1
WB JEE 2021
+1
-0.25
Let $$A = \left( {\matrix{ 1 & 0 & 0 \cr 0 & {\cos t} & {\sin t} \cr 0 & { - \sin t} & {\cos t} \cr } } \right)$$

Let $$\lambda$$1, $$\lambda$$2, $$\lambda$$3 be the roots of $$\det (A - \lambda {I_3}) = 0$$, where I3 denotes the identity matrix. If $$\lambda$$1 + $$\lambda$$2 + $$\lambda$$3 = $$\sqrt 2$$ + 1, then the set of possible values of t, $$-$$ $$\pi$$ $$\ge$$ t < $$\pi$$ is
A
a void set
B
$$\left\{ {{\pi \over 4}} \right\}$$
C
$$\left\{ { - {\pi \over 4},{\pi \over 4}} \right\}$$
D
$$\left\{ { - {\pi \over 3},{\pi \over 3}} \right\}$$
2
WB JEE 2021
+1
-0.25
Let A and B two non singular skew symmetric matrices such that AB = BA, then A2B2(ATB)$$-$$1(AB$$-$$1)T is equal to
A
A2
B
$$-$$ B2
C
$$-$$ A2
D
AB
3
WB JEE 2021
+1
-0.25
If an (> 0) be the nth term of a G.P. then

$$\left| {\matrix{ {\log {a_n}} & {\log {a_{n + 1}}} & {\log {a_{n + 2}}} \cr {\log {a_{n + 3}}} & {\log {a_{n + 4}}} & {\log {a_{n + 5}}} \cr {\log {a_{n + 6}}} & {\log {a_{n + 7}}} & {\log {a_{n + 8}}} \cr } } \right|$$ is equal to
A
1
B
2
C
$$-$$2
D
0
4
WB JEE 2021
+1
-0.25
Let T and U be the set of all orthogonal matrices of order 3 over R and the set of all non-singular matrices of order 3 over R respectively. Let A = {$$-$$1, 0, 1}, then
A
there exists bijective mapping between A and T, U.
B
there does not exist bijective mapping between A and T, U.
C
there exists bijective mapping between A and T but not between A and U.
D
there exists bijective mapping between A and U but not between A and T.
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