Two angles whose sum is 180 degrees are

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: 1024

Explanation:

Fruits reduced by 1/4.
Total no. of bags N = 5
Formula to find no. of fruits in 1st bag = 4^n
Last Bag = 4 fruits.
That means, 4th bag = 4 x 4 = 16 fruits
3rd bag = 16 x 4 = 64 fruits
2nd bag = 64 x 4 = 256 fruits
1st bag = 256 x 4= 1024 fruits.

Correct Answer: 25

Explanation:

Let x be number of houses and y be colors.

on the basis of question
x = 4y+1
x = 5(y-1)
on solving these 2 equations x = 25

Correct Answer: 900/19 %

Explanation:

First ten odd numbers form an arithmetic progression of the form
1,3,5,7,9......
here a = first term = 1
d = common difference = 2
Average of first n numbers = (2a + (n - 1)d)/2
n th term of the AP = a + (n - 1)d
Substituting a = 1, d = 2 and n = 10 in the above formulas
average of first 10 numbers = 10
10 th term of the AP = 19
Therefore average of first 10 terms is 19 - 10 = 9 greater than
the last term. Hence the average is greater than the sum by
9/19 X 100 = 900/19 %

Correct Answer: 48

Explanation:

No. of students will be 98 x 12 = 1176
let us consider n circles then 1 + 2 + 3 + ....+ n = 1176
n(n+1)/2 = 1176
n = 48 circles.

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: 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: 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: 9

Explanation:

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.

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.