1
JEE Main 2022 (Online) 27th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

Let X have a binomial distribution B(n, p) such that the sum and the product of the mean and variance of X are 24 and 128 respectively. If $$P(X>n-3)=\frac{k}{2^{n}}$$, then k is equal to :

A
528
B
529
C
629
D
630
2
JEE Main 2022 (Online) 27th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

A six faced die is biased such that

$$3 \times \mathrm{P}($$a prime number$$)\,=6 \times \mathrm{P}($$a composite number$$)\,=2 \times \mathrm{P}(1)$$.

Let X be a random variable that counts the number of times one gets a perfect square on some throws of this die. If the die is thrown twice, then the mean of X is :

A
$$\frac{3}{11}$$
B
$$\frac{5}{11}$$
C
$$\frac{7}{11}$$
D
$$\frac{8}{11}$$
3
JEE Main 2022 (Online) 27th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

The angle of elevation of the top P of a vertical tower PQ of height 10 from a point A on the horizontal ground is $$45^{\circ}$$. Let R be a point on AQ and from a point B, vertically above $$\mathrm{R}$$, the angle of elevation of $$\mathrm{P}$$ is $$60^{\circ}$$. If $$\angle \mathrm{BAQ}=30^{\circ}, \mathrm{AB}=\mathrm{d}$$ and the area of the trapezium $$\mathrm{PQRB}$$ is $$\alpha$$, then the ordered pair $$(\mathrm{d}, \alpha)$$ is :

A
$$(10(\sqrt{3}-1), 25)$$
B
$$\left(10(\sqrt{3}-1), \frac{25}{2}\right)$$
C
$$(10(\sqrt{3}+1), 25)$$
D
$$\left(10(\sqrt{3}+1), \frac{25}{2}\right)$$
4
JEE Main 2022 (Online) 27th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

Let $$S=\left\{\theta \in\left(0, \frac{\pi}{2}\right): \sum\limits_{m=1}^{9} \sec \left(\theta+(m-1) \frac{\pi}{6}\right) \sec \left(\theta+\frac{m \pi}{6}\right)=-\frac{8}{\sqrt{3}}\right\}$$. Then

A
$$ S=\left\{\frac{\pi}{12}\right\} $$
B
$$ S=\left\{\frac{2 \pi}{3}\right\} $$
C
$$ \sum\limits_{\theta \in S} \theta=\frac{\pi}{2} $$
D
$$ \sum\limits_{\theta \in S} \theta=\frac{3\pi}{4} $$
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