Question 1 :
If $\frac{5x}{3}-4=\frac{2x}{5}$, then the numerical value of 2x – 7 is
Question 4 :
State whether the statement is TRUE or FALSE : Any value of the variable which makes both sides of an equation equal is known as a solution of the equation.
Question 5 :
State whether the statement is TRUE or FALSE : x = –12 is the solution of the linear equation 5x –3(2x + 1) = 21 + x.
Question 8 :
Solve 4t – 3 – (3t +1) = 5t – 4.
Question 10 :
On dividing Rs. 200 between A and B such that twice of A’s share is less than 3 times B’s share by 200, B’s share is?
Question 12 :
Hamid has three boxes of different fruits. Box A weighs $2\frac{1}{2}$ kg more than Box B and Box C weighs $10\frac{1}{4}$ kg more than Box B. The total weight of the three boxes is $48\frac{3}{4}$ kg. How many kilograms (kg) does Box A weigh?
Question 14 :
State whether the statement is TRUE or FALSE : In the equation 3x – 3 = 9, transposing –3 to RHS, we get 3x = 9.
Question 15 :
The denominator of a rational number is greater than the numerator by 10. If the numerator is increased by 1 the and denominator is decreased by 1, then expression for new denominator is
Question 16 :
The value of x for which the expressions 3x – 4 and 2x + 1 become equal is
Question 18 :
In a two digit number, digit in units place is twice the digit in tens place. If 27 is added to it, digits are reversed. Find the number.
Question 19 :
State whether the statement is TRUE or FALSE : If the sum of two consecutive numbers is 93 and one of them is x, then the other number is 93–x.
Question 20 :
If 3x – 4 (64 – x) = 10, then the value of x is
Question 21 :
The age of A is five years more than that of B. 5 years ago, the ratio of their ages was 3:2. Find their present ages.
Question 22 :
The shifting of a number from one side of an equation to other is called
Question 23 :
State whether the statement is TRUE or FALSE : In an equation, variables can be transposed from one side of the equation to the other.
Question 24 :
After 18 years, Swarnim will be 4 times as old as he is now. His present age is
Question 25 :
Find a number whose fifth part increased by 30 is equal to its fourth part decreased by 30.
Question 26 :
State whether the statement is TRUE or FALSE : If 6x = 18, then 18x = 54.
Question 28 :
Fifteen added to thrice a whole number gives 93. The number is
Question 29 :
State whether the statement is TRUE or FALSE : An algebraic equation is an equality involving variables.
Question 30 :
State whether the statement is TRUE or FALSE : Three consecutive even numbers whose sum is 156 are 51, 52 and 53.
Question 31 :
State whether the statement is TRUE or FALSE : If $\frac{15}{8}-7x=9$, then $-7x=9+\frac{15}{8}$.
Question 32 :
State whether the statement is TRUE or FALSE : If $\frac{x}{3}+1=\frac{7}{15}$, then $\frac{x}{3}=\frac{6}{15}$.
Question 33 :
State whether the statement is TRUE or FALSE : In a linear equation, the highest power of the variable appearing in the equation is one.
Question 35 :
If a and b are positive integers, then the solution of the equation ax = b has to be always
Question 36 :
Solve 1 – (x – 2) – [(x – 3) – (x – 1)] = 0.
Question 37 :
Sum of the digits of a two-digit number is 11. The given number is less than the number obtained by interchanging the digits by 9. Find the number.
Question 38 :
A carpenter charged Rs. 2500 for making a bed. The cost of materials used is Rs. 1100 and the labour charges are Rs. 200/hr. For how many hours did the carpenter work?
Question 39 :
A family spent Rs. 52.00 for circus tickets. This cost included a Rs. 3.25 service fee for the order, with the cost of the circus tickets being Rs. 9.75 each. How many tickets did the family buy?
Question 40 :
Two equal sides of a triangle are each 4m less than three times the third side. Find the dimensions of the triangle, if its perimeter is 55m.
Question 44 :
Anushka and Aarushi are friends. They have equal amount of money in their pockets. Anushka gave $\frac{1}{3}$ of her money to Aarushi as her birthday gift. Then Aarushi gave a party at a restaurant and cleared the bill by paying half of the total money with her. If the remaining money in Aarushi’s pocket is Rs.1600, find the sum gifted by Anushka.
Question 45 :
The solution of which of the following equations is neither a fraction nor an integer .
Question 50 :
State whether the statement is TRUE or FALSE : In a 2 digit number, the units place digit is x. If the sum of digits be 9, then the number is (10x – 9).
