1
WB JEE 2023
MCQ (Single Correct Answer)
+1
-0.25
Change Language

Let $$A = \left( {\matrix{ 2 & 0 & 3 \cr 4 & 7 & {11} \cr 5 & 4 & 8 \cr } } \right)$$. Then

A
det A is divisible by 11
B
det A is not divisible by 11
C
det A = 0
D
A is orthogonal matrix
2
WB JEE 2023
MCQ (Single Correct Answer)
+1
-0.25
Change Language

If the matrix Mr is given by $${M_r} = \left( {\matrix{ r & {r - 1} \cr {r - 1} & r \cr } } \right)$$ for r = 1, 2, 3, ... then det (M1) + det (M2) + ... + det (M2008) =

A
2007
B
2008
C
(2008)$$^2$$
D
(2007)$$^2$$
3
WB JEE 2023
MCQ (Single Correct Answer)
+1
-0.25
Change Language

Let $$\alpha,\beta$$ be the roots of the equation $$a{x^2} + bx + c = 0,a,b,c$$ real and $${s_n} = {\alpha ^n} + {\beta ^n}$$ and $$\left| {\matrix{ 3 & {1 + {s_1}} & {1 + {s_2}} \cr {1 + {s_1}} & {1 + {s_2}} & {1 + {s_3}} \cr {1 + {s_2}} & {1 + {s_3}} & {1 + {s_4}} \cr } } \right| = k{{{{(a + b + c)}^2}} \over {{a^4}}}$$ then $$k = $$

A
$${b^2} - 4ac$$
B
$${b^2} + 4ac$$
C
$${b^2} + 2ac$$
D
$$4ac - {b^2}$$
4
WB JEE 2023
MCQ (Single Correct Answer)
+1
-0.25
Change Language

Let A, B, C are subsets of set X. Then consider the validity of the following set theoretic statement:

A
A $$\cup$$ (B \ C) = (A $$\cup$$ B) \ (A $$\cup$$ C)
B
(A \ B) \ C = A \ (B $$\cup$$ C)
C
(A $$\cup$$ B) \ A = A \ B
D
A \ C = B \ C
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