Sujeet Kumar

Question 1.Two numbers differ by 3. The sum of twice the smaller number and thrice the greater number is 19. Find the numbers.Solution:Let the greater number be x and the smaller number be y.According to the first condition, x – y = 3 …(i)According to the second condition,3x + 2y = 19 …(ii)Multiplying equation (i) … Read more

Question 1.Solve the following simultaneous equations.Solution:i. The given simultaneous equations are ∴ Equations (i) and (ii) become2p – 3q = 15 …(iii)8p + 5q = 77 …(iv)Multiplying equation (iii) by 4, we get8p – 12q = 60 …(v)Subtracting equation (v) from (iv), we get ii. The given simultaneous equations areSubstituting x = 3 in equation … Read more

Question 1.Fill in the blanks with correct number.Solution: Question 2.Find the values of following determinants. Solution: Question 3.Solve the following simultaneous equations using Cramer’s rule.i. 3x – 4y = 10 ; 4x + 3y = 5ii. 4x + 3y – 4 = 0 ; 6x = 8 – 5yiii. x + 2y = -1 ; … Read more

Question 1.Complete the following table to draw graph of the equations.i. x + y = 3ii. x – y = 4Answer:i. x + y = 3ii. x – y = 4 Question 2.Solve the following simultaneous equations graphically.i. x + y = 6 ; x – y = 4ii. x + y = 5 ; … Read more

Chapter 1 Linear Equations in Two Variables Set 1.1 Question 1.Complete the following activity to solve the simultaneous equations.5x + 3y = 9 …(i)2x-3y=12 …(ii)Solution:5x + 3y = 9 …(i)2x-3y=12 …(ii)Add equations (i) and (ii). Question 2.Solve the following simultaneous equations.i. 3a + 5b = 26; a + 5b = 22ii. x + 7y = … Read more

(I) Choose the correct option from the given alternatives: Question 1.The mean and the variance of a binomial distribution are 4 and 2 respectively. Then the probability of 2 successes is(a) √50(b) 5(c) 25(d) 10Answer:(b) 5 Question 2.The mean and the variance of a binomial distribution are 4 and 2 respectively. Then the probablity of … Read more

Question 1.A die is thrown 6 times. If ‘getting an odd number’ is a success, find the probability of(i) 5 successes(ii) at least 5 successes(iii) at most 5 successes.Solution:Let X = number of successes, i.e. number of odd numbers.p = probability of getting an odd number in a single throw of a dieThe p.m.f. of … Read more

(I) Choose the correct option from the given alternatives: Question 1.P.d.f. of a c.r.v. X is f(x) = 6x(1 – x), for 0 ≤ x ≤ 1 and = 0, otherwise (elsewhere) If P(X < a) = P(X > a), then a = Question 3. Question 5. Question 7. Question 8.If the d.r.v. X has … Read more

Question 1.Verify which of the following is p.d.f. of r.v. X: (ii) f(x) = x, for 0 ≤ x ≤ 1 and -2 – x for 1 < x < 2(iii) fix) = 2, for 0 ≤ x ≤ 1.Solution:f(x) is the p.d.f. of r.v. X if(a) f(x) ≥ 0 for all x ∈ R … Read more

Chapter 7 Probability Distributions Ex 7.1 Question 1.Let X represent the difference between a number of heads and the number of tails when a coin is tossed 6 times. What are the possible values of X?Solution:When a coin is tossed 6 times, the number of heads can be 0, 1, 2, 3, 4, 5, 6.The … Read more