Q 1 - What is y if 2y, y+10, 3y+2 are in an A.P.?
As numbers are in A.P.
Thus (y + 10) - 2y = (3y + 2) - (y + 10)
=> 10 - y = 2y - 8
=> -3y = -18
=> y = 6
Q 2 - Which of the following is equal to 205x15?
205x15= (200+5) x15
=200x15+5x15
Q 3 - If -2≤X≤3 and 3≤Y≤6, the least possible value of 3Y-2X is
For 3Y-2X to be minimum the condition is that Y must be substituted with least value and X must be with large value
=> 3(3)-2(3)
=3.
Q 4 - ((991+771)2-(991-771)2)/(991x771)=?
((991+771)2-(991-771)2)/(991x771)=((A+B)2-(A-B)2)/(AxB)
(4xAB)/AB=4
Q 5 - How many numbers between 100 and 200 are exactly divisible by 6 and 9?
L.C.M. of 9 and 6 = 18
∴ required numbers are 108, 126, 144, 162, 180, 198 which are 6.
Q 6 - What is the sum of all even numbers between 100 and 200 including both?
Required sum = 100 + 102 + ... + 200 which is an A.P. where a = 100, d = 2, l = 200.
Using formula Tn = a + (n - 1)d
Tn = 100 + (n-1)2 = 200
=> 2n = 200 - 98 = 102
=> n = 51
Now Using formula Sn = (n/2)(a + l)
∴ Required sum = (51/2)(100+200) = 51 x 150 = 7550
Q 7 - Which term of 5, 10, 20, 40,.... is 1280?
Here numbers are in G.P. Here a = 5, r = 2, l = 1280. Using formula Tn = arn- 1 Tn = 5 x 2(n-1) = 1280 =2(n-1) = 256 =2(n-1) = 28 => n - 1 = 8 => n = 9
Q 8 - In a club, member's ages are in A.P. with common difference of 3 months. If youngest member is 7 years old and sum of ages of all members is 250 years then how many members are there in the club?
let the ages be 7 , 7.25, 7.5 and so on Here a = 7, d = 1/4 , Sn = 250 Using formula Sn = (n/2)[2a + (n-1)d] => (n/2)[14+(n-1)(1/4)] = 250 => n[14 + (n-1)/4] = 500 => n[56 + (n-1)] = 2000 => n[n + 55] = 2000 => n2 + 55n - 2000 = 0 => n2 + 80n -25n - 2000 = 0 => n(n-80) -25(n-80) = 0 => (n-80)(n-25) = 0 => n = 25
Q 9 - If an A.P. have 4th term as 16 and 12th term as 80. What will be its first term?
Let's have first term as a, common difference is d then
a + 3d = 16 ... (i)
a + 11d = 80 ... (ii)
Subtracting (i) from (ii)
=> 8d = 64 => d = 8
Using (i)
=> a = 14 - 3d = -10
Q 10 - If an A.P. have 4th term as 16 and 12th term as 80. What will be its 17th term?
Let's have first term as a, common difference is d then
a + 3d = 16 ... (i)
a + 11d = 80 ... (ii)
Subtracting (i) from (ii)
=> 8d = 64
=> d = 8
Using (i)
=> a = 14 - 3d = -10
Using formula Tn = a + (n - 1)d
T17 = -10 + (17 - 1) x 8
= 118