PPF : QUADRATIC EQUATION

I. x2 -. 31xl + 2 < 0, then x belongs to :

(d) ,- 4. Ll

(d) none of these.

(d) [1, 2]

(d) none of these.

(d)(- 3,5)

(J) none of these.

(c) [0,1)

££H- 2, ~ i) u (1, 2)

(b)(2, (0)

(.a) [_1. 1]'.- 2'

fill (- 2, (0)

J.

(a) (1 2) (b) (- 2, - 1)

2. log.) (x2 - 3x + 18) < 4, then x belongs to :

i:;!}(1,2) (b)(2, 16) (c)(I,16)(x ..·1)(x2 - 5x + 7) <: (x -1), then x belongs to:

(~~)'~1,2) u (3, co) (b) (2,3) 1£l (- 00, 1) u (2, 3)

4. If a2 + b2 + c2 = 1, then ab + be + ca lies in the interval:

(1)1 r 0 llJ') I ' 2L

,.2 + 2x-IIf R I . A •• II I I' h . b5. I x E ,t le expreSSIOn -.--.---- tnkes a rea va ues except t ose which he behveen a & , then a & bare:x-3

(a)--12,-4 (b)-12,2 1£l4,12

6. The solution of the inequation 4-X+0.5 -7.rx < 4; x E R, is :

(c) (2, ~)

(d) none of these.

@ none of these

· ,':'.0. If l'ne root ofax~ + ox + c = 0 is n times it's other root, then:

(a) nb2 =an(n2+-1) (b) n2 +l:::~bc ill (1+n)2ae=nb2 (c) none oftnese

21. Let S be the set of values of '0' fur which 2 lies between the roots of quadratic equation x2 + (c .~.2)x -,~ -- 3 == 0 . Ti1en

S is given by :fu}(-00,-5) (b)(5,<:o) (;':)(-00,5) (d)(-5,00)

22. Number ofre.ll roots of the equation x3 + x2 + lOx + sinx = 0, is:

fa) on~ (b) two (c) three (d) infinite

23. If f/." 13 are the roots of 2x:! + 6x + b = 0 and a + fJ < 2 then b lies in the interval:fJ a

ill). (- co, 0'; (b)(O,oo) (c) R (d) none ofthesC'.

24. If a, b are the roots of x2 + px + q = 0 and C, d are the roots of x2 - px + r == 0, then a2 + b2 + c2 + d2 equal~:

(a)p2-q-r (b)p2orq+r (c)p2+q2_r2 @2(p2_q-r)

25. The '/'llnes of a for which both the roots oftne equati':m x2 - (2a -1)x + a = 0 are positive is:

(a) (~-J3 I2 ,co)(d) none of these

,"'

(d) 0

(d) none of these

~ 26. If Xl + 2ax + b ;?: c, V X E R, then:

ful b -c ;?: a2 (h) c - a '2:.b2 (c) a - b;?: c2

log J3 log 4 log 3627. If (121) 3 + 5 2 == 10 x then x is equalto :

\ t:1l10 (b) e (c) 1 (d) no~ of these

28~'If (a -1 )x2 + (a2 - 3a + 2)x + a2 -1 = 0 have more than two rc' I roots then a is equal to :

(a) 2 ill 1 (c) 0 (d) none of these

29, The m~mber of solution of the equation sine aX) + cos( aX) = aX + a -x is a > 0 :

{-'\ 0 (h) 1 ("\ ') (,~)1.l.!!L l .••. ? ,-/ - ••••/ -

30. The number of points ofintersection of the two curves y:= 2 sinx and .v = 5x2 + 2x + 3 is:

" .. ~ f'" 1 .-' } (n \L:li il \~J • ("J -, _/ CI.)

31. Let 2 si.i.1: ;-; + 3 sin x - 2 > 0 and Xl - X - 2 < G (x is ,'l~:aSi.:red in rad; am), Then x lies in the interval:/ ." / _" .r ~.

(a) l~,~~j (b) l-l, );j (c)(-1,2) @ l:,2)32. If the roots of the equation x2 - 2ax + a2 + a - 3 = 0 are real less Ulan 3, the~ :

{!ll a <.: 2 (b) 2 ::;a ::;3 (c) 3 < a ::;4 (d) a > 4

33. If a and 13 (a < 13); are the roots of the equation x2 + bx + c = 0, where C < U< b, then:

(a) 0 < a.< 13 ill a < 0 < 13 < Ia I (c) o. <: 13 <: 0 (d) a < 0 < Ia I< 13

34. The number of solutions of log} (x -1) = 2log2 (x -- 3) is:(a) 3 (Q} 1 (c) 2

35. The set of aB l'eal numbers x for which x2 -Ix -I- 2!+ x > 0, is:

(.I) (- 00, - 2) u i.2,00) (b) (- 00, - 1) u (1, ex:) (c)(.fi, (0) @(- 00, - .fi) u (fl, OJ)

36. If fIX) = x2 + 2bx+ 2c2 &g(x) = _x2 - 2cx+b2 such that min/(x) > maxg(x), then the relation between b nc is:

(a) lcl < Ibl.J2 (b) 0 < c < b.fi (c) jel < IblJ2 @ Ici > Ibl.fi1 1 1

37, If tlw roots of the equation -- +--. = - are equal in magnitude but oFpnsite in sign, then their product ;s :x+a x+b c

1 -1 1 -1(a) _(a2 +b2) ill-(a2 +b2) (c) -ah (d) -ab222 2

38. If2, 3 be the roots of 2x3 + mx2 -13x -I- n = 0, then the values ofm and n are respectively:

(a) - 5, - 30 ill- 5, 30 (e) 5, 30 (d) none of these,

39. For a > 0, the roots of the equation logax a + logy a2 + k'g":,, a3 = 0, are given by:

ll!l a-4/3 (b) a-3/4 (c) a' 1 (d) a-I