1
JEE Advanced 2021 Paper 1 Online
MCQ (More than One Correct Answer)
+4
-2
For any 3 $$\times$$ 3 matrix M, let | M | denote the determinant of M. Let

$$E = \left[ {\matrix{ 1 & 2 & 3 \cr 2 & 3 & 4 \cr 8 & {13} & {18} \cr } } \right]$$, $$P = \left[ {\matrix{ 1 & 0 & 0 \cr 0 & 0 & 1 \cr 0 & 1 & 0 \cr } } \right]$$ and $$F = \left[ {\matrix{ 1 & 3 & 2 \cr 8 & {18} & {13} \cr 2 & 4 & 3 \cr } } \right]$$

If Q is a nonsingular matrix of order 3 $$\times$$ 3, then which of the following statements is(are) TRUE?
A
F = PEP and $${P^2} = \left[ {\matrix{ 1 & 0 & 0 \cr 0 & 1 & 0 \cr 0 & 0 & 1 \cr } } \right]$$
B
| EQ + PFQ$$-$$1 | = | EQ | + | PFQ$$-$$1 |
C
| (EF)3 | > | EF |2
D
Sum of the diagonal entries of P$$-$$1EP + F is equal to the sum of diagonal entries of E + P$$-$$1FP
2
JEE Advanced 2021 Paper 1 Online
MCQ (More than One Correct Answer)
+4
-2
Let f : R $$\to$$ R be defined by $$f(x) = {{{x^2} - 3x - 6} \over {{x^2} + 2x + 4}}$$

Then which of the following statements is (are) TRUE?
A
f is decreasing in the interval ($$-$$2, $$-$$1)
B
f is increasing in the interval (1, 2)
C
f is onto
D
Range of f is $$\left[ { - {3 \over 2},2} \right]$$
3
JEE Advanced 2021 Paper 1 Online
MCQ (More than One Correct Answer)
+4
-2
Let E, F and G be three events having probabilities $$P(E) = {1 \over 8}$$, $$P(F) = {1 \over 6}$$ and $$P(G) = {1 \over 4}$$, and let P (E $$\cap$$ F $$\cap$$ G) = $${1 \over {10}}$$. For any event H, if Hc denotes the complement, then which of the following statements is (are) TRUE?
A
$$P(E \cap F \cap {G^c}) \le {1 \over {40}}$$
B
$$P({E^c} \cap F \cap G) \le {1 \over {15}}$$
C
$$P(E \cup F \cup G) \le {{13} \over {24}}$$
D
$$P({E^c} \cup {F^c} \cup {G^c}) \le {5 \over {12}}$$
4
JEE Advanced 2021 Paper 1 Online
MCQ (More than One Correct Answer)
+4
-2
For any 3 $$\times$$ 3 matrix M, let |M| denote the determinant of M. Let I be the 3 $$\times$$ 3 identity matrix. Let E and F be two 3 $$\times$$ 3 matrices such that (I $$-$$ EF) is invertible. If G = (I $$-$$ EF)$$-$$1, then which of the following statements is (are) TRUE?
A
| FE | = | I $$-$$ FE| | FGE |
B
(I $$-$$ FE)(I + FGE) = I
C
EFG = GEF
D
(I $$-$$ FE)(I $$-$$ FGE) = I
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