Q) Solve the following pair of linear equations: 152x – 378y = – 74– 378 x + 152y = – 604 Ans: Given the equations: Solve the following pair of linear equations:152 x – 378 y = – 74 ….. (i)– 378 x + 152 y = – 604 ….. (ii) We need to first […]
Solve the following pair of linear equations: 152x – 378y = -74, -378 x + 152y = -604 Read More »
Q) Solve the following pair of linear equations: ax + by = c bx + ay = 1 + c Ans: Given the equations: a x + b y = c ….. (i)b x + a y = 1 + c ….. (ii) Let’s multiply equation (i) with a and equation (ii) with b and we get: a2
Solve the following pair of linear equations: ax + by = c, bx + ay = 1 + c Read More »
Q) Solve the following pair of linear equations:px + qy = p – qqx – py = p + q Ans: Given the equations: Solve the following pair of linear equations:px + qy = p – q …………. (i)qx – py = p + q ………….. (ii) Let’s multiply equation (i) with p and equation
Solve the following pair of linear equations: px + qy = p – q, qx – py = p + q Read More »
Q) Find two consecutive odd positive integers, the sum of whose squares is by using the quadratic formula. Ans: Let’s consider the 1st odd positive integer be XThen the next consecutive odd positive integers will be X + 2 Now it is given, that the sum of the squares of these two numbers is 290∴ X2
Q) Find the HCF of 506 and 1155. Ans: By prime factorisation, we get: 506 = 2 x 11 x 23 1155 = 3 x 5 x 7 x 11 Since HCF is all the factors between the two numbers and here 11 is the only factor between the two numbers ∴ HCF = 11
Find the HCF of 506 and 1155. Read More »
Q) Find the LCM and HCF of 404 and 96 and verify that LCM x HCF = product of the two numbers.120. Ans: By prime factorisation, we get: 404 = 22 x 101 96 = 25 x 3 ∴ LCM = 25 x 3 x 101 = 9696 And HCF = 22 = 4 Now
Q) ABCD is a rectangle if the value of AB= 12 is given, find the values of x and y. Ans: We know, opposite sides of a rectangle are equal, ∴ x + y = 12 —-(1) and, x – y = 8 —-(2) By elimination method, we subtract (2) from (1), Therefore, 2y =
ABCD is a rectangle if the value of AB=12 is given. Find the values of x and y. Read More »
Q) Mrs. Gupta arranged some snacks for her child’s birthday party. After the guest left she had some food left over. She did not want to waste food and so she contacted a local NGO. She gave 60 pieces of pastries,168 pieces of cookies, and 330 chocolate bars to the team. Now the NGO workers want
Mrs. Gupta arranged some snacks for her child’s birthday party. Read More »
Q) A number consists of two digits. Where the number is divided by the sum of its digits, the quotient is 7. If 27 is subtracted from the number, the digits interchange their places, find the number Ans: Let’s consider X and Y are the digits of the given number. Hence the given number is 10 X
A number consists of two digits. Where the number is divided by the sum of its digits, Read More »
Q) Solve for x and y: = -1; = 3 Ans: Let’s take the equations one by one: = -1 3X + 4 Y = – 6 ………. (i) Similarly, = 3 We can write this as: = 3 3X – Y = 9 ….. (ii) By solving equations (i) and (ii), we get: X =
Solve for x and y : x / 2 + 2y / 3 = − 1; x − y / 3 = 3 Read More »