List of practice Questions

The probability of hitting the target by a trained sniper is three times the probability of not hitting the target on a stormy day due to high wind speed. The sniper fired two shots on the target on a stormy day when wind speed was very high. Find the probability that:
(i) target is hit
(ii) atleast one shot misses the target.

Consider the differential equation \[ \frac{dy}{dx}=x^{2}-y,\qquad y(0)=1. \] Using the Simple Euler's Method with a step size of \(h=0.1\), the value of \(y(0.1)\) is

Assertion (A): If \(X\sim N(\mu,\sigma^{2})\), then \[ P(X<\mu)=0.5. \] Reason (R): Normal distribution is symmetric about its mean.

If $X \sim N(\mu,\sigma^2)$ then:

Assertion (A): Spearman rank correlation coefficient is used for ordinal data.
Reason (R): It is based on ranks rather than actual values.

Consider the differential equation \[ \frac{dy}{dx}=x^{2}-y,\qquad y(0)=1. \] Using the Simple Euler's Method with a step size of \(h=0.1\), the value of \(y(0.1)\) is

Assertion (A): If \(X\sim N(\mu,\sigma^{2})\), then \[ P(X<\mu)=0.5. \] Reason (R): Normal distribution is symmetric about its mean.

Choose a possible probability density function from the given functions:

The probability density function of a continuous random variable is \[ f(x)= \begin{cases} \dfrac35 e^{-3x/5}, & x>0 \\ 0, & x\le0 \end{cases} \] The mean of the distribution is

If \(Z\) is a standard normal variable, \[ P(Z>z_1)=\alpha, \] \[ P(Z<z_2)=\beta \] and \(z_2<z_1\), then a possible value of \[ P(z_2<Z<z_1) \] is

While evaluating \(\int_{a}^{b} f(x) \, dx\) using Trapezoidal rule and Simpson's one-third rule, \([a,b]\) is divided into n number of subintervals so that both the methods can be applied for the same division, then a possible value of n is

Newton-Raphson method is used to find the root of \(x^2 - 3 = 0\). If the initial solution is taken as \(x = -2\), then the iterations tend to

If 2 coins are tossed and 2 dice are thrown, probability of getting at least 1 head and sum at least 9 is

A card is drawn from 52 cards. If A = diamond, B = ace, probability that exactly one occurs is

If \(E_1\) and \(E_2\) are two events of a sample space such that \(P(E_1)=0.8\), \(P(E_2)=0.7\) and \(P(E_1\cap E_2)\geq c\), then \(c=\)

In a bolt factory, machines \(A\), \(B\), and \(C\) manufacture \(25\%\), \(35\%\), and \(40\%\) of the total output respectively. There is a chance of having \(5\%\), \(4\%\), and \(2\%\) defective bolts manufactured by \(A\), \(B\), and \(C\) respectively. If a bolt is drawn at random from the output, then the probability that it is defective is:

If \( b \) and \( c \) are numbers chosen at random from the set \( \{1,2,3,\ldots,10\} \) with replacement, then the probability that the quadratic equation \[ x^2 + bx + c = 0 \] has real roots is:

Let \( E_1, E_2 \) and \( E_3 \) be mutually independent events. Statement I: \( E_1 \) and \( E_2 \cup E_3 \) are independent. Statement II: \( E_1 \) and \( E_2 \cap E_3 \) are independent. Which one of the following options is correct?

A pair of dice is thrown independently \(3\) times. The probability of getting a total score of at least \(9\) twice, is:

If a 4-digit number is chosen from all possible 4-digit numbers, probability of getting exactly three odd digits and one even digit is

Let \[ S=\{2,3,5,7,11,13\} \] Consider all onto functions from \(S\) to \(S\). If function \(f\) is chosen randomly, probability that \[ f(3)>3f(2) \] is

From the set of numbers \[ \{1,2,3,4,5,6,7,8,9,10,11,12\}, \] two numbers are selected at random. The probability that the two numbers selected differ by a prime number is

Box I contains 30 cards numbered 1 to 30 and Box II contains 20 cards numbered 31 to 50. A box is selected at random and a card is drawn. If the number is non-prime, the probability that it came from Box I is:

A hunter is firing at a target. He has only 10% chance of hitting it in one round. The number of rounds he must fire in order to have at least 50% chance of hitting the target at least once, is

Two symmetric cubical dice are rolled once. Match the items of Column-I with the items of Column-II. center tabular|l|l|l|l| 2|c|Column-I & 2c|Column-II
A & Probability that the numbers appearing are equal & I & 1/12
B & Probability that the numbers are all distinct & II & 5/36
C & Probability that the sum of numbers is 10 & III & 1/6
D & Probability that the sum of numbers is 6 & IV & 4/36
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