Copy Set-1 CP Star-2012 XII going [SAT+MAT] - Career Point

Multiple correct type (Q.66 to 75)
Q.66 The equation
in the -
sin 2 x cos x
81 + 81 2
= 30 has two roots
(1) I quadrant (2) II quadrant
(3) III quadrant (4) IV quadrant
Q.67 Let there be two parabolas with the same axis,
focus of each being exterior to the other and
latus rectum being 4a and 4b. The locus of the
middle points of the intercepts between the
parabolas made on the lines parallel to the
common axis is a -
(1) straight line if a = b
(2) parabola if a ≠ b
(3) parabola for all a, b
(4) None of these
Q.68 If A and B are two points on the circle
x 2 + y 2 – 4x + 6y – 3 = 0 which are farthest and
nearest respectively from the point (7, 2) then -
(1) A = (2 – 2 2 , – 3 – 2 2 )
(2) B = (2 + 2 2 , – 3 + 2 2 )
(3) A = (2 + 2 2 , –3 + 2 2 )
(4) B = (2 – 2 2 , –3 + 2 2 )
Multiple correct type (Q.66 to 75)
sin x
Q.66 lehdj.k 81 2 cos x
+ 81 2
= 30 ds nks ewy gS -
(1) I prqFkkZa'k esa (2) II prqFkkZa'k esa
(3) III prqFkkZa'k esa (4) IV prqFkkZa'k esa
Q.67 ekuk nks ijoy; gS ftuds v{k leku gS] izR;sd dh
ukfHk nwljs ds ckgj fLFkr gS rFkk ukfHkyEc 4a ,oa 4b
gSA mHk;fu"B v{k ds lekUrj js[kkvksa ij ijoy;ksa ds
e/; cus vUr%[k.Mkas ds e/; fcUnqvksa dk fcUnqiFk gS-
(1) ,d ljy js[kk ;fn a = b
(2) ,d ijoy; ;fn a ≠ b
(3) lHkh a, b ds fy, ,d ijoy;
(4) buesa ls dksbZ ugha
Q.68 ;fn A rFkk B o`Ùk x 2 + y 2 – 4x + 6y – 3 = 0 ij nks
fcUnq gS tks fcUnq (7, 2) ls Øe'k% nwjLFk rFkk
fudVLFk gS] rc -
(1) A = (2 – 2 2 , – 3 – 2 2 )
(2) B = (2 + 2 2 , – 3 + 2 2 )
(3) A = (2 + 2 2 , –3 + 2 2 )
(4) B = (2 – 2 2 , –3 + 2 2 )
Q.69 If f(x) = 27x 3 +
1
3 and α, β are the roots of
x
Q.69 ;fn f(x) = 27x 3 +
1
3
x
rFkk α, β lehdj.k
3x + x
1 = 2 then -
(1) f(α) = f(β) (2) f(α) = 0
(3) f(β) = –10 (4) f(α) = 10
3x +
x
1 = 2 ds ewy gS] rc -
(1) f(α) = f(β) (2) f(α) = 0
(3) f(β) = –10 (4) f(α) = 10
Space for rough work
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