Applications of Integrals Practice Questions - DPP for JEE

 Page 1


PART-I (Single Correct MCQs) 
1. The area above the x–axis enclosed by the curvesx
2
–y
2
 = 0 and x
2 
+ y –
2 = 0 is
(a)
(b)
(c)
(d)
2. The area bounded by the x-axis, the curve y = f(x) and the lines x =1, x
=b, is equal to  for all b > 1, then f(x) is
(a)
(b)
Page 2


PART-I (Single Correct MCQs) 
1. The area above the x–axis enclosed by the curvesx
2
–y
2
 = 0 and x
2 
+ y –
2 = 0 is
(a)
(b)
(c)
(d)
2. The area bounded by the x-axis, the curve y = f(x) and the lines x =1, x
=b, is equal to  for all b > 1, then f(x) is
(a)
(b)
(c) (d) 
3. If the area enclosed by  and line  is 1/3 sq. units , then
the area enclosed by y = 4x with same parabola is
(a) 8 sq. units
(b) 4 sq. units
(c) 4/3 sq. units
(d) 8/3 sq. units
4. The sine and cosine curves intersects infinitely many times giving
bounded regions of equal areas. The area of one of such region is
(a)
(b)
(c)
(d)
5. The figure shows as triangle AOB and the parabola y = x
2
. The ratio of
the area of the triangle AOB to the area of the region AOB of the
parabola y = x
2
 is equal to 
(a)
(b)
(c)
(d)
Page 3


PART-I (Single Correct MCQs) 
1. The area above the x–axis enclosed by the curvesx
2
–y
2
 = 0 and x
2 
+ y –
2 = 0 is
(a)
(b)
(c)
(d)
2. The area bounded by the x-axis, the curve y = f(x) and the lines x =1, x
=b, is equal to  for all b > 1, then f(x) is
(a)
(b)
(c) (d) 
3. If the area enclosed by  and line  is 1/3 sq. units , then
the area enclosed by y = 4x with same parabola is
(a) 8 sq. units
(b) 4 sq. units
(c) 4/3 sq. units
(d) 8/3 sq. units
4. The sine and cosine curves intersects infinitely many times giving
bounded regions of equal areas. The area of one of such region is
(a)
(b)
(c)
(d)
5. The figure shows as triangle AOB and the parabola y = x
2
. The ratio of
the area of the triangle AOB to the area of the region AOB of the
parabola y = x
2
 is equal to 
(a)
(b)
(c)
(d)
6. The triangle formed by the tangent to the curve f(x) = x
2
 + bx - b at the
point (1, 1) and the coordinate axes, lies in the first quadrant. If its area
is 2, then the value of b is
(a) -1
(b) 3
(c) -3
(d) 1
7. The area included between the parabolas y
2
 = 4a (x + a) and y
2
 = 4b(x –
a), b > a > 0, is
(a) sq. units
(b) sq. units
(c) sq. units
(d) sq. units
8. The area bounded by the curves  and the line x = 1 is
(a)
(b)
(c)
(d)
9. The area common to the ellipse  and , 0 < b <
a is
(a)
Page 4


PART-I (Single Correct MCQs) 
1. The area above the x–axis enclosed by the curvesx
2
–y
2
 = 0 and x
2 
+ y –
2 = 0 is
(a)
(b)
(c)
(d)
2. The area bounded by the x-axis, the curve y = f(x) and the lines x =1, x
=b, is equal to  for all b > 1, then f(x) is
(a)
(b)
(c) (d) 
3. If the area enclosed by  and line  is 1/3 sq. units , then
the area enclosed by y = 4x with same parabola is
(a) 8 sq. units
(b) 4 sq. units
(c) 4/3 sq. units
(d) 8/3 sq. units
4. The sine and cosine curves intersects infinitely many times giving
bounded regions of equal areas. The area of one of such region is
(a)
(b)
(c)
(d)
5. The figure shows as triangle AOB and the parabola y = x
2
. The ratio of
the area of the triangle AOB to the area of the region AOB of the
parabola y = x
2
 is equal to 
(a)
(b)
(c)
(d)
6. The triangle formed by the tangent to the curve f(x) = x
2
 + bx - b at the
point (1, 1) and the coordinate axes, lies in the first quadrant. If its area
is 2, then the value of b is
(a) -1
(b) 3
(c) -3
(d) 1
7. The area included between the parabolas y
2
 = 4a (x + a) and y
2
 = 4b(x –
a), b > a > 0, is
(a) sq. units
(b) sq. units
(c) sq. units
(d) sq. units
8. The area bounded by the curves  and the line x = 1 is
(a)
(b)
(c)
(d)
9. The area common to the ellipse  and , 0 < b <
a is
(a)
(b)
(c)
(d)
10. Area between the curve axis and the ordinates of two
minima of curve is
(a)
(b)
(c)
(d)
11. The area bounded by y –1 = |x|, y = 0 and |x| =  will be :
(a)
(b)
(c)
(d) None of these
12. What is the area of the parabola y
2
 = 4bx bounded by its latus rectum ?
(a) 2b
2
/3 square unit
(b) 4b
2
/3 square unit
(c) b
2
 square unit
(d) 8b
2
/3 square unit
13. The area enclosed by the curve  and the positive
Page 5


PART-I (Single Correct MCQs) 
1. The area above the x–axis enclosed by the curvesx
2
–y
2
 = 0 and x
2 
+ y –
2 = 0 is
(a)
(b)
(c)
(d)
2. The area bounded by the x-axis, the curve y = f(x) and the lines x =1, x
=b, is equal to  for all b > 1, then f(x) is
(a)
(b)
(c) (d) 
3. If the area enclosed by  and line  is 1/3 sq. units , then
the area enclosed by y = 4x with same parabola is
(a) 8 sq. units
(b) 4 sq. units
(c) 4/3 sq. units
(d) 8/3 sq. units
4. The sine and cosine curves intersects infinitely many times giving
bounded regions of equal areas. The area of one of such region is
(a)
(b)
(c)
(d)
5. The figure shows as triangle AOB and the parabola y = x
2
. The ratio of
the area of the triangle AOB to the area of the region AOB of the
parabola y = x
2
 is equal to 
(a)
(b)
(c)
(d)
6. The triangle formed by the tangent to the curve f(x) = x
2
 + bx - b at the
point (1, 1) and the coordinate axes, lies in the first quadrant. If its area
is 2, then the value of b is
(a) -1
(b) 3
(c) -3
(d) 1
7. The area included between the parabolas y
2
 = 4a (x + a) and y
2
 = 4b(x –
a), b > a > 0, is
(a) sq. units
(b) sq. units
(c) sq. units
(d) sq. units
8. The area bounded by the curves  and the line x = 1 is
(a)
(b)
(c)
(d)
9. The area common to the ellipse  and , 0 < b <
a is
(a)
(b)
(c)
(d)
10. Area between the curve axis and the ordinates of two
minima of curve is
(a)
(b)
(c)
(d)
11. The area bounded by y –1 = |x|, y = 0 and |x| =  will be :
(a)
(b)
(c)
(d) None of these
12. What is the area of the parabola y
2
 = 4bx bounded by its latus rectum ?
(a) 2b
2
/3 square unit
(b) 4b
2
/3 square unit
(c) b
2
 square unit
(d) 8b
2
/3 square unit
13. The area enclosed by the curve  and the positive
directions of x-axis and y-axis is
(a)
(b)
(c)
(d)
14. Find the area bounded by the curve x = 2 – y – y
2
 and y-axis.
(a)
(b)
(c) 9 (d)  – 9
15. Area between the curve y = cos
2 
x, x-axis and ordinatesx = 0 and x = p
in the interval (0, p) is
(a)
(b) 2 p
(c) p
(d)
16. The area bounded by the curve  and the lines x = 1 and
y = 4a is equal to :
(a) sq unit
(b) 5a sq unit
(c) sq unit
(d) None of these
17. The coordinates of the point  of  so that the area
formed by the coordinate axes and the tangent at P is greatest, are