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

Correct Answer: 31

Explanation:

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.

Correct Answer: a = b = c

Explanation:

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.

Correct Answer: 2

Explanation:

Binary system is what the representation uses only two digits 0 & 1.

It uses only the powers of 2.

Correct Answer: Supplementary angles

Explanation:

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

Correct Answer: -2

Explanation:

We know that in A.P series
18th term = a + 17d
29th term = a + 28d
But given
a + 17d = 29..........(i)
a + 28d = 18......... (ii)
Solving equation (i) and (ii), we get
d = -1
put d = -1 in any of the above equations and we get,
a = 46
Now, we know 49th term can be written as, a + 48d
putting the value of a and d in the above equation,
a + 48d = 46 + 48(-1)
= 46 - 48
= -2

Hence, the 49th term is -2.

Correct Answer: 2015736

Explanation:

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.

Correct Answer: 5.008 x 10^3 kms

Explanation:

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.

Correct Answer: Any one pair of A and B, B and C or C and A is sufficient

Explanation:

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.

Correct Answer: 240 gms

Explanation:

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.

Correct Answer: 11 days

Explanation:

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).