Question 1 :
State true or false: The product or quotient of a non-zero rational number and an irrational number is irrational.
Question 3 :
For any positive integer n, $n^3$– n is divisible by 6. Is it True or False?
Question 5 :
Without actually performing the long division, state whether $\frac{6}{15}$ will have a terminating decimal expansion or a non-terminating repeating decimal expansion.
Question 6 :
State True or False, Let p be a prime number. If p divides $a^2$ , then p divides a, where a is a positive integer.
Question 7 :
A/An __________ is a series of well defined steps which gives a procedure for solving a type of problem.
Question 9 :
The rational number $\frac{257}{5000}$ in the form $2^m × 5^n$ , where m, n are non-negative integers. Find the value of n.
Question 10 :
Choose the correct answer from the given four options in the question: For some integer m, every even integer is of the form.
Question 11 :
One says, “Give me a hundred, friend! I shall then become twice as rich as you”. The other replies, “If you give me ten, I shall be six times as rich as you”. Tell me what is the amount of their (respective) capital?
Question 12 :
A train covered a certain distance at a uniform speed. If the train would have been10 km/h faster, it would have taken 2 hours less than the scheduled time. And, if the train were slower by 10 km/h; it would have taken 3 hours more than the scheduled time. Find the distance covered by the train.
Question 13 :
The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number.
Question 14 :
Solve the following pair of linear equations by the substitution method : $x + y = 14 ; x - y = 4$
Question 16 :
The students of a class are made to stand in rows. If 3 students are extra in a row, there would be 1 row less. If 3 students are less in a row, there would be 2 rows more. Find the number of students in the class.
Question 17 :
For which value of k will the following pair of linear equations have no solution? $3x + y = 1; (2k – 1)x + (k – 1) y = 2k + 1$
Question 18 :
Given the linear equation 2x + 3y – 8 = 0, write another linear equation in two variables such that the geometrical representation of the pair so formed are intersecting lines.
Question 19 :
Find out whether the lines representing a pair of linear equations are consistent or inconsistent: $2x + y – 6 = 0 , 4x – 2y – 4 = 0$
Question 20 :
Is the pair of equations x + 2y – 3 = 0 and 6y + 3x – 9 = 0 consistent?