MATHEMATICS

Target
JEE ADVANCED 2016
CLASS : CC (Advanced) Area under the curve + Differential Equation WORKSHEET-26

M.M.: 69 PART-A Time: 60 Min

Q.1 The area of region, in the first quadrant, bounded by the parabola y = 9x2 and the line x = 0, y = 1 and
y = 4, is
(A) 2/9 (B) 14/9 (C) 7/9 (D) 11/9
Q.2 The area bounded by the curve y = ln x and the lines y = 0, y = ln 3 and x = 0 is equal to
(A) 3 (B) 3ln 3 – 2 (C) 2 (D) 3ln 3 + 2

Q.3 The area under the curve y = | cos x – sin x |, 0  x  and above x-axis is
2
(A) 2 2 (B) 2 2 – 2 (C) 0 (D) 2 2 + 2
Q.4 The equation of the curve passing through the origin and satisfying the differential equation
dy
(1 + x2) + 2xy = 4x2, is
dx
(A) 3 (1 + x2) y = 4x3 (B) (1 + x2) y = 3x3 (C) 3 (1 + x2) y = 2x3 (D) (1 + x2) y = x3

Q.5 The area bounded by the curves y = x , 2y – x + 3 = 0, x-axis and lying in the first quadrant is
(A) 36 (B) 18 (C) 27/4 (D) 9
1
Q.6 The area of the region enclosed by the curves y = x, x = e, y = and the positive x-axis, is
x
2
e 3 3 5 1
(A) (B) (C) (D)
2 2 2 2
3
Q.7 The area bounded by the curve y = cos x and y = sin x between the ordinates x = 0 and x = , is
2
(A) 4 2 + 2 (B) 4 2 – 1 (C) 4 2 + 1 (D) 4 2 – 2
dy x  y
Q.8 The solution of the differential equation  satisfying the condition y(1) = 1, is
dx x
(A) y = x + ln x (B) y = x ln x + x2 (C) y = x ex–1 (D) y = x ln x + x

Q.9 The area of the plane region bounded by the curves x + 2y2 = 0 and x + 3y2 = 1, is equal to
(A) 5/3 (B) 1/3 (C) 2/3 (D) 4/3
Q.10 The area enclosed between the curve y = loge(x + e) and the coordinate axes is
(A) 1 (B) 2 (C) 3 (D) 4
Q.11 The parabolas y2 = 4x and x2 = 4y divide the square region bounded by the lines x = 4, y = 4 and
the coordinate axes. If S1, S2, S3 are respectively the areas of these parts numbered from top to
bottom, then S1 : S2 : S3 is
(A) 1 : 2 : 1 (B) 1 : 2 : 3 (C) 2 : 1 : 2 (D) 1 : 1 : 1
Q.12 The degree of the differential equation whose solution is y = c1x + c1 , is
(A) 2 (B) 3 (C) 1 (D) 0
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 d3 y d2y dy
Q.13 If y = c1e2x + c2 ex + c3e–x satisfies the differential equation 3
 a 2
b + cy = 0, then the
dx dx dx
a 3  b3  c3
value of is equal to
abc
(A) –1/2 (B) 1/2 (C) –1/4 (D) 1/4
Q.14 Let f : R  R and g : R  R be twice differentiable functions satisfying f "(x) = g"(x),
2f '(1) = g'(1) = 4 and 3f (2) = g(2) = 9. The value of f (4)  g(4)  is equal to
(A) –6 (B) –16 (C) –10 (D) –8
Q.15 The value of positive real parameter 'a' such that the area of the region bounded by the parabolas
y = x – ax2, ay = x2 attains its maximum value is equal to
(A) 1/2 (B) 2 (C) 1 (D) 5/2
1
Q.16 Number of solutions of the equation max.(sin , cos ) = in  (–2, 5) is equal to
2
(A) 3 (B) 5 (C) 7 (D) 9
Q.17 If A(n) represents the area bounded by the curve y = n ln x, where n  N and n > 1, the x-axis and
the lines x = 1 and x = e, then the value of A(n) + nA(n – 1) =
n2 n2
(A) (B) (C) n2 (D) en2
e 1 e 1
Q.18 Let f (x) = ax2 + bx + c, where a  R+ and b2 – 4ac < 0. Area bounded by y = f (x), x-axis and the
lines x = 0, x = 1 is equal to
1 1
(A) 3f (1)  f (1)  2f (0)  (B) 5f (1)  f (1)  8f (0) 
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1 1
(C) 3f (1)  f (1)  2f (0)  (D) 5f (1)  f (1)  8f (0) 
6 12
Q.19 A point P moves in xy plane in such a way that [x + y + 1] = [x] where [x] is the greatest integer
less than or equal to x, and x  (0, 2).Area of the region representing all possible positions of the point
P is equal to
(A) 2 (B) 8 (C) 2 (D) 4
1 t2 2t
Q.20 Area enclosed by the curve which is defined parametrically as x = 2 , y =
1 t 1 t2
(t is parameter) is equal to
 3 3
(A)  (B) (C) (D)
2 4 2

Q.21 Solution of the differential equation cos x dy = y(sin x – y)dx, 0 < x < is
2
(A) y sec x = tan x + c (B) y tan x = sec x + c
(C) tan x = (sec x + c)y (D) sec x = (tan x + c)y
dy
Q.22 If x = y (log y – log x + 1), then the solution of equation is
dx
x y y x
(A) y log   = cx (B) x log   = cy (C) log   = cx (D) log   = cy
y x x y
Q.23 The differential equation which represents the family of curves y = c1ec2 x , where c1 and c2 are
arbitrary constants, is
(A) y' = y2 (B) y" = y' y (C) y y" = y' (D) y y" = (y')2
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