Probability

01

PYQ 2006

medium

mathematics ID: viteee-2

The probability density of a continuous random variable is given by for . Then the value of is:}

1

2

$2$

3

$1$

4

$4$

Official Solution

Correct Option: (1)

$Step 1: Use the normalization condition. The total probability for a continuous random variable must equal 1, so we normalize the probability density function by integrating over its entire range and solving for . Step 2: Conclusion. Thus, the value of is .$

02

PYQ 2006

medium

mathematics ID: viteee-2

$In rolling two fair dice, what is the probability of obtaining a sum greater than 3 but not exceeding 6?$

1

2

3

4

Official Solution

Correct Option: (2)

$Step 1: Count favorable outcomes. The possible sums greater than 3 but not exceeding 6 are: 4, 5, and 6. Count the number of outcomes for each sum. Step 2: Conclusion. The probability is .$

03

PYQ 2006

medium

mathematics ID: viteee-2

$Team A has probability of winning whenever it plays. Suppose A plays four games. What is the probability that A wins more than half of its games?$

1

2

3

4

Official Solution

Correct Option: (1)

$Step 1: Use binomial distribution. Since the probability of winning is, we apply the binomial distribution formula to calculate the probability that A wins more than half of the games (i.e., at least 3 games). Step 2: Conclusion. The probability that A wins more than half of the games is .$

04

PYQ 2006

medium

mathematics ID: viteee-2

$An unprepared student takes five questions of true-false type quiz and guesses every answer. What is the probability that the student will pass the quiz if at least four correct answers is the passing grade?$

1

2

3

4

Official Solution

Correct Option: (2)

$Step 1: Binomial distribution application. The number of correct answers follows a binomial distribution with parameters and . We calculate the probability of getting at least 4 correct answers. Step 2: Conclusion. Thus, the probability that the student will pass the quiz is .$

05

PYQ 2007

medium

mathematics ID: viteee-2

$If the probability density function of a random variable is for, then is equal to$

1

2

3

4

Official Solution

Correct Option: (3)

$Step 1: Conditional probability formula. We use the formula to find the conditional probability. Calculate and using the given probability density function. Step 2: Conclusion. Thus, the correct answer is option (C). Final Answer:$

06

PYQ 2007

medium

mathematics ID: viteee-2

$A box contains 9 tickets numbered 1 to 9 inclusive. If 3 tickets are drawn from the box one at a time, the probability that they are alternatively either {odd, even}or {even, odd} is$

1

2

3

4

Official Solution

Correct Option: (4)

$Step 1: Probability of drawing odd/even tickets. There are 5 odd and 4 even numbered tickets. We calculate the probability of drawing three tickets alternatively as odd and even. Step 2: Conclusion. Thus, the correct probability is, which simplifies to . Hence, the correct answer is option (D). Final Answer:$

07

PYQ 2007

medium

mathematics ID: viteee-2

$If and, then is equal to$

1

2

3

4

Official Solution

Correct Option: (3)

$Step 1: Using the formula for . We can calculate . Using the given information, . Step 2: Conclusion. Thus, the correct answer is option (C). Final Answer:$

08

PYQ 2007

medium

mathematics ID: viteee-2

$If is a Poisson variate such that is equal to$

1

$1$

2

$1.5$

3

$2$

4

$1.75$

Official Solution

Correct Option: (2)

$Step 1: Using the Poisson distribution. The Poisson distribution is given by . Using the given condition, solve for and calculate . Step 2: Conclusion. Thus, the correct answer is option (B). Final Answer:$

09

PYQ 2007

medium

mathematics ID: viteee-2

$The number of positive integral solutions of the equation is$

1

$1870$

2

$1875$

3

$1865$

4

$1880$

Official Solution

Correct Option: (2)

$Step 1: Applying the stars and bars method. This is a typical application of the stars and bars method, which is used to find the number of solutions to an equation of the form, where each is a positive integer. The solution is . Step 2: Conclusion. Thus, the correct answer is option (B). Final Answer:$

10

PYQ 2007

medium

mathematics ID: viteee-2

$If and then is equal to$

1

2

3

4

Official Solution

Correct Option: (1)

$Given We know that But,$

11

PYQ 2008

medium

mathematics ID: viteee-2

$Probability of getting positive integral roots of the equation for the integer is$

1

2

3

4

Official Solution

Correct Option: (3)

$Step 1: Condition for positive integral roots. Equation: Roots are integers only if is a perfect square. Step 2: Count perfect squares between 1 and 40. Perfect squares : Total = 6 numbers. Step 3: Total possible values of . Step 4: Probability. Final Answer:$

12

PYQ 2008

medium

mathematics ID: viteee-2

$A manufacturer of cotter pins knows that 5% of his product is defective. He sells pins in boxes of 100 and guarantees that not more than one pin will be defective in a box. In order to find the probability that a box will fail to meet the guaranteed quality, the probability distribution he should use is$

1

$Binomial$

2

$Poisson$

3

$Normal$

4

$Exponential$

Official Solution

Correct Option: (2)

$Step 1: Identify experiment type. We check number of defective pins in a box of 100. Each pin can be defective or not defective. Step 2: Conditions for Poisson approximation. Poisson is used when: - number of trials is large - probability is small - expected value is moderate Here: Step 3: Conclusion. Since is large and we deal with defect counts, Poisson distribution is suitable for approximating defective items. Final Answer:$

13

PYQ 2008

medium

mathematics ID: viteee-2

$A random variable follows binomial distribution with mean and variance . Then$

1

2

3

4

Official Solution

Correct Option: (2)

$Step 1: Recall mean and variance of binomial distribution. If , then: Step 2: Compare and . Since \(0 Also both are positive: Step 3: Conclusion. Final Answer:$

14

PYQ 2008

medium

mathematics ID: viteee-2

$The probability that a certain kind of component will survive a given shock test is . The probability that exactly 2 of the next 4 components tested survive is$

1

2

3

4

Official Solution

Correct Option: (4)

$Step 1: Identify distribution. Each component either survives or fails. So binomial distribution applies. Step 2: Define parameters. Step 3: Probability of exactly 2 successes. Step 4: Substitute values. Final Answer:$

15

PYQ 2008

medium

mathematics ID: viteee-2

$Probability of getting positive integral roots of the equation x - n = 0 for the integer n, 1 n 40 is$

1

2

3

4

Official Solution

Correct Option: (3)

$For each integral value of x [1, 40], There is a positive root. Hence for 40 integral values of x from 1 to 40, there are 40 positive roots, out of which only six roots 1, 2, 3, 4, 5 and 6 are positive integral roots. Hence, probability of getting positive integral roots =$

16

PYQ 2009

medium

mathematics ID: viteee-2

$If is a binomial variable with the range and, then the parameter of is$

1

2

3

4

Official Solution

Correct Option: (1)

$Step 1: Identify . Since range is, Step 2: Write probability expressions. Step 3: Use given relation. Step 4: Simplify. Cancel : Take positive root (since): Final Answer: "$

17

PYQ 2009

medium

mathematics ID: viteee-2

$If is a binomial variate with the range and then the parameter of is$

1

2

3

4

Official Solution

Correct Option: (1)

$Here, According to the question cannot be negative)$

18

PYQ 2010

medium

mathematics ID: viteee-2

$The chances of defective screws in three boxes are respectively. A box is selected at random and a screw drawn from it at random is found to be defective. The probability that it came from box, is$

1

2

3

4

Official Solution

Correct Option: (4)

$Step 1: Let events be defined. Let be the events of selecting box respectively. Let be the event that the screw is defective. Since box is selected at random: Given defective probabilities: Step 2: Apply Bayes’ theorem. Step 3: Substitute values. Cancel : Step 4: Simplify denominator. LCM of . Step 5: Final probability. Final Answer:$

19

PYQ 2011

medium

mathematics ID: viteee-2

$If is a Poisson variate such that, then is equal to:$

1

2

3

4

Official Solution

Correct Option: (3)

$Step 1: Use the Poisson distribution. We use the fact that for a Poisson distribution, the probability is given by: Given that, we solve for and use it to find . Step 2: Conclusion. Thus, . Final Answer:$

20

PYQ 2011

medium

mathematics ID: viteee-2

$A die is rolled twice and the sum of the numbers appearing on them is observed to be 7. What is the conditional probability that the number 2 has appeared at least once?$

1

2

3

4

Official Solution

Correct Option: (2)

$Step 1: Conditional probability. The conditional probability is calculated by dividing the probability of the desired event (at least one 2) by the probability of the event that the sum is 7. Step 2: Conclusion. Thus, the conditional probability is . Final Answer:$

21

PYQ 2011

medium

mathematics ID: viteee-2

$A dice is rolled twice and the sum of the numbers appearing on them is observed to be . What is the conditional probability that the number has appeared at least once ?$

1

2

3

4

Official Solution

Correct Option: (2)

$Let and be two events such that getting number 2 at least once getting 7 as the sum of the numbers on two dice Here, and Required probability$

22

PYQ 2011

medium

mathematics ID: viteee-2

$If is a poisson variate such that, then is equal to$

1

2

3

4

Official Solution

Correct Option: (3)

$Given :$

23

PYQ 2012

medium

mathematics ID: viteee-2

$The probability that at least one of the events A and B occurs is 0.6. If A and B occur simultaneously with probability 0.2, then is:$

1

$0.4$

2

$0.8$

3

$1.2$

4

$1.4$

Official Solution

Correct Option: (3)

$Step 1: Understanding the given data. We are given the following information: - The probability that at least one of events A and B occurs is 0.6. This can be written as: - The probability that A and B occur simultaneously is 0.2. This can be written as: Step 2: Using the formula for the union of two events. The formula for the union of two events is: Substituting the given values into the formula: Step 3: Solving for . Now, solving for : Step 4: Conclusion. Therefore, the value of is 1.2. The correct answer is (c) 1.2.$

24

PYQ 2012

medium

mathematics ID: viteee-2

$There are 5 letters and 5 different envelopes. The number of ways in which all the letters can be put in wrong envelopes is:$

1

$119$

2

$44$

3

$59$

4

$40$

Official Solution

Correct Option: (2)

$This is a classical problem of derangements, where we are asked to find the number of ways to arrange 5 letters in 5 envelopes such that no letter is in the correct envelope. The number of derangements (denoted as) of objects is given by the formula: For, we calculate as follows: First, calculate . Now, calculate the sum: Simplify the sum: Now, multiply by : Thus, the number of ways in which all the letters can be put in wrong envelopes is, and the correct answer is (b).$

25

PYQ 2013

medium

mathematics ID: viteee-2

$If two events A and B. If odds against A are 2:1 and those in favour of are 3:1, then$

1

2

3

4

$None of these$

Official Solution

Correct Option: (2)

$Step 1: Using probability relations. The odds against give, and the odds in favor of give . By using these values, we can solve for the range of . Step 2: Conclusion. The probability lies between and, corresponding to option (2).$

26

PYQ 2014

medium

mathematics ID: viteee-2

$Let denote the sum of the numbers obtained when two fair dice are rolled. The variance and standard deviation of are?$

1

2

3

4

Official Solution

Correct Option: (2)

$The variance of a sum of two dice rolls can be calculated by first determining the mean and then using the formula for the variance of the sum of independent random variables.$

27

PYQ 2014

medium

mathematics ID: viteee-2

$A four digit number is formed by the digits 1, 2, 3, 4 with no repetition. The probability that the number is odd is?$

1

$0$

2

3

4

$None of these$

Official Solution

Correct Option: (4)

$For a number to be odd, the last digit must be odd. Since there are two odd digits (1 and 3), the probability is calculated by considering the number of favorable outcomes and total possible outcomes.$

28

PYQ 2015

medium

mathematics ID: viteee-2

$From a city population, the probability of selecting a male or smoker is, a male smoker is and a male, if a smoker is already selected, is . Then, the probability of$

1

$selecting a male is$

2

$selecting a smoker is$

3

$selecting a non-smoker is$

4

$selecting a smoker, if a male is first selected, is$

Official Solution

Correct Option: (4)

$The probability is calculated using the basic conditional probability and the principle of inclusion and exclusion for multiple events.$

29

PYQ 2015

medium

mathematics ID: viteee-2

$If the mean and variance of a binomial distribution are 4 and 2, respectively. Then, the probability of at least 7 successes is$

1

2

3

4

Official Solution

Correct Option: (3)

$The probability for a binomial distribution can be calculated using the formula for binomial probability. Given that the mean and variance, we calculate the values for and . Then we apply these values to find the probability of getting at least 7 successes.$

30

PYQ 2015

medium

mathematics ID: viteee-2

$If are three events associated with a random experiment, then is$

1

2

3

4

Official Solution

Correct Option: (3)

$The conditional probability is given by the ratio of the probability of the intersection of A and B, divided by the probability of A.$

31

PYQ 2016

medium

mathematics ID: viteee-2

$The probability of India winning a test match against Australia is assuming independence from match to match. The probability that in a match series India�s second win occurs at third test match is$

1

2

3

4

Official Solution

Correct Option: (2)

$Required probability = P (First win) P(First win) P(Second win) + P(First Defeat) P(First win) P(Second win)$

32

PYQ 2016

medium

mathematics ID: viteee-2

$The probability of India winning a test match against Australia is, assuming independence from match to match. The probability that in a match series India’s second win occurs at third test match is$

1

2

3

4

Official Solution

Correct Option: (1)

$Step 1: Applying Probability Formula. The event we are looking for is the occurrence of the second win in the third match, which means the first two tests should be losses and the third one should be a win. The probability of this event is: Step 2: Conclusion. The correct answer is (A), .$

33

PYQ 2016

medium

mathematics ID: viteee-2

$While shuffling a pack of 52 playing cards, 2 are accidentally dropped. The probability that the missing cards to be of different colours is$

1

2

3

4

Official Solution

Correct Option: (2)

$Step 1: Probability of Different Colours. There are 26 red and 26 black cards in a deck. The probability that the two missing cards are of different colours is calculated as the product of selecting one red and one black card. Step 2: Conclusion. The correct answer is (B), .$

34

PYQ 2016

medium

mathematics ID: viteee-2

$A box contains 20 identical balls of which 10 are blue and 10 are green. The balls are drawn at random from the box one at a time with replacement. The probability that a blue ball is drawn 4th time on the 7th draw is$

1

2

3

4

Official Solution

Correct Option: (2)

$The probability of drawing a blue ball on the 4th draw is . The probability of the blue ball appearing on the 7th draw can be calculated as by considering the total number of possible outcomes. Step 2: Conclusion. The correct answer is (B), .$

35

PYQ 2016

medium

mathematics ID: viteee-2

$Which of the following is INCORRECT for the hyperbola ?$

1

$Its eccentricity is$

2

$Its equation is$

3

$Length of the transverse axis is$

4

$Length of the conjugate axis is$

Official Solution

Correct Option: (4)

$Step 1: Use the standard equation of hyperbola. By converting the given equation into the standard form of a hyperbola and comparing terms, we calculate the length of the axes. The conjugate axis length is incorrect as stated in option (D). Step 2: Conclusion. The correct answer is (D).$

36

PYQ 2016

medium

mathematics ID: viteee-2

$The mean of a binomial distribution is 25, then its standard deviation lies in the interval$

1

$(0,5)$

2

$(0,25)$

3

$(0,0.25)$

4

$(0,5)$

Official Solution

Correct Option: (2)

$The standard deviation for a binomial distribution is given by . Substituting the values and solving the inequality for the standard deviation gives the required interval. Step 2: Conclusion. The correct answer is (B), (0, 25).$

37

PYQ 2017

medium

mathematics ID: viteee-2

$A and B are two independent witnesses (i.e., there is no collision between them) in a case. The probability that A will speak the truth is and the probability that B will speak the truth is . A and B agree in a certain statement. The probability that the statement is true is$

1

2

3

4

Official Solution

Correct Option: (4)

$Step 1: Understand the probability of truth. The probability that A and B agree on the truth is the product of their individual probabilities of speaking the truth, plus the probability that they both lie. Step 2: Conclusion. Thus, the probability that the statement is true is . Final Answer:$

38

PYQ 2017

medium

mathematics ID: viteee-2

$A and B are events such that,, and . Then the probability that is$

1

2

3

4

Official Solution

Correct Option: (2)

$Step 1: Use the formula for the union of two events. The formula for the union of two events is: Substituting the known values, we solve for . Step 2: Conclusion. Thus, the correct probability is . Final Answer:$

39

PYQ 2017

medium

mathematics ID: viteee-2

$A random variable has the probability distribution For the events and, then is$

1

$0.50$

2

$0.77$

3

$0.35$

4

$0.87$

Official Solution

Correct Option: (2)

$The union of events and is calculated by adding the probabilities of each event and subtracting the intersection. Final Answer:$

40

PYQ 2018

medium

mathematics ID: viteee-2

$The mean and variance of a random variable having binomial distribution are 4 and 2 respectively, then is:$

1

2

3

4

Official Solution

Correct Option: (3)

$Step 1: For a binomial distribution, the mean and variance . Given the mean and variance, solve for and . Step 2: Use the binomial probability formula to find . Final Answer:$

41

PYQ 2018

medium

mathematics ID: viteee-2

$A signal which can be green or red with probability and respectively, is received by station A and then transmitted to station B. The probability of each station receiving the signal correctly is . If the signal received at station B is given, then the probability that the original signal is green is:$

1

2

3

4

Official Solution

Correct Option: (3)

$Step 1: Use Bayes' Theorem to find the probability that the signal is green, given the signal received at station B. Step 2: The probability of receiving a green signal correctly at station B is, and the probability of receiving a red signal correctly is . Step 3: Use Bayes' formula to find the conditional probability, which gives . Final Answer:$

42

PYQ 2018

medium

mathematics ID: viteee-2

$If and are events such that,, and, then: I. II. III.$

1

$Only I and III are correct$

2

$Only I and II are correct$

3

$Only I and III are true$

4

$All three statements are correct$

Official Solution

Correct Option: (4)

$Step 1: Using the complementary rule, . Step 2: Similarly, . Step 3: Using the formula for the union of two events: Final Answer:$

43

PYQ 2019

medium

mathematics ID: viteee-2

$It is given that the events and are such that \text{Then is:}$

1

2

3

4

Official Solution

Correct Option: (2)

$Using the formula, we calculate as . Final Answer:$

44

PYQ 2019

medium

mathematics ID: viteee-2

$Six identical coins are arranged in a row. The number of ways in which the number of tails is equal to the number of heads is:$

1

$20$

2

$9$

3

$120$

4

$40$

Official Solution

Correct Option: (1)

$The number of ways to arrange 3 heads and 3 tails in a row is given by . Final Answer:$

45

PYQ 2021

medium

mathematics ID: viteee-2

$Let then$

1

2

3

4

$None of these$

Official Solution

Correct Option: (2)

$The integral can be simplified and turns out to be the inverse sine function .$

46

PYQ 2022

medium

mathematics ID: viteee-2

$Find the probability of getting the sum as a perfect square number when two dice are thrown together.$

1

2

3

4

$None of these$

Official Solution

Correct Option: (3)

$Step 1: The possible sums when two dice are thrown range from 2 to 12. The perfect square numbers within this range are and . So, we need to find the probability of getting a sum of or . Step 2: To calculate the probability, we first determine the number of favorable outcomes for each perfect square sum: - For a sum of : The possible pairs are, which gives 3 favorable outcomes. - For a sum of : The possible pairs are, which gives 4 favorable outcomes. Step 3: Total favorable outcomes for getting a perfect square sum = . Step 4: The total number of possible outcomes when two dice are thrown is . Step 5: Therefore, the probability of getting a perfect square sum is:$

47

PYQ 2022

medium

mathematics ID: viteee-2

$The total number of 3-digit numbers, the sum of whose digits is even, is equal to:$

1

$450$

2

$350$

3

$250$

4

$325$

Official Solution

Correct Option: (1)

$Step 1: A 3-digit number can be represented as, where are the hundreds, tens, and ones digits, respectively. - can be any digit from 1 to 9 (since it’s a 3-digit number), so there are 9 choices for . - and can be any digit from 0 to 9, so there are 10 choices for both and . Thus, the total number of 3-digit numbers is: Step 2: For the sum to be even, the sum of the digits must be even. This can happen in two cases: - Case 1: is even, is even. - Case 2: is odd, is odd. In Case 1, can be (4 choices). For to be even, both and must be even, so there are 5 choices for and 5 choices for . Therefore, the number of such numbers is: In Case 2, can be (5 choices). For to be odd, one of or must be odd, and the other must be even. There are 5 choices for odd digits and 5 choices for even digits. The number of such numbers is: Thus, the total number of 3-digit numbers where the sum of the digits is even is:$

48

PYQ 2022

medium

mathematics ID: viteee-2

$What was the ratio between the ages of P and Q four years ago? I. The ratio between the present ages of P and Q is 3 : 4. II. The ratio between the present ages of Q and R is 4 : 5.$

1

$if the data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question.$

2

$if the data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question.$

3

$if the data in both the statements I and II together are not sufficient to answer the question.$

4

$if the data in both the statements I and II together are necessary to answer the question.$

Official Solution

Correct Option: (3)

$Step 1: From statement I, the ratio of the present ages of P and Q is 3:4. Let the present ages of P and Q be and, respectively. Step 2: From statement II, the ratio of the present ages of Q and R is 4:5. Let the present ages of Q and R be and, respectively. Step 3: We have two variables and, and no further relationship is provided between and . Therefore, we cannot determine the ratio of P’s and Q’s ages four years ago with the information given in both statements. Thus, the answer is .$

49

PYQ 2022

medium

mathematics ID: viteee-2

$An urn contains five balls. Two balls are drawn and found to be white. The probability that all the balls are white is:$

1

2

3

4

Official Solution

Correct Option: (4)

$Step 1: There are 5 balls in total. Two balls are drawn and found to be white. The total number of ways to choose 2 balls from 5 is: Step 2: If all balls are white, there are only 3 white balls in the urn. The number of ways to choose 2 white balls from 3 is: Step 3: The probability that all the balls are white, given that two white balls were drawn, is: Thus, the probability that all the balls are white is .$

50

PYQ 2022

hard

mathematics ID: viteee-2

$What was the cost price of the suitcase purchased by Samir? I. Samir got a 25 percent concession on the labelled price. II. Samir sold the suitcase for Rs. 2000 with 25 percent profit on the labelled price.$

1

$if the data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question.$

2

$if the data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question.$

3

$if the data in both the statements I and II together are not sufficient to answer the question.$

4

$if the data in both the statements I and II together are necessary to answer the question.$

Official Solution

Correct Option: (4)

$Step 1: From statement I, we know that Samir got a 25% concession on the labelled price. Let the labelled price be, so Samir paid for the suitcase. Step 2: From statement II, we know that Samir sold the suitcase for Rs. 2000 with a 25% profit on the labelled price. The selling price is, so: Solving for : Step 3: Now, using statement I, the cost price is: Thus, the cost price of the suitcase is Rs. 1200, which requires both statements.$

51

PYQ 2022

medium

mathematics ID: viteee-2

$How many students have got 60% or more marks in all the subjects?$

1

$One$

2

$Two$

3

$Three$

4

$Four$

Official Solution

Correct Option: (2)

$Step 1: Let's assume the marks obtained by students in different subjects are provided as follows: Step 2: To check whether a student has 60% or more marks in all subjects, we need to see if the student’s marks in each subject are 60 or above. Student 1 has marks, all above 60, so Student 1 qualifies. Student 2 has marks above 60 in all subjects, so Student 2 qualifies. Student 3 has marks below 60 in some subjects, so Student 3 does not qualify. Student 4 has marks below 60 in one subject, so Student 4 does not qualify. Thus, only Student 1 and Student 2 qualify.$

52

PYQ 2022

medium

mathematics ID: viteee-2

$The variance of the data is:$

1

$8$

2

$7$

3

$6$

4

$None of these$

Official Solution

Correct Option: (1)

$Step 1: To calculate the variance, we use the formula: where is the mean of the data and is the number of data points. Step 2: Calculate the mean: Step 3: Compute the squared differences from the mean: Step 4: Compute the variance:$

53

PYQ 2023

medium

mathematics ID: viteee-2

$If the vertex of a parabola is and the equation of its directrix is then the length of its latus rectum is:$

1

$2$

2

$8$

3

$12$

4

$16$

Official Solution

Correct Option: (2)

$Step 1: Finding the focus. The focus lies on the perpendicular bisector of the vertex and the directrix. Using the perpendicular distance formula, So, the focal distance is 2. Step 2: Finding the latus rectum. The length of the latus rectum is given by: where, giving Thus, the correct answer is (B).$

54

PYQ 2023

medium

mathematics ID: viteee-2

$The angle between the two lines: is:$

1

2

3

4

Official Solution

Correct Option: (2)

$Step 1: Extracting direction vectors. For a line in symmetric form: the direction vector is . For the first line: The direction vector is: For the second line: The direction vector is: Step 2: Using the angle formula. The angle between two lines with direction vectors and is given by: Step 3: Computing the dot product. Step 4: Computing magnitudes. Step 5: Computing . Step 6: Computing the angle. Thus, the correct answer is (B) .$

55

PYQ 2023

medium

mathematics ID: viteee-2

$The particular solution of is:$

1

2

3

4

Official Solution

Correct Option: (4)

$Step 1: Converting the equation. Rewriting the given equation: Separating variables: Integrating both sides: Multiplying by -4: Using, solving for, we get: Thus, the correct answer is (D).$

56

PYQ 2023

easy

mathematics ID: viteee-2

$Eccentricity of ellipse if it passes through point and is:$

Official Solution

Correct Option: (1)

57

PYQ 2023

hard

mathematics ID: viteee-2

$What is the percentage drop in the production of Ludo from 1992 to 1994?$

1

2

3

4

Official Solution

Correct Option: (4)

$Step 1: Identifying the production values. Let the production of Ludo in 1992 be and in 1994 be . Step 2: Percentage decrease formula. Step 3: Substituting values and calculating. Using the given values, we get: Computing the values, we find that the drop is 10%. Thus, the correct answer is (D) .$

58

PYQ 2024

hard

mathematics ID: viteee-2

$If defined as given below, is continuous on, then the value of is equal to: % Function Definition$

1

$0$

2

$2$

3

$-2$

4

$3$

Official Solution

Correct Option: (3)

$For the function to be continuous at the boundaries and, the left-hand limit and the right-hand limit must be equal at these points. At : From the piecewise function, the left-hand side is: The right-hand side is: For continuity at : At : The left-hand limit is: The right-hand limit is: For continuity at : Solving for : Final Calculation: Final Answer: (c) -2 .$

59

PYQ 2024

medium

mathematics ID: viteee-2

$In four schools, the number of students is given as follows: A student is selected at random from any of the schools. The probability that the student is from school is:$

1

2

3

4

Official Solution

Correct Option: (2)

$Step 1: Calculate the Total Number of Students Step 2: Determine the Probability Since one student is selected at random, the total number of ways to select one student is: The number of students in school is: So the number of ways to select a student from is: Step 3: Compute the Required Probability Final Answer: The probability that the selected student is from is:$

60

PYQ 2025

medium

mathematics ID: viteee-2

$The number of ways to arrange the letters of the word ``MISSISSIPPI'' is:$

1

$34650$

2

$12600$

3

$9450$

4

$69300$

Official Solution

Correct Option: (1)

61

PYQ 2025

medium

mathematics ID: viteee-2

$If the coefficient of correlation between and is 0.8, then the regression coefficient of on is:$

1

$Always 0.8$

2

$Always greater than 0.8$

3

$Depends on standard deviations$

4

$Always less than 0.8$

Official Solution

Correct Option: (3)

$Hence it depends on standard deviations.$

62

PYQ 2025

medium

mathematics ID: viteee-2

$A die is rolled 5 times. The probability of getting at least one six is:$

1

2

3

4

Official Solution

Correct Option: (4)

63

PYQ 2025

medium

mathematics ID: viteee-2

$A bag contains 5 red and 3 blue balls. Two balls are drawn one by one with replacement. The probability that both are red is:$

1

2

3

4

Official Solution

Correct Option: (1)

64

PYQ 2025

medium

mathematics ID: viteee-2

$The probability of getting exactly 2 heads in 4 tosses of a fair coin is:$

1

2

3

4

Official Solution

Correct Option: (1)

High-Yield Trend

Chapter Questions 64 MCQs

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Chapter Questions
64 MCQs