MATHEMATICS
Target JEE ADVANC ADVANCED ED 2016
CLASS : C CC C (A (Advanced)
SOT + TE TE + AU AUC+ DE
WORKSHEET-31
M.M.: 69
Time: 60 Min
[SINGL [SINGLE E CORREC CORRECT T CHOICE CHOICE TYPE] TYPE] Q.1 Q.1 to Q.10 Q.10 has ONLY ONE is correct. has four four choi choice cess (A), (A), (B), (B), (C), (C), (D) (D) out out of whic which h ONLY correct.
Q.1
In a triangle ABC, A– B =
[10×3=30]
2
and and R = 8r wher wheree R is the the radi radius us of circ circu umcir mcircl clee and and r is the the radi radiu us 3 of inci incirc rcle le,, then then cos C is equa equall to
(A*)
7
(B)
8
1
(C)
6
1
(D)
16
5 8
Q.2
AD, BE, CF are the median medianss of of trian triangle gle ABC ABC whose whose centro centroid id is G. If the points points A, F, G, G, E are concyclic concyclic then (A) 2b2 = a2 + c2 (B) 2c2 = a2 + b2 (C*) 2a2 = b2 + c2 (D) 2b2 = 2a2 + c2
Q.3
In a triangleAB leABC, if a, c, Aare Aare given b 1 = 2b2 where b1, b2 are are two two valu values es of the the thir third d side side then then the the 2
valu valuee of
c 1 8 sin A a
(A) 5
Q.4 Q.4
is equa equall to
(B*) 3
(C ) 2
(D) 1
If a, b, c the the sid sides ofa tria trian ngleABC leABC (in that hat order rder)) are are inA. inA.P. and and
2!
1! 9!
2! 3! 7!
1! 5! 5!
8a ( 2 b) !
then then inrad inradius iusof of thetri the trian angl glee ABC ABC is equa equall to (A)
7
(B)
2
5 2
(C*)
3 2
(D)
1 2
Q.5 Q.5
The The numb umber of solu soluti tio ons of 2 sin sin 3x + 2 c o s 3x – 3 s i n 2 x + 2 = 0 i n [ 0 , 4 ] is (A) 2 (B) 3 (C*) 4 (D) 5
Q.6
The particular lar solut lution of cos y dx + (1 + 2e –x) s i n y d y = 0 when x = 0, y=
Q. 7
4
is
(A) ex – 2 = – 2 cos y
(B) ex + 3 = 4 2 cos y
(C*) ex + 2 = 3 2 cos y
(D) ex – 3 = –2 2 sin y
y dx – dy = e –x y4 dy and y = 1 at x = – l then at y = 3, x = l n k, k is l n 3 then (A) 21 (B) 24 (C*) 27 (D) 81
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Q.8
3 The area bounded by f (x) = tan –1 (tanx) + cos –1 (cos x) and x-axis when x , is equal to 2 2 (A)
2
Q.9
2
4
(C)
2
3 3 2
(B) 1
(C)
(D) 22
4
1
The area enclosed by the curve y = 0, y = f (x), x
(A*)
Q.10
(B*)
3
2
, where f (x) = cos –1 (4x3 – 3x) is
3
(D)2 3
2
If there is no point on the curve 2sin y + 8 sin3 x = a which also lies on theline y = 3x, then (A*) a (– , –6) (6, ) (B) a {– 6, 6} (C) a (–6, 6) (D) a {– 3, 3}
[PARAGRAPH TYPE] Q.11 to Q.13 has four choices (A), (B), (C), (D) out of which ONLY ONE is correct.
[3 × 3 = 9]
Paragraph for question nos. 11 to 13
ABC is a triangle in which a= 6, b = 3, cos (A– B) = Q.11
Q.12
Triangle ABC is (A) isosceles (C) obtuse angled
5
, AD is median through A , BAD = .
(B*) right angled (D) isosceles right angled
Length of median AD is equal to (A) 3
Q.13
4
(B) 6
(C*) 3 2
(D) 3 5
sin is equal to (A)
1 2
(B)
1 2
(C)
1 5
(D*)
1 10
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[INTEGER TYPE] Q.1 to Q.6 are "Integer Type" questions. (The answer to each of the questions are upto 4 digits) [6×5=30]
Q.1
Let f: [0,1] 0,
1
bea functionsuch that f (x) is a polynomial of 2nd degree satisfythe following 2
conditions f (0) = 0, and has a maximum value of
1 3 at x = 1, also f = . If A be the area 2 2 8
1
bounded by y = f (x), y = f –1 (x) and the line 2x + 2y – 3 = 0 is I st quadrat then find the value of 24A. [Ans. 0005]
Q.2
Find the number of ordered pair (x, y) satisfy sin x + sin y = sin (x + y) and | x | + | y | = 1. [Ans. 0006]
Q.3
Find the number of solution of trigonometric equation tan 4x cos 7x = sin 7|x | in [– , ]. [Ans. 0015]
Q.4
If the area of the region bounded by the curve y = x 2 , y = sec –1 [–sin2x] is
4 k
, then find
the value of k. [Note : [x] denotes the greatest integer less than or equal to x.] [Ans. 0003] Q.5
If solution ofequation
dy dx
2
=y+
y dx
is y(x), then find the value y(2) .
0
[Note : Given y(0) = 1 and [x] denotes greatest integer less than or equal to x.] [Ans. 0004]
Q.6
2 If the area boundedbycircle x2 + y2 = 4, the parabola y= x2 +x+1andthecurvey= sin
and x-axis is 3
x cos 4 4
x
2
1 thenfind the value of k . 3 k
[Note : [x] denotes the greatest integer less than or equal to x.] [Ans. 0006]
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