CLASS 10th Math, Pair f Linear Equation in Two Variables   (NCERT)  Exercise: 3.1 (Solution), Question-1 to Question-3 Exercise: 3.2 (Solution), Question-1 to Question-7 ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; Q1. Aftab tells his daughter, “Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be.” (Isn’t this interesting?) Represent this situation algebraically and graphically. Solution ..read more

CLASS 10th Math, Polynomials  (NCERT)  Exercise: 2.1 To Exercise: 2.4 ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; Exercise 2.1 (Solution) Q1. The graphs of y = p(x) are given in Fig. 2.10 below, for some polynomials p(x). Find the number of zeroes of p(x), in each case. Solutions:- Graphical method to find zeroes:- Total number of zeroes in any polynomial equation = total number of times the curve intersects x-axis. In the given graph, the number of zeroes of p(x) is 0 ..read more

CLASS 10th Math, Real Number   (NCERT)  Exercise: 1.3 (Solution), Question-1 to Question-3 Exercise: 1.4 (Solution), Question-1 to Question-3 ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; Q1. Prove that √5 is irrational. Q2. Prove that 3 + 2√5 is irrational. Q3. Prove that the following are irrationals: (i) 1/√2 (ii) 7√5 (iii) 6 + √2 Exercise: 1.4 (Solution), Question-1 to Question-3 ..read more

CLASS 10th Math, Real Number   (NCERT)  Exercise: 1.2 (Solution), Question-1 to Question-7 ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; Q1. Express each number as a product of its prime factors: 140 156 3825 5005 7429 Solutions:- (i) 140 By Taking the LCM of 140, we will get the product of its prime factor. Therefore, 140 = 2 × 2 × 5 × 7 × 1 = 22 × 5 × 7 (ii) 156 By Taking the LCM of 156, we will get the product of its prime factor. Hence, 156 = 2 × 2 ..read more

CLASS 10th, PROBABILITY    (NCERT)  Exercise: 15.2 (Solution), Question-1 to Question-5 ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; Q1. Two customers Shyam and Ekta are visiting a particular shop in the same week (Tuesday to Saturday). Each is equally likely to visit the shop on any day as on another day. What is the probability that both will visit the shop on (i) the same day? (ii) consecutive days? (iii) different days? Solution:- Since there are 5 days and both ..read more

CLASS 10th, PROBABILITY    (NCERT)  Exercise: 15.1 (Solution 2), Question-13 to Question-25 ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; Q13. A die is thrown once. Find the probability of getting (i) a prime number; (ii) a number lying between 2 and 6; (iii) an odd number. Solution:- Total possible events when a dice is thrown = 6 (1, 2, 3, 4, 5, and 6) P(E) = (Number of favorable outcomes/ Total number of outcomes) (i) Total number of prime numbers = 3 (2, 3 and 5 ..read more

CLASS 10th, PROBABILITY    (NCERT)  Exercise: 15.1 (Solution 1), Question-1 to Question-12 ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; Q1. Complete the following statements: (i) Probability of an event E + Probability of the event ‘not E’ = ___________ . (ii) The probability of an event that cannot happen is __________. Such an event is called ________ . (iii) The probability of an event that is certain to happen is _________ . Such an event is called ________ ..read more

Class 10th,- Statistics  Exercise: 14.4 (Solution), Q1 to Q3 ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; Q1. The following distribution gives the daily income of 50 workers if a factory. Convert the distribution above to a less than type cumulative frequency distribution and draw its ogive. Daily income in Rupees 100-120 120-140 140-160 160-180 180-200 Number of workers 12 14 8 6 10 Solution:- Convert the given distribution table to a less than type cumulative ..read more

Class 10th,- Statistics  Exercise: 14.2 (Solution), Q1 to Q7 ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; Q1. The following frequency distribution gives the monthly consumption of an electricity of 68 consumers in a locality. Find the median, mean and mode of the data and compare them. Monthly consumption(in units) No. of customers 65-85 4 85-105 5 105-125 13 125-145 20 145-165 14 165-185 8 185-205 4 Solution:- Find the cumulative frequency of ..read more

Class 10th,- Statistics  Exercise: 14.2 (Solution), Q1 to Q6 ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; Q1. The following table shows the ages of the patients admitted in a hospital during a year: Age (in years) 5-15 15-25 25-35 35-45 45-55 55-65 Number of patients 6 11 21 23 14 5 Find the mode and the mean of the data given above. Compare and interpret the two measures of central tendency. Solution: To find out the modal class, let us the consider the clas ..read more