JEE Main 2024 (Online) 5th April Morning Shift | Probability Question 31 | Mathematics

The coefficients $$a, b, c$$ in the quadratic equation $$a x^2+b x+c=0$$ are chosen from the set $$\{1,2,3,4,5,6,7,8\}$$. The probability of this equation having repeated roots is :

$$\frac{1}{128}$$

$$\frac{1}{64}$$

$$\frac{3}{256}$$

$$\frac{3}{128}$$

JEE Main 2024 (Online) 4th April Evening Shift

MCQ (Single Correct Answer)

-1

If the mean of the following probability distribution of a radam variable $$\mathrm{X}$$ :

$$\mathrm{X}$$	0	2	4	6	8
$$\mathrm{P(X)}$$	$$a$$	$$2a$$	$$a+b$$	$$2b$$	$$3b$$

is $$\frac{46}{9}$$, then the variance of the distribution is

$$\frac{581}{81}$$

$$\frac{566}{81}$$

$$\frac{151}{27}$$

$$\frac{173}{27}$$

JEE Main 2024 (Online) 4th April Morning Shift

MCQ (Single Correct Answer)

-1

Three urns A, B and C contain 7 red, 5 black; 5 red, 7 black and 6 red, 6 black balls, respectively. One of the urn is selected at random and a ball is drawn from it. If the ball drawn is black, then the probability that it is drawn from urn $$\mathrm{A}$$ is :

$$\frac{4}{17}$$

$$\frac{5}{16}$$

$$\frac{5}{18}$$

$$\frac{7}{18}$$

JEE Main 2024 (Online) 1st February Evening Shift

MCQ (Single Correct Answer)

-1

Let Ajay will not appear in JEE exam with probability $\mathrm{p}=\frac{2}{7}$, while both Ajay and Vijay will appear in the exam with probability $\mathrm{q}=\frac{1}{5}$. Then the probability, that Ajay will appear in the exam and Vijay will not appear is :

$\frac{9}{35}$

$\frac{3}{35}$

$\frac{24}{35}$

$\frac{18}{35}$

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