Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app

NTA Abhyas 2020

Exam: NTA Abhyas
Year: 2020
Subject: Mathematics
Chapter: Area Under Curves

NTA Abhyas 2020 · Mathematics · Area Under Curves

The parabolas y^ 2 = 4x and x^ 2 = 4y divide the square region...

The parabolas

y^{2} = 4x

and

x^{2} = 4y

divide the square region bounded by the lines

x = 4

,

y = 4

and the coordinate axes. If

{S}_{1}, {S}_{2}, {S}_{3}

are respectively the areas of these parts numbered from top to bottom of the square region, then

{S}_{1}: {S}_{2}: {S}_{3}

is

The parabolas y^ 2 = 4x and x^ 2 = 4y divide the square region bounded by the lines x = 4 , y = 4 and the coordinate

Options

A $2: 1: 2$
B $1: 1: 1$
C $1: 2: 1$
D $1: 2: 3$

Correct answer

B. $1: 1: 1$

Step-by-step solution

y^{2} = 4x

and

x^{2} = 4y

are symmetric about line

y = x

⇒

Area bounded between

y^{2} = 4x

and

y = x

is

{∫}_{0}^{4}\left(2\sqrt{x} - x\right)dx = \dfrac{8}{3}

The parabolas y^ 2 = 4x and x^ 2 = 4y divide the square region bounded by the lines x = 4 , y = 4 and the coordinate

⇒ {A}_{{S}_{2}}= \dfrac{16}{3}

and

{A}_{S1} = {A}_{S3} = \dfrac{16}{3} { \dfrac{\text{Area of rectangle} - {S}_{2}}{2} }

⇒{A}_{{S}_{1}}: {A}_{{S}_{2}}: {A}_{{S}_{2}}: : 1: 1: 1

.

Practice Area Under Curves on Quantrex Academy →

More from Area Under Curves

Passage: Consider the curve C_1 given by y = e^ -x for x ∈ [0, 10π] , and the curve C_2… JEE Advanced 2026 Passage: Consider the ellipses given by x^2 + 4y^2 = 1 and 4x^2 + y^2 = 1 . Question: If… JEE Advanced 2026 The area of the region \ (x, y) : x^2 - 8x ≤ y ≤ -x\ is : JEE Main 2026 The area of the region \ (x, y) : 0 ≤ y ≤ 6 - x, y^2 ≥ 4x - 3, x ≥ 0\ is: JEE Main 2026 The area of the region R = \ (x, y): xy ≤ 27, 1 ≤ y ≤ x^2\ is equal to: JEE Main 2026 The area of the region bounded by the curves x+3y^2=0 and x+4y^2=1 is equal to: JEE Main 2026 The area of the region \ (x, y): y ≤ π - |x|, y ≤ |x x|, y ≥ 0\ is: JEE Main 2026 If the area of the region bounded by 16x^2 - 9y^2 = 144 and 8x - 3y = 24 is A, then 3(A +… JEE Main 2026 Let P_ 1 : y=4 x^ 2 and P_ 2 : y=x^ 2 +27 be two parabolas. If the area of the bounded… JEE Main 2026 The area of the region R=\ (x, y): x y ≤ 8,1 ≤ y ≤ x^ 2 , x ≥ 0\ is JEE Main 2026 Let f(α) denote the area of the region in the first quadrant bounded by x=0, x=1, y^ 2 =x… JEE Main 2026 Let A_ 1 be the bounded area enclosed by the curves y=x^ 2 +2, x+y=8 and y -axis that… JEE Main 2026 The area of the region enclosed between the circles x^ 2 +y^ 2 =4 and x^ 2 +(y-2)^ 2 =4… JEE Main 2026 Let the area of the region bounded by the curve y= \ x, x\ , lines x=0, x=(3 π)/(2) , and… JEE Main 2026 The area of the region A=\ (x, y): 4 x^ 2 +y^ 2 8. and .y^ 2 4 x\ is: JEE Main 2026 Let the line x=-1 divide the area of the region \ (x, y): 1+x^ 2 ≤ y ≤ 3-x\ in the ratio… JEE Main 2026 Full Area Under Curves list Area Under Curves JEE Maths PYQs JEE Mathematics PYQs All NTA Abhyas JEE Main PYQs