Area Under Curves PYQs Set 5 (PDF)

Set 5 of 7 · Questions 121-150 of 201

In the print window choose “Save as PDF”. The file prints without a web address or date line.

Mere Teacher · Previous Year Questions JEE Main Mathematics · Area Under Curves · Set 5 (Q121-150)
Scan or visit mereteacher.com for free PYQ practice, timed CBT tests, step-by-step solutions and BroBot AI. Answers and solutions are free with a sign-up.
121. $The area bounded by the curve, y = - x^{2}, x -axis; x = 1 and x = 4, is$ (1) $21 sq. units$ (2) $\frac{21}{2} sq. units$ (3) $20 sq. units$ (4) $10 sq. units$ 122. $Area of the region ((x, y) : x^{2} + (y - 2)^{2} \leq 4, x^{2} \geq 2 y) is$ (1) $π + \frac{8}{3}$ (2) $2 π + \frac{16}{3}$ (3) $π - \frac{8}{3}$ (4) $2 π - \frac{16}{3}$ 123. $The area of the region enclosed by the curve y = x^{3} and its tangent at the point (-1, -1) is$ (1) $\frac{19}{4}$ (2) $\frac{23}{4}$ (3) $\frac{31}{4}$ (4) $\frac{27}{4}$ 124. $The area of the region bounded by the parabola (y - 2)2 = x - 1, the tangent to the parabola at the point (2, 3) and the x-axis is$ (1) $6 sq unit$ (2) $9 sq unit$ (3) $12 sq unit$ (4) $3 sq unit$ 125. $The area (in sq. units) of the region ((x, y) : 0 \leq y \leq 2 \| x \| + 1, 0 \leq y \leq x^{2} + 1, \| x \| \leq 3) is$ (1) $\frac{80}{3}$ (2) $\frac{64}{3}$ (3) $\frac{32}{3}$ (4) $\frac{17}{3}$ 126. $If the area (in sq. units) of the region ((x, y) : y^{2} \leq 4 x), x + y \leq 1, x \geq 0, y \geq 0} is a 2 + b, then a - b is equal to :$ (1) $\frac{10}{3}$ (2) $6$ (3) $\frac{8}{3}$ (4) $- \frac{2}{3}$ 127. $The area enclosed by the curves y^{2} + 4 x = 4 and y - 2 x = 2 is$ (1) $\frac{25}{3}$ (2) $\frac{22}{3}$ (3) $9$ (4) $\frac{23}{3}$ 128. $Let the straight line x = b divide the area enclosed by y = (1 - x)2, y = 0, and x = 0 into two parts R1 (0 \leq x \leq b) and R2(b \leq x \leq 1) such that R1 - R2 = \frac{1}{4} . Then b equals$ (1) $\frac{3}{4}$ (2) $\frac{1}{2}$ (3) $\frac{1}{3}$ (4) $\frac{1}{4}$ 129. $The area (in sq. units) of the triangle formed by the X -axis, the tangent and the normal drawn to the circle x^{2} + y^{2} = 10 x at the point (9, 3) is$ (1) $\frac{75}{4}$ (2) $\frac{75}{8}$ (3) $75$ (4) $25$ 130. $The area of the region A = {(x, y) : 0 \leq y \leq x \| x \| + 1 and - 1 \leq x \leq 1} in sq. units is:$ (1) $\frac{2}{3}$ (2) $2$ (3) $\frac{4}{3}$ (4) $\frac{1}{3}$ 131. $If the area (in sq. units) bounded by the parabola y^{2} = 4 λx and the line y = λx, λ > 0, is \frac{1}{9}, then λ is equal to :$ (1) $26$ (2) $48$ (3) $24$ (4) $43$ 132. $The area of the region bounded by y - x = 2 and x^{2} = y is equal to :-$ (1) $\frac{16}{3}$ (2) $\frac{2}{3}$ (3) $\frac{9}{2}$ (4) $\frac{4}{3}$ 133. $The area of the region x, y : x^{2} \leq y \leq \| x^{2} - 4\|, y \geq 1 is$ (1) $\frac{4}{3} (42 - 1)$ (2) $\frac{4}{3} (42 + 1)$ (3) $\frac{3}{4} (42 + 1)$ (4) $\frac{3}{4} (42 - 1)$ 134. $The area bounded by the curve y = \| x - 2 \|, x = 1, x = 3 and X -axis is$ (1) $3 sq. units$ (2) $2 sq. units$ (3) $1 sq. units$ (4) $4 sq. units$ 135. $The area (in sq. units) of the portion lying above the X -axis and enclosed between the curves y^{2} = 2 ax - x^{2} and y^{2} = ax is$ (1) $a^{2} (\frac{- π}{2} + \frac{2}{3})$ (2) $a^{2} (\frac{2}{3} - \frac{π}{4})$ (3) $a^{2} (\frac{π}{4} - \frac{2}{3})$ (4) $a^{2} (\frac{π}{4} + \frac{2}{3})$ 136. $Let P_{1} : y = 4 x^{2} and P_{2} : y = x^{2} + 27 be two parabolas. If the area of the bounded region enclosed between P_{1} and P_{2} is six times the area of the bounded region enclosed between the line y = αx, α > 0 and P_{1}, then α is equal to :$ (1) $12$ (2) $6$ (3) $15$ (4) $8$ 137. $The area of the region enclosed by the curves y = x, x = e, y = \frac{1}{x} and the positive x-axis is$ (1) $\frac{1}{2} square units$ (2) $1 square units$ (3) $\frac{3}{2} square units$ (4) $\frac{5}{2} square units$ 138. $The area (in square units) of the region enclosed by the ellipse x^{2} + 3 y^{2} = 18 in the first quadrant below the line y = x is$ (1) $3 π - \frac{3}{4}$ (2) $3 π + 1$ (3) $3 π$ (4) $3 π + \frac{3}{4}$ 139. $If the area of the region ((x, y) : \frac{a}{x ^{2}} \leq y \leq \frac{1}{x}, 1 \leq x \leq 2, 0 < a < 1) is (log_{e} 2) - \frac{1}{7} then the value of 7 a - 3 is equal to:$ (1) $0$ (2) $2$ (3) $-1$ (4) $1$ 140. $Let the line x = - 1 divide the area of the region ((x, y) : 1 + x^{2} \leq y \leq 3 - x) in the ratio m : n, gcd (m, n) = 1 . Then m + n is equal to$ (1) $27$ (2) $25$ (3) $28$ (4) $26$ 141. $The area (in sq. units) of the region enclosed by the curves y = x^{2} - 1 and y = 1 - x^{2} is equal to:$ (1) $\frac{7}{2}$ (2) $\frac{4}{3}$ (3) $\frac{8}{3}$ (4) $\frac{16}{3}$ 142. $The area of the region bounded by the line y = x + 1, and the lines x = 3 and x = 5 is$ (1) $\frac{11}{2} sq. units$ (2) $10 sq. units$ (3) $7 sq. units$ (4) $\frac{7}{2} sq. units$ 143. $The area (in sq. units) of the region {(x, y) : 0 \leq y \leq x^{2} + 1, 0 \leq y \leq x + 1, \frac{1}{2} \leq x \leq 2} is:$ (1) $\frac{79}{16}$ (2) $\frac{23}{6}$ (3) $\frac{79}{24}$ (4) $\frac{23}{16}$ 144. $The area common to the curves x^{2} + y^{2} = 2 and x^{2} + 4 y^{2} = 4 is$ (1) $tan^{- 1} 22$ (2) $2 tan^{- 1} 22$ (3) $4 tan^{- 1} 2$ (4) $4 tan^{- 1} 22$ 145. $The area of the region: R = ((x, y) : 5 x^{2} \leq y \leq 2 x^{2} + 9) is:$ (1) $93 square units$ (2) $123 square units$ (3) $113 square units$ (4) $63 square units$ 146. $Area bounded by y = x^{3}, y = 8 and x = 0 is$ (1) $14 sq. units$ (2) $6 sq. units$ (3) $2 sq. units$ (4) $12 sq. units$ 147. $If A is the area in the first quadrant enclosed by the curve C : 2 x^{2} - y + 1 = 0, the tangent to C at the point (1,3) and the line x + y = 1, then the value of 60 A is................$ 148. $If the area of the region {(x, y) : \| x - 5 \| \leq y \leq 4 x} is A, then 3 A is equal to _________ .$ 149. $If the line y=mx bisects the area enclosed by the lines x=0, y=0, x = \frac{3}{2} and the curve y = 1 + 4 x - x^{2}, then 12m is equal to .$ 150. $Let Y = Y (X) be a curve lying in the first quadrant such that the area enclosed by the line Y - y = Y^{’} (x) (X - x) and the co-ordinate axes, where (x, y) is any point on the curve, is always \frac{- y ^{2}}{2 Y ^{’} ( x )} + 1, Y^{’} (x) \neq = 0 . If Y (1) = 1, then 12 Y (2) equals________$