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What is the area of the largest triangle that can be fitted into a rectangle of length l units and width w units? (a) lw /2 (b) lw /3 (c) lw/6 (d) lw/4

Answer: (a) lw/2 The area of a triangle is defined as the total region that is enclosed by the three sides of any particular triangle. Basically,... View Article

A circle of maximum possible size is cut from a square sheet of board. Subsequently, a square of maximum possible size is cut from the resultant circle. What will be the area of the final square? (a) 3/4 of the original square. (b) 1/2 of the original square. c) 1/4 of the original square. (d) 2/3 of the original square.

Answer: (b) 1/2 of the original square Let a be the side of the square sheet Thus, the area of the bigger square sheet = a2... View Article

A cube of side 4 cm is cut into 1 cm cubes. What is the ratio of the surface areas of the original cubes and cut-out cubes? (a) 1 : 2 (b) 1 : 3 (c) 1 : 4 (d) 1 : 6

Answer: (c) 1: 4 The cube side is 4cm The side of cube 4cm is cut into small cubes, in which each of 1 cm ∴ The total number of cubes = 4... View Article

A cube of side 5 cm is painted on all its faces. If it is sliced into 1 cubic centimetre cubes, how many 1 cubic centimetre cubes will have exactly one of the (a) 27 (b) 42 (c) 54 (d) 142

Answer: (c) 54 The cube side = 5 cm The side of cube 5cm is cut into 5 equal parts, in which each of 1 cm Therefore, the total number of cubes of... View Article

Find the least value that must be given to number a so that the number 91876a2 is divisible by 8. State whether the statement given is true (T) or false (F).

Answer: a= 3 By using the divisibility test of 8, if a number is divisible by 8, then the last three digit of a number should be divisible by 8.... View Article

If N ÷ 5 leaves remainder 3 and N ÷ 2 leaves remainder 0, then N ÷ 10 leaves remainder 4. State whether the statement given is true (T) or false (F).

Answer: False N ÷ 5 Remainder 3 N ÷ 2 Remainder 0 N ÷ 10 Remainder 4 N = 5n + 3 Where, n = 0,1,2,3,... Given that, when N... View Article

If 213x 27 is divisible by 9, then the value of x is 0. State whether the statement given is true (T) or false (F).

Answer: False If 213 x 27 is divisible by 9, then the sum of the digits of a number is a multiple of 9. 2 + 1 + 3 + x + 2 + 7 = 15 + x Then 15x... View Article

If AB + 7C = 102, where B ≠ 0, C ≠ 0, then A + B + C = 14. State whether the statement given is true (T) or false (F).

Answer: True From the given number, B + C is either 2 or the two-digit number that gives the unit digit as 2. It is given that B ≠ 0, C ≠... View Article

If AB × 4 = 192, then A + B = 7. State whether the statement given is true (T) or false (F).

Answer: False From the given question, the value of B should be either 3 or 8. If you take the value of B as 3, it should be equal to 19. Hence,... View Article

If a number a is divisible by b, then it must be divisible by each factor of b. State whether the statement given is true (T) or false (F).

Answer: True Let a = 27 b = 9 Here, when 27 is divisible by 9, we will get 3 Now, consider the factor of 9 = 1, 3 and 9 In this case, 27 is... View Article

Number 7N + 1 will leave remainder 1 when divided by 7. State whether the statement given is true (T) or false (F).

Answer: True The given number is of the form 7N + 1 It can be written as (multiples of 7) + 1 When the given number 7N + 1 is divide by 7, we... View Article

Number of the form 3N + 2 will leave remainder 2 when divided by 3. State whether the statement given is true (T) or false (F).

Answer: True The given number is of the form 3N + 2 It can be written as (multiples of 3) + 2 When the given number 3N+2 is divide by 3, we will... View Article

A three-digit number abc is divisible by 6 if c is an even number and a + b + c is a multiple of 3. State whether the statement given is true (T) or false (F).

Answer: True In case, if a number is divisible by 6, it is also divisible by 2 and 3. If c is an even number, then the sum of digits is divisible by 3.... View Article

A four-digit number abcd is divisible by 4 if ab is divisible by 4. State whether the statement given is true (T) or false (F).

Answer: False A four-digit number is divisible by 4 if the number is formed by its digit units and 10′s place is divisible by 4. Example:... View Article

A three-digit number abc is divisible by 5 if c is an even number. State whether the statement given is true (T) or false (F).

Answer: False If a number with three digits and if the unit digit is an even number, then the number is said to be an even number. A number is... View Article

A two-digit number ab is always divisible by 2 if b is an even number. State whether the statement given is true (T) or false (F).

Answer: True If a number with two digits and the number in the unit place is even, then the number is said to be an even number and it is... View Article

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