1
JEE Main 2022 (Online) 28th June Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let a function f : N $$\to$$ N be defined by

$$f(n) = \left[ {\matrix{ {2n,} & {n = 2,4,6,8,......} \cr {n - 1,} & {n = 3,7,11,15,......} \cr {{{n + 1} \over 2},} & {n = 1,5,9,13,......} \cr } } \right.$$

then, f is

A
one-one but not onto
B
onto but not one-one
C
neither one-one nor onto
D
one-one and onto
2
JEE Main 2022 (Online) 28th June Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If the system of linear equations

$$2x + 3y - z = - 2$$

$$x + y + z = 4$$

$$x - y + |\lambda |z = 4\lambda - 4$$

where, $$\lambda$$ $$\in$$ R, has no solution, then

A
$$\lambda$$ = 7
B
$$\lambda$$ = $$-$$7
C
$$\lambda$$ = 8
D
$$\lambda$$2 = 1
3
JEE Main 2022 (Online) 28th June Morning Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

Let A be a matrix of order 3 $$\times$$ 3 and det (A) = 2. Then det (det (A) adj (5 adj (A3))) is equal to _____________.

A
512 $$\times$$ 106
B
256 $$\times$$ 106
C
1024 $$\times$$ 106
D
256 $$\times$$ 1011
4
JEE Main 2022 (Online) 28th June Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The total number of 5-digit numbers, formed by using the digits 1, 2, 3, 5, 6, 7 without repetition, which are multiple of 6, is :

A
36
B
48
C
60
D
72
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