Number system

Q-1 7x36- 3615 = 4321, Find x
(a) 6 (b) 9 (c) 8 (d) 10
Q-2 If largest two digits number in subtracted from smallest three digits numbers them find the value.
(a) 2 (b) 1 (c) 4 (d) 9
Q-3 Find the sum of natural no. from 1to 30
(a) 460 (b) 465 (c) 471 (d) None
Q-4 How many even prime numbers are these which are last then 10.
(a) 1 (b) 2 (c) 3 (d) 4
Q-5 Which is smallest even prime number?
(a) 2 (b) 4 (c) 6 (d) 8
Q-6 Find the sum of prime no. between 10to 20?
(a) 30 (b) 60 (c) 80 (d) 90
Q-7 8+27+64+---------1000
(a) (106)2 - 1 (b) (105)2-1 (c) (105)2+1 (d) None
Q-8 1+4+9+-----------+100
(a) 1165 (b) 1155 (c) 1168 (d) None
Q-9 41+42 +-----------+60
(a) 1011 (b) 1010 (c) 1120 (d) None
Q-10 3(199×199)
(a) 120203 (b) 121315 (c) 121203 (d) None
Q-11 136532 is Divisible by
(a) 9 (b) 11 (c) 18 (d) 25
Q-12 In 9×6 find the value of x if It in divisible by 4
(a) 3 (b) 4 (c) 6 (d) None
Q-13 Difference of two consecutive even numbers is always divisible by
(a) 24 (b) 12 (c) 36 (d) None
Q-14 Ö-25 = ?
(a) 6; (b) 5 (c) 5; 2 (c) 5;
Q-15 What is value of =?
(a) Ö-25 (b) Ö-1 (c) Ö-9 (d) None
Q-16 From the following which nearest to 561which is divisible by 5
(a) 560 (b) 565 (c) 569 (d) None
Q-17 If two number are in 3:5
(a) 21, 35 (b) 21, 40 (c) 21, 63 (d) None
Q-18 Sum of two no. in 38 &they are in ratio of 2:17, find the largest no.
(a) 30 (b) 34 (c) 24 (d) None
Q-19 Find 50th term 12+14 + 18+ --------
(a) 112 (b) 110 (c) 114 (d) None
Q-20 4x/9 +3x/7=?
(a) 55x/62 (b) 55x/63 (c) 55x/66 (d) None
Q-21 Which value we have to add in 515 so that it in completely divided by 3
(a) 6 (b) 1 (c) 3 (d) 9
Q-22 Let x+y=13 & x-y =3 find x2-y2
(a) 40 (b) 36 (c) 39 (d) 50
Q-23 If 155 in divided by 3 them we obtain 9 as remainder, them what
Will be its quotient?
(a) 40 (b) 36 (c) 30 (d) None
Q-24 (2/3)n = 16/87
(a) 4 (b) 5 (c) 6 (d) 8
Q-25 Find unit digit is 365×721×615×411
(a) 6 (b) 5 (c) 8 (d) 9



Answer:-
1 (b) 9
2 (b) 1
3 (b) 465
4 (a) 1
5 (a) 2
6 (b) 60
7 (b) (105)2-1
8 (b) 1155
9 (b) 1010
10 (c) 121203
11 (b) 11
12 (a) 3
13 (b) 12
14 (c) 5;
15 (b) Ö-1
16 (a) 560
17 (a) 21, 35
18 (b) 34
19 (b) 110
20 (b) 55x/63
21 (b) 1
22 (c) 39
23 (c) 30
24 (a) 4
25 (b) 5


Reasons:-

1 4321+3615 = 7×36
2 100-99= 1
3 1+2+3+--------+30=å 30
= 30(30+1)/2
= 15(31) = 465
5 Here only even prime no. = 2
6 11, 13, 17, 19
There sum = 60
7 (13+23+33+43+-----------+103) -13
=å103 -1
= (10(10+1)/2)2 -1
= (5(21)2) -1
= (105)2
8 å102= 10(10+1) (2(10) +1)/2
= 5(11) (21) =1155
9 [(1+2+3+--------+40) +(41+42+-------+60)]-[1+2+ ------+40]
= å60 - å40
= 60(60+1)/2 - 40(40+1)/2
= 30(61) - 20(41)
= 1830 - 820 = 1010
10 3(1997)2 =(200-1)2
= 3(40000+1-400)
= 3(40400+1)
= 3 (40401) = 21203
11 Sum of digit at odd place = 5+2+3 =10
Sum of digit at even place= 6+3+1=10
Diff =10-10=0
\ it in divisible by 11
12 936 If last two digit no. are divisible 4
14 Ö-25
=Ö-1 Ö25
= i (5) = 5i
16 When 561 in divided by 5
Them remainder in 5
Them after adding on
Subtracting we obtain 565&560
\ 560 in more nears to 561
17 Let no. are 3x&5x
3x+ 5x =56
8x =56
x = 7
18 2x +17x= 38
19x =38
X=L
\ No. are 4&34
\ Largest no. in 34
19 Here a= 121 r=2
\T50 = a +(n-1) d
T50 = 12+ (49)2
= 12+98= 98 =110
20 28x/62+27x/63 = 55x/63
22 x2-y2=(x-y) (x-y)
= (13) (3) = 39
23 5 155/5 f
\ 155=5f+5
= 150 = 5f
30 = f
25 5×1×5×1
=25 = 5