3. 12.If ,α ÎČ are the roots of the equation 2
3 4 7 0x xâ + = ,then the value of
1 1
α ÎČ
+
(a)
4
7
(b)
7
3
(c)
3
4
(d)
4
3
13.If one root of a quadratic equation 2 3â ,then the equation will beÂ
(a)Â 2
4 7 0x xâ + = Â (b)Â 2
4 7 0x x+ + = Â (c)Â 2
4 7 0x x+ â =  (d) none of theseÂ
14.If ( )( )3 6 0x xâ â †, then xâÂ
(a)Â ( ],3ââ Â Â (b)Â [ )6,â Â (c)Â ( )3,6 Â (d)Â [ ]3,6 Â
15.If 2 2 2
x a b c ab bc ac= + + â â â  ,then Â
(a) 0x â„ Â (b) 0x >  (c) 0x <  (4) 0x †Â
16. The number 90 90
107 76â is divisible by
(a) 61 (b) 62 (c) 64 (d) none of these
17.Number of three digit number from the digits 3,5,6 ,7(without
repetition)
(a) 6 (b) 12 (c) 24 (d) none of these
18.Number of words can be formed from the letters of the word
TERMINAL
(a) 64 (b) 120 (c) 8! (d) none of these
19.The value of 10
2P  is Â
(a)Â 20Â Â (b)Â 100Â Â (c)Â 90Â Â (d)Â 50Â
20. Given 2 2
2 3 35,x y+ = then the number of ordered pairs (x,y) where (x,y)
are integers satisfying the above equation is
4. (a) 2 (b) 4 (c) 8 (d) 16
21. For how many integers n is ( )
2
9 2nâ + a real number?
(a) 3 (b) 5 (c) 7 (d) infinitely many
Linked comprehensive type
Paragraph for Question Nos.22 to 24
If a and b are two integers and n is a positive integer, then a is said to be
congruent to b modulo m if m / a â b in notation form we express it as a bâĄ
(mod m) or 0a bâ ⥠(mod m)
22.The remainder in the division of
20
2
by 7
(a) 4 (b) 2 (c) 0 (d) 3
23. The remainder in the division of
40
3
by 23
(a) 4 (b) 2 (c) 0 (d) 3
24.The remainder when
57
2
is divided by 8
(a) 4 (b) 2 (c) 0 (d) 3
Paragraph for Questions Nos. 53 to 55
If x is any real number, then the largest integer, which does not exceed x is
called the integers part of x, the integer [ ]x is often called the bracket
function / step function.
25. For a real number x, [ ]x denotes the integral part of x the value of
1
2
1 1 1 1 2 1 99
......
2 2 100 2 100 2 100
⥠†⥠†⥠†⥠â€
+ + + + + +âą â„ âą â„ âą â„ âą â„⣠⊠⣠⊠⣠⊠⣠âŠ
is
5. (a)50 (b) 47 (c) 45 (d) 52
26. The number of zeros at the end of 400!
(a) 67 (b) 99 (c) 78 (d) 85
27. If ânâ is any positive integer then
1 2 4
........
2 4 8
n n n
is
+ + +⥠†⥠†⥠â€
+ + +âą â„ âą â„ âą â„⣠⊠⣠⊠⣠âŠ
(a)n (b)
2
n
(c)
4
n
(d)
8
n
28. The factors of the polynomial expressions 2
15 16x xâ â are
(a) (3x +5) and (2x +3) (b) ( 5 â 3x) and ( 2x + 3)
(c) (3 â 2x) and ( 3x + 5) (d) none of these
29. The value of P for which x â 4 may be a factor of ( )3 2
5 ( 4) 4x P x Px Pâ + â â +
is
(a) 2 (b) 12 (c) 8 (d) none of these
30. If the polynomials 3 2
4 3 4ax x x+ + â and 3
4x x aâ + leave the same
remainder when divided by x â 3 then the value of a is
(a) 2 (b) 1 (c) -1 (d) 3