Select the option that represents the number of parallelograms in the given figure.

 

 

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.

Total number of cards = 1500
total columns = 45
so, total punches=1500 x 45 = 67500
for 1 hour if we make 9000 punches,
we require 67500/9000 = 7.5
so 7hours:30mins.

7 boxes & 24 Balls.
Let, n = No. of boxes ; m = No. of fruits
3n+3 = m---------->(1)
4(n-1)= m---------->(2)
=>4n-4 = 3n+3;
=>4n-3n = 4+3
n = 7
Put n=7 in eqn(1)
=> 3(7)+3 = m
21+3 = m
m = 24;

Number of boxes = 7 and fruits = 24

At 1 pm ... Distance between A and B = 2x3.5 = 7 kms
at 2 pm .....Distance between A and B = 7 + 3.5 - 1 = 9.5 kms
At 3 pm ....Distance between A and B = 9.5 + 3.5 - 2 = 11 kms.
..
..
..
At 7 pm distance between A and B = 3 kms.
From 7 pm to 8 pm, speed of A = 3.5 kmph
speed of B = 8 kmph
Relative speed = 4.5 kmph

Time taken by B to meet A = 3/4.5 hrs = 30/45 hrs = 120/3 mins = 40 mins.

So meeting time is 7 : 40 PM.

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

After 5 mins ..... 3 persons will get rumour
After 10 mins .... 3x2 + 3 = 9 = 32 persons will get
after 15 =5x3 min ......9x2 + 9 =27 = 33 persons will get news.
.
.
after 5x6 mins ... 36 = 729 persons will get news.

Therefore, time taken to spread the rumour to 729 persons is 30 minutes.

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.

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