Q) February 14 is celebrated as International Book Giving Day and many countries in the world celebrate this day. Some people in India also started celebrating this day and donated the following number of books of various subjects to a public library : History = 96, Science = 240, Mathematics = 336. These books have to […]
real numbers
Q) Solve the following pair of linear equations: Ans: Given the equations: ……….. (i) ………….(ii) Step 1: Let’s multiply equation (i) by b2 and add to equation (ii), we get: ……….. (i) ∴ ……….. (i) ∴ ……….. (i) ∴ b2 x + a2 x = a ( a2 + b2 ) ∴ x (a2 + b2
Solve the following pair of linear equations: x/a – y/b =0, a x + b y = a2 + b2 Read More »
Q) Solve the following pair of linear equations: (a – b) x + (a + b) y = a2 – 2 a b – b2 (a + b) (x + y) = a2 + b2 Ans: Given the equations: (a – b) x + (a + b) y = a2 – 2 a b – b2……
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 »