Chapter 1 Euclid Division Algorithm: Given positive integers a and b , there exist unique integers q and r satisfying a = bq + r , 0 ≤ r < b How to find HCF and LCM using Euclid's Algorithm I) 135 and 225 let a = 225 , b = 135 Apply Euclid's Algorithm till remainder becomes zero , the corresponding divisor will be the HCF 225 = 135 × 1 + 90 135 = 90 × 1 + 45 90 = 45×2 + 0 So , HCF = 45 . I) 455 and 42 let a = 455 , b = 42 Apply Euclid's Algorithm till remainder becomes zero , the corresponding divisor will be the HCF 445 = 42 ×10 + 35 42 = 35 × 1 + 7 35 = 7×5 + 0 So , HCF = 7 . Fundamental theorem of Arithmetic: "Every Composite number can be expressed as a product of primes and this factorizaion is unique." Example : Let's take a composite number '12' It can be written as factorization of prime numbers. i.e. 12 = 2 ×2 ×3 and this factorization is unique. this is the fundamental the...

Boat and stream Question no. 1 A person can swim in still water at 4 km/h. If the speed of water is 2 km/h, how many hours will the man take to swim back against the current for 6 km. looks_one 3 looks_two 4 looks_3 4.5 looks_4 None of these Answer Option looks_one 3 Solution Solution : Speed of swim = 4 km/hr Speed of water = 2 km/ hr against the water speed of swim = 2 km/hr Time taken by man = distance/ speed = 6 / 2 = 3 hr Question no. 2 A man can swim in still water at 4.5 km/h, buttakes thrice as long to swim upstream than downstream. The speed of the stream is looks_one 2.25 looks_two 2 looks_3 3 looks_4 None of these Answer Option looks_one 2.25 Solution Solution : speed of swim = 4.5 km/hr Time taken to downstream = x hr Time taken to upstream = 3x hr Speed of stream = z distance of upstream = distance of downstream (4.5 - z) * 3x = (4.5 + z )* x ( 4.5 - z )* 3 = 4.5 + z 4.5 + z = 13.5 - 3...

Change the direct into indirect Question no. 1 She said to me, "I have seen the Taj twice". looks_one She told me that she had seen the taj twice. looks_two She said to me that she had seen the taj twice. looks_3 She told me that she had been seen the taj twice. looks_4 She told me that she saw the taj twice. Question no. 2 Our teacher said , "The earth moves round the sun." looks_one Our teacher told that the earth moves round the sun. looks_two Our teacher said that the earth moved round the sun. looks_3 Our teacher said that the earth moves round the sun. looks_4 None of these Question no. 3 He said , "If I were you , I would help her." looks_one He told that if he were you, he would help her. looks_two He said that if he were you, he should help her. looks_3 He said that if he were you, he would have helped her. looks_4 He said that if he were you, he would help her. ...

Permutation and Combination Question no. 16 What is the number of three digit odd numbers formed by using the digits 1,2,3,4,5,6 if repetition of digits is allowed ? looks_one 60 looks_two 108 looks_3 120 looks_4 216 Answer Option looks_two 108 Solution Solution : Number of digits at one's place = 1 , 3 , 5 [Total number is 3] Number of digits at ten's place = 6 [1,2,3,4,5,6] Number of digits at hundred place =6 [ 1, 2 , 3 , 4 , 5 , 6 ] Total number of ways = 3 * 6 * 6 = 108 Question no. 17 What is the number of ways of arranging the letters of the word "BANANA" so that no two N's appear together? looks_one 60 looks_two 40 looks_3 80 looks_4 100 Answer Option looks_two 40 Solution Solution : Total no. of ways = 6!/(3!2!) = 60 Two N's come together = 4!*5 / 3! = 20 No. of ways no two N's appear together = 60 - 20 = 40 Question no. 18 How many times does the ...

profit and loss Question no. 1 If the manufacturer gains 10%, the wholesale dealer 15% and the retailer 25%, then find the cost of production of a table, the retail price of which is $ 1265? looks_one $800 looks_two $1000 looks_3 $900 looks_4 $600 Answer Option looks_one $800 Solution Solution : the cost of production of a table is x 110 % of x = wholesale cost price 115% of 110% of x = retailer cost price 125 % 115% of 110% of x = retailer selling price Question no. 2 If the cost price is 96% of the selling price, then what is the profit percent? looks_one 4.5 % looks_two 4 % looks_3 4.2 % looks_4 None of these Answer Option looks_3 4.2 % Solution Solution : CP = 0.96 SP Question no. 3 A man buys 50 pencils for Rs 100 and sells 45 pencils for Rs 90. Find his gain or loss %. looks_one 20 % looks_two 35 % looks_3 25 % looks_4 none of these Answer option looks_4 none of thes...