Question 1

Two angles whose sum is 180 degrees are

Accepted Answer

Two angles whose sum is 180 degrees are called supplementary angles.

Question 2

The binary system uses powers of

Accepted Answer

Binary system is what the representation uses only two digits 0 & 1. It uses only the powers of 2.

Question 3

a2 + b2 + c2 -ab- bc - ca = 0, iff

Accepted Answer

Here given formula is a 2 + b 2 + c 2 - ab - bc - ca = 0 and it is possible if and only if a = b = c. From the trial and error method, 1) Let a = b = c = 1 Now substitute these values of a, b, c in the above formula. We get 1 + 1 + 1 - 1 - 1 - 1 = 3 - 3 = 0 2) Now, let a = b = c = 4 Now substitute these values of a, b, c in the above formula. We get 16 + 16 + 16 - 16 - 16 - 16 = 48 - 48 = 0. Hence, it is possible that a 2 + b 2 + c 2 - ab - bc - ca = 0 iff a = b = c.

Question 4

3x3x3+3+3/3 = ?

Accepted Answer

We all know about BODMAS rule, by using that 3x3x3+3+3/3 = 3x3x3+3+1 = 27+3+1 = 27 + 4 = 31 Hence, 3x3x3+3+3/3 = 31.

Question 5

How many rectangles can be drawn with 36 cm as the perimeter, given that the sides are positive integers in cm?

Accepted Answer

Perimeter = 36 ⇒ 2 ( l + w ) = 36 ⇒ l + w = 18 Since length and width are positive integers in centimeters. Therefore, possible dimensions are : ( 1, 17 )cm , ( 2, 16 ) cm , ( 3, 15 ) cm, (4 , 14) cm, ( 5,13) cm, ( 6, 12) cm , ( 7, 11) cm, ( 8, 10 ) cm, ( 9, 9) cm. Hence, there are 9 rectangles.

Question 6

Which of the following number is divisible by 24?

Accepted Answer

Divisibility rule for 24 is the number should be divisible by 3 and 8. As we know that 24 = 3 x 8 Now, Divisibility rule for 3 : If the sum of the digits of a number is divisible by 3, then the number is divisible by 3. Divisibility rule for 8 : The last three digits of a number should be divisible by 8. Hence, check for the given options, A) 37804 => 804 is not divible by 8. C) 36718 => 718 is not divible by 8. D) 53810 => 810 is not divible by 8. B) 2015736 => 736 is divisble by 8 and sum 2 + 0 + 1 + 5 + 7 + 3 + 6 = 24 which is divisible by 3. Hence, 2015736 is divisible by 24.

Question 7

The expression of 5008 km in scientific notation is

Accepted Answer

We know that, any decimal number when multiplied by the multiples of 10, the decimal point moves to right the number of zeroes in the multiplying number. For example :: 0.0410 x 100 = 4.10 (Number of zeros in 100 are 2. So, the decimal point in 0.0410 moves two places to the right and becomes 4.10.) Similarly, here in the option C) 5.008 x 10^3 kms it makes 5008 kms as the number of zeros in 10^3 i.e, 1000 are 3 and 5.008 becomes 5008.

Question 8

What is the value of a two–digit number? A. The sum of the digits is 15. B. The difference of the squares of the digits is 45. C. The difference of their digits is 3.

Accepted Answer

From the given data, Let the two gits of a number be x & y A) x + y = 15 B) x 2 - y 2 = 45 (x+y) (x - y) = 45 C) x - y = 3 From any 2 of the given 3 statements, we can find that 2 digit number as 2x = 18 => x = 9 => y = 6 Hence, 2 digit number is 96. Any one pair of A and B, B and C or C and A is sufficient to find.

Question 9

Hemavathi cut a cake into two halves and cuts one half into smaller pieces of equal size. Each of the small pieces is fifteen grams in weight. If she has nine pieces of the cake in all with her, how heavy was the original cake ?

Accepted Answer

The nine pieces consist of 8 smaller equal pieces and one half cake piece. Weight of each small piece = 15 g. So, total weight of the cake = [2 x (15 x 8)]g = 240 g.

Question 10

An intelligent boy is doing a jigsaw with 275 pieces. Each day that he fits pieces together there are fewer pieces left, and it is reasonable to assume that he fits more pieces each day because the number left to sort out diminishes progressively. H…

Accepted Answer

Let 'n' number of days it take to complete. we know that sum of n number= n/2[2a+(n-1)d] where a=20,d=1; n/2[2x20+(n-1)1]=275 n[n+39]=550 n 2 + 39n - 550 = 0 n 2 + 50n - 11n - 550 = 0 (n-11) (n-50) = 0 n-11 = 0; n = 11(Days).

Question 11

In three coloured boxes - Red, Green and Blue, 108 balls are placed. There are twice as many balls in the green and red boxes combined as there are in the blue box and twice as many in the blue box as there are in the red box. How many balls are the…

Accepted Answer

Let R, G and B represent the number of balls in red, green and blue boxes respectively. Then, . R + G + B = 108 ...(i), G + R = 2B ...(ii) B = 2R ...(iii) From (ii) and (iii), we have G + R = 2x 2R = 4R or G = 3R. Putting G = 3R and B = 2R in (i), we get: R + 3R + 2R = 108 6R = 108 R = 18. Therefore Number of balls in green box = G = 3R = (3 x 18) = 54.

Question 12

In a class there are certain no. of boys and girls. If 15 girls are absent then no. of boys will be twice that of girls. If 45 boys are absent then girls strength will be 5 times that of boys. Find number of boys actually present ?

Accepted Answer

15 girls are absent => b = 2(g-15)...... eqn...(1) 45 boys are absent => g - 15 = 5(b-45).....eqn...(2) => g = 5(b-45) + 15 => b = 2((5(b-45)+15)-15) => b = 2(5b - 225 + 15 - 15) => b = 2(5b-225) => b = 10b - 450 => 9b = 450 => b = 50 so from equation(2) g - 15 = 5(b - 45) => g - 15 = 5(50-45) => g - 15 = 5(5) => g = 25 + 15 => g = 40 Therefore, the number of boys = 50 and girls = 40

Question 13

A plane is an undefined term because it

Accepted Answer

In geometry, we can define plane as a flat surface with no thickness. The surface extends with no ends. A plane does not have any edges even if we draw it on paper with edges, it does't mean it has edges. Hence, A plane is an undefined term because it is described generally, not using a formal definition.

Question 14

What is the product of a number and its reciprocal?

Accepted Answer

The product of a number and its reciprocal is always equals to 1. For Example : Let the number be 4. Now, its reciprocal is 1/4 Hence, required product = 4 x 1/4 = 1. Now, take the number as -15. Then its reciprocal is -1/15 Required product = -15 x -1/15 = 1. Hence, the product of a number and its reciprocal is 1.

Question 15

Multiplicative inverse of 7?

Accepted Answer

Multiplicative inverse is nothing but a reciprocal of a number. It is defined as one of a pair of numbers that when multiplied with another number equals the number 1. Multiplicative inverse or reciprocal of 7 is 7 x n = 1 => n = 1/7. Hence, Multiplicative inverse or reciprocal of 7 is 1/7.

Question 16

Two angles whose sum is 90 are

Accepted Answer

Complimentary angles are those two angles whose sum is 90 whereas two angles whose sum is 180 are called Supplementary angles.

Question 17

Which set represents a pythagorean triple?

Accepted Answer

A Pythagorean triple consists of three positive integers a, b, and c, such that a² + b² = c². Here we know, that 3, 4, 5 are pythagorean triplets as 25 = 9 + 16. Hence, its multiple will also be a pythagorean triple. In the options given, (3 x 11 , 4 x 11 , 5 x 11) = 33, 44, 55 is a pythagorean triplet.

Question 18

Which letter has at least one line of symmetry?

Accepted Answer

The letter A has a vertical axis of symmetry. The letter C has a horizontal axis of symmetry. The letter O has more than one axis of symmetry, including vertical axis and horizontal axis.

Question 19

A tangent contains at most how many chords?

Accepted Answer

A tangent contains ZERO chords, as it touches the circle at only one point. Hence, it does not contain any chord.

Question 20

Weight of Sona is four times that of Mona. Weight of Mona is 2.5 times of Hona. Weight of Hona is 1.5 times of Dhona. Weight of Dhona is 2.5 times of Rona. Who is the heaviest?

Accepted Answer

Sona

Arithmetic Reasoning Questions