + y) = f(x) + f(y),\,\forall x,y \in R$$. If f(x) is differentiable at x = 0, then

A
f(x) is differentiable only in a finite interval containing zero.
B
f(x) is continuous $$\forall x \in R$$.
C
f'(x) is constant $$\forall x \in R$$.
D
f(x) is differentiable except at finitely many points.
2
IIT-JEE 2011 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1

Let M and N be two 3 $$\times$$ 3 non-singular skew symmetric matrices such that MN = NM. If PT denotes the transpose of P, then M2N2(MTN)$$-$$1(MN$$-$$1)T is equal to

A
M2
B
$$-$$N2
C
$$-$$M2
D
MN
3
IIT-JEE 2011 Paper 1 Offline
+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)

If the point P(a, b, c), with reference to (E), lies on the plane 2x + y + z = 1, then the value of 7a + b + c is

A
0
B
12
C
7
D
6
4
IIT-JEE 2011 Paper 1 Offline
+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 $$\omega$$ be a solution of $${x^3} - 1 = 0$$ with $${\mathop{\rm Im}\nolimits} (\omega ) > 0$$. If a = 2 with b and c satisfying (E), then the value of $${3 \over {{\omega ^a}}} + {1 \over {{\omega ^b}}} + {3 \over {{\omega ^c}}}$$ is equal to

A
$$-$$2
B
2
C
3
D
$$-$$3
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