CTET Maths MCQ - Algebra

11 Anita bought some pencils, erasers and graph papers from a stationary shop. If the ratio of the pencils and the erasers is the same as that of erasers and graph papers and she bought 10 pencils and 40 graph papers. Find the number of eraser bought by her.

Let number of eraser be x, then 10 : x = x : 40 ⇒ 10/x = x/40 ⇒ x ²= 40 × 10 = 400.⇒ x = 20

12 Suppose, y varies as the sum of two quantities of which one varies directly as x and the other inversely as x.If y= 6 when x=4 and

when x = 3, then the relation between x and y is

Let y = a + b, where a∝x and b∝1/x.
Let a = K₁x and b=K2/x.
where K₁ and K₂ are constants.
y = K₁ x+ K₂/x . .. (i).
Given, y = 6 when x = 4.
6 = K₁4 + K₂/4.
⇒16K₁ + K₂ = 24 . .. (ii)
Also,

when x = 3 .
⇒10/3 = 3K₁ + K₂/3
⇒9K₁ + K₂ = 10 . .. (iii)
From Eqs. (i) and (ii), we get
K₁ = 2 and K₂ = - 8.
y=2x-8/x .

13 Average of four numbers is 10.5. If three of these numbers be 4,9 and 13, find the fourth number.

Let fourth number be x. Average = Sum of numbers / Number of numbers ⇒ 10.5 = (4 + 9 + 13 + x) / 4 ⇒ 10.5 x 4 = 26 + x ⇒ 42-26=x ⇒ X= 16

14 Average age of a group of five students is 14 yr. If a new student also admitted the group, new average age becomes 13 yr. Find the age of new student.

Average age of five students = 14 :. Sum of ages of five students = 14 x5 =70 Again, average age of six students = 13 :. Sum of ages of six students = 13 x 6 =78 Thus, age of new student = 78 - 70 = 8 yr

15 A bike covers a distance of 240 km in 5h. Again, it covers an another distance of 260 km in 5 h . Find the average speed of the bike.

Average speed = Total distance covered / Total time taken. = (240 + 260) / (5+5) = 500/10 = 50 km/h

CTET Maths MCQ - Algebra

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