1
JEE Main 2022 (Online) 25th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The number of real values of $$\lambda$$, such that the system of linear equations

2x $$-$$ 3y + 5z = 9

x + 3y $$-$$ z = $$-$$18

3x $$-$$ y + ($$\lambda$$2 $$-$$ | $$\lambda$$ |)z = 16

has no solutions, is

A
0
B
1
C
2
D
4
2
JEE Main 2022 (Online) 25th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The number of bijective functions $$f:\{1,3,5,7, \ldots, 99\} \rightarrow\{2,4,6,8, \ldots .100\}$$, such that $$f(3) \geq f(9) \geq f(15) \geq f(21) \geq \ldots . . f(99)$$, is ____________.

A
$${ }^{50} P_{17}$$
B
$${ }^{50} P_{33}$$
C
$$33 ! \times 17$$!
D
$$\frac{50!}{2}$$
3
JEE Main 2022 (Online) 25th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The remainder when $$(11)^{1011}+(1011)^{11}$$ is divided by 9 is

A
1
B
4
C
6
D
8
4
JEE Main 2022 (Online) 25th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

$$\lim\limits_{x \rightarrow \frac{\pi}{4}} \frac{8 \sqrt{2}-(\cos x+\sin x)^{7}}{\sqrt{2}-\sqrt{2} \sin 2 x}$$ is equal to

A
14
B
7
C
14$$\sqrt2$$
D
7$$\sqrt2$$
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