Area Under the Curves

151 questions · Mathematics · JEE Main

Area Under the Curves

151 questions · Mathematics · JEE Main

If the area of the region ${(x, y) : 4 - x^{2} \leq y \leq x^{2}, y \leq 4, x \geq 0}$ is $(\frac{80 2}{α} - β), α, β \in N$ , then $α + β$ is equal to …2025 · 2 Apr · Shift 1 · Q48 · Numerical
The area of the region bounded by the curve $y = max {∣ x ∣, x ∣ x - 2∣}$ , the $x$ -axis and the lines $x = - 2$ and $x = 4$ is equal to 2025 · 3 Apr · Shift 1 · Q49 · Numerical
The area of the region ${(x, y) : ∣ x - y ∣ \leq y \leq 4 x}$ is2025 · 3 Apr · Shift 2 · Q26 · MCQ
Let $f : [0, \infty) \to R$ be a differentiable function such that $f (x) = 1 - 2 x + \int_{0}^{x} e^{x - t} f (t) d t$ for all $x \in [0, \infty)$ . Then the area of the region bounded by $y = f (x)$ and the coordinate axes is2025 · 4 Apr · Shift 1 · Q35 · MCQ
If the area of the region ${(x, y) : ∣ x - 5∣ \leq y \leq 4 x}$ is $A$ , then $3 A$ is equal to .2025 · 4 Apr · Shift 1 · Q49 · Numerical
If the area of the region bounded by the curves $y = 4 - \frac{x ^{2}}{4}$ and $y = \frac{x - 4}{2}$ is equal to $α$ , then $6 α$ . equals2025 · 7 Apr · Shift 1 · Q41 · MCQ
If the area of the region ${(x, y) : 1 + x^{2} \leq y \leq min {x + 7, 11 - 3 x}}$ is $A$ , then $3 A$ is equal to :2025 · 7 Apr · Shift 2 · Q37 · MCQ
Let the area of the bounded region ${(x, y) : 0 \leq 9 x \leq y^{2}, y \geq 3 x - 6}$ be $A$ . Then $6 A$ is equal to .2025 · 8 Apr · Shift 2 · Q47 · Numerical
The area of the region, inside the circle $(x - 23)^{2} + y^{2} = 12$ and outside the parabola $y^{2} = 23 x$ is :2025 · 22 Jan · Shift 1 · Q25 · MCQ
The area of the region enclosed by the curves $y = x^{2} - 4 x + 4$ and $y^{2} = 16 - 8 x$ is :2025 · 22 Jan · Shift 2 · Q37 · MCQ
If the area of the larger portion bounded between the curves $x^{2} + y^{2} = 25$ and $y = ∣ x - 1∣$ is $\frac{1}{4} (b π + c), b, c \in N$ , then $b + c$ is equal to …2025 · 23 Jan · Shift 1 · Q50 · Numerical
If the area of the region ${(x, y) : - 1 \leq x \leq 1, 0 \leq y \leq a + e^{∣ x ∣} - e^{- x}, a > 0}$ is $\frac{e ^{2} + 8 e + 1}{e}$ , then the value of $a$ is :2025 · 23 Jan · Shift 2 · Q33 · MCQ
The area of the region ${(x, y) : x^{2} + 4 x + 2 \leq y \leq ∣ x + 2∣}$ is equal to2025 · 24 Jan · Shift 1 · Q40 · MCQ
The area of the region enclosed by the curves $y = e^{x}, y = ∣ e^{x} - 1 ∣$ and $y$ -axis is :2025 · 24 Jan · Shift 2 · Q30 · MCQ
The area (in sq. units) of the region ${(x, y) : 0 \leq y \leq 2∣ x ∣ + 1, 0 \leq y \leq x^{2} + 1, ∣ x ∣ \leq 3}$ is2025 · 28 Jan · Shift 1 · Q45 · MCQ
The area of the region bounded by the curves $x (1 + y^{2}) = 1$ and $y^{2} = 2 x$ is:2025 · 28 Jan · Shift 2 · Q26 · MCQ
Let the area of the region $(x, y) : 2 y \leq x^{2} + 3, y + ∣ x ∣ \leq 3, y \geq ∣ x - 1∣$ be $A$ . Then $6 A$ is equal to :2025 · 29 Jan · Shift 1 · Q40 · MCQ
Let the area enclosed between the curves $∣ y ∣ = 1 - x^{2}$ and $x^{2} + y^{2} = 1$ be $α$ . If $9 α = β π + γ; β, γ$ are integers, then the value of $∣ β - γ ∣$ equals:2025 · 29 Jan · Shift 2 · Q42 · MCQ
The area enclosed by the curves $x y + 4 y = 16$ and $x + y = 6$ is equal to :2024 · 1 Feb · Shift 1 · Q40 · MCQ
Three points $O (0, 0), P (a, a^{2}), Q (- b, b^{2}), a > 0, b > 0$ , are on the parabola $y = x^{2}$ . Let $S_{1}$ be the area of the region…2024 · 1 Feb · Shift 2 · Q51 · Numerical
The sum of squares of all possible values of $k$ , for which area of the region bounded by the parabolas $2 y^{2} = k x$ and $ky^{2} = 2 (y - x)$ is maximum, is equal to :2024 · 1 Feb · Shift 2 · Q52 · Numerical
One of the points of intersection of the curves $y = 1 + 3 x - 2 x^{2}$ and $y = \frac{1}{x}$ is $(\frac{1}{2}, 2)$ . Let the area of the region enclosed by these curves be $\frac{1}{24} (l 5 + m) - n lo g_{e} (1 + 5)$ …2024 · 4 Apr · Shift 1 · Q32 · MCQ
The area (in sq. units) of the region described by ${(x, y) : y^{2} \leq 2 x, and y \geq 4 x - 1}$ is2024 · 4 Apr · Shift 2 · Q38 · MCQ
The area of the region enclosed by the parabolas $y = x^{2} - 5 x$ and $y = 7 x - x^{2}$ is .2024 · 5 Apr · Shift 1 · Q51 · Numerical
The area enclosed between the curves $y = x ∣ x ∣$ and $y = x - ∣ x ∣$ is :2024 · 5 Apr · Shift 2 · Q47 · MCQ
Let the area of the region enclosed by the curves $y = 3 x, 2 y = 27 - 3 x$ and $y = 3 x - x x$ be $A$ . Then $10 A$ is equal to2024 · 6 Apr · Shift 1 · Q37 · MCQ
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 $(lo g_{e} 2) - \frac{1}{7}$ then the value of $7 a - 3$ is equal to :2024 · 6 Apr · Shift 2 · Q39 · MCQ
Let the area of the region enclosed by the curve $y = min {sin x, cos x}$ and the $x$ axis between $x = - π$ to $x = π$ be $A$ . Then $A^{2}$ is equal to .2024 · 8 Apr · Shift 1 · Q59 · Numerical
The area of the region in the first quadrant inside the circle $x^{2} + y^{2} = 8$ and outside the parabola $y^{2} = 2 x$ is equal to :2024 · 8 Apr · Shift 2 · Q34 · MCQ
The parabola $y^{2} = 4 x$ divides the area of the circle $x^{2} + y^{2} = 5$ in two parts. The area of the smaller part is equal to :2024 · 9 Apr · Shift 1 · Q34 · MCQ
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 $y = x$ is2024 · 9 Apr · Shift 2 · Q47 · MCQ
Let the area of the region ${(x, y) : x - 2 y + 4 ⩾ 0, x + 2 y^{2} ⩾ 0, x + 4 y^{2} \leq 8, y ⩾ 0}$ be $\frac{m}{n}$ , where $m$ and $n$ are coprime numbers. Then $m + n$ …2024 · 27 Jan · Shift 1 · Q56 · Numerical
If the area of the region ${(x, y) : 0 \leq y \leq min {2 x, 6 x - x^{2}}}$ is $A$ , then $12 A$ is equal to .2024 · 27 Jan · Shift 2 · Q55 · Numerical
The area (in sq. units) of the part of the circle $x^{2} + y^{2} = 169$ which is below the line $5 x - y = 13$ is $\frac{π α}{2 β} - \frac{65}{2} + \frac{α}{β} sin^{- 1} (\frac{12}{13})$ , where $α, β$ are coprime…2024 · 29 Jan · Shift 1 · Q51 · Numerical
If the points of intersection of two distinct conics $x^{2} + y^{2} = 4 b$ and $\frac{x ^{2}}{16} + \frac{y ^{2}}{b ^{2}} = 1$ lie on the curve $y^{2} = 3 x^{2}$ , then $33$ times the area of the rectangle formed by the intersection points is …2024 · 29 Jan · Shift 1 · Q56 · Numerical
Let the area of the region ${(x, y) : 0 \leq x \leq 3, 0 \leq y \leq min {x^{2} + 2, 2 x + 2}}$ be A. Then $12 A$ is equal to .2024 · 29 Jan · Shift 2 · Q52 · Numerical
The area (in square units) of the region bounded by the parabola $y^{2} = 4 (x - 2)$ and the line $y = 2 x - 8$ , is :2024 · 30 Jan · Shift 1 · Q50 · MCQ
The area of the region enclosed by the parabola $(y - 2)^{2} = x - 1$ , the line $x - 2 y + 4 = 0$ and the positive coordinate axes is .2024 · 30 Jan · Shift 2 · Q57 · Numerical
The area of the region ${(x, y) : y^{2} \leq 4 x, x 0, x e q 3}$ is2024 · 31 Jan · Shift 1 · Q45 · MCQ
The area of the region enclosed by the parabolas $y = 4 x - x^{2}$ and $3 y = (x - 4)^{2}$ is equal to :2024 · 31 Jan · Shift 2 · Q39 · MCQ
Let $A$ be the area bounded by the curve $y = x ∣ x - 3∣$ , the $x$ -axis and the ordinates $x = - 1$ and $x = 2$ . Then $12 A$ is equal to .2023 · 1 Feb · Shift 1 · Q41 · Numerical
The area of the region given by ${(x, y) : x y \leq 8, 1 \leq y \leq x^{2}}$ is :2023 · 1 Feb · Shift 2 · Q31 · MCQ
If the area of the region $S = {(x, y) : 2 y - y^{2} \leq x^{2} \leq 2 y, x \geq y}$ is equal to $\frac{n + 2}{n + 1} - \frac{π}{n - 1}$ , then the natural number $n$ is equal to .2023 · 6 Apr · Shift 1 · Q37 · Numerical
The area bounded by the curves $y = ∣ x - 1∣ + ∣ x - 2∣$ and $y = 3$ is equal to :2023 · 6 Apr · Shift 2 · Q25 · MCQ
The area of the region ${(x, y) : x^{2} \leq y \leq 8 - x^{2}, y \leq 7}$ is :2023 · 8 Apr · Shift 1 · Q30 · MCQ
Let the area enclosed by the lines $x + y = 2, y = 0, x = 0$ and the curve $f (x) = min {x^{2} + \frac{3}{4}, 1 + [x]}$ where $[x]$ denotes the greatest integer $\leq x$ , be $A$ . Then the value of $12 A$ is …2023 · 8 Apr · Shift 2 · Q36 · Numerical
Let $y = p (x)$ be the parabola passing through the points $(- 1, 0), (0, 1)$ and $(1, 0)$ . If the area of the region ${(x, y) : (x + 1)^{2} + (y - 1)^{2} \leq 1, y \leq p (x)}$ is A, then $12 (π - 4 A)$ is equal to .2023 · 10 Apr · Shift 1 · Q40 · Numerical
If the area of the region ${(x, y) : x^{2} - 2 \leq y \leq x}$ is $A$ , then $6 A + 162$ is equal to .2023 · 10 Apr · Shift 2 · Q34 · Numerical
Area of the region ${(x, y) : x^{2} + (y - 2)^{2} \leq 4, x^{2} \geq 2 y}$ is2023 · 11 Apr · Shift 1 · Q36 · MCQ
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 …2023 · 11 Apr · Shift 2 · Q40 · Numerical
The area of the region enclosed by the curve $y = x^{3}$ and its tangent at the point $(- 1, - 1)$ is :2023 · 12 Apr · Shift 1 · Q33 · MCQ
The area of the region enclosed by the curve $f (x) = max {sin x, cos x}, - π \leq x \leq π$ and the $x$ -axis is2023 · 13 Apr · Shift 1 · Q23 · MCQ
The area of the region ${(x, y) : x^{2} \leq y \leq x^{2} - 4, y \geq 1}$ is2023 · 13 Apr · Shift 2 · Q31 · MCQ
If the area bounded by the curve $2 y^{2} = 3 x$ , lines $x + y = 3, y = 0$ and outside the circle $(x - 3)^{2} + y^{2} = 2$ is $A$ , then $4 (π + 4 A)$ is equal to .2023 · 15 Apr · Shift 1 · Q40 · Numerical
The area enclosed by the curves $y^{2} + 4 x = 4$ and $y - 2 x = 2$ is :2023 · 24 Jan · Shift 1 · Q31 · MCQ
If the area of the region bounded by the curves $y^{2} - 2 y = - x, x + y = 0$ is A, then 8 A is equal to 2023 · 24 Jan · Shift 2 · Q43 · Numerical
If the area enclosed by the parabolas $P_{1} : 2y = 5 x^{2}$ and $P_{2} : x^{2} - y + 6 = 0$ is equal to the area enclosed by $P_{1}$ and $y = α x, α > 0$ , then $α^{3}$ is equal to .2023 · 25 Jan · Shift 1 · Q45 · Numerical
Let $Δ$ be the area of the region ${(x, y) \in R^{2} : x^{2} + y^{2} \leq 21, y^{2} \leq 4 x, x \geq 1}$ . Then $\frac{1}{2} (Δ - 21 sin^{- 1} \frac{2}{7})$ is equal to2023 · 29 Jan · Shift 1 · Q33 · MCQ
Let $[x]$ denote the greatest integer $\leq x$ . Consider the function $f (x) = max {x^{2}, 1 + [x]}$ . Then the value of the integral $0 \int 2 f (x) d x$ is2023 · 29 Jan · Shift 1 · Q36 · MCQ
Let $A = {(x, y) \in R^{2} : y \geq 0, 2 x \leq y \leq 4 - (x - 1)^{2}}$ and $B = {(x, y) \in R \times R : 0 \leq y \leq min {2 x, 4 - (x - 1)^{2}}} .$ . Then…2023 · 29 Jan · Shift 1 · Q37 · MCQ
The area of the region $A = {(x, y) : ∣ cos x - sin x ∣ \leq y \leq sin x, 0 \leq x \leq \frac{π}{2}}$ is2023 · 29 Jan · Shift 2 · Q32 · MCQ
Let $α$ be the area of the larger region bounded by the curve $y^{2} = 8 x$ and the lines $y = x$ and $x = 2$ , which lies in the first quadrant. Then the value of $3 α$ is equal to .2023 · 30 Jan · Shift 1 · Q36 · Numerical
Let $q$ be the maximum integral value of $p$ in $[0, 10]$ for which the roots of the equation $x^{2} - p x + \frac{5}{4} p = 0$ are rational. Then the area of the region ${(x, y) : 0 \leq y \leq (x - q)^{2}, 0 \leq x \leq q}$ is :2023 · 30 Jan · Shift 2 · Q29 · MCQ
Let $A$ be the area of the region ${(x, y) : y \geq x^{2}, y \geq (1 - x)^{2}, y \leq 2 x (1 - x)}$ . Then $540 A$ is equal to :2023 · 30 Jan · Shift 2 · Q38 · Numerical
Let for $x \in R$ , $f (x) = \frac{x + ∣ x ∣}{2}$ and $g (x) = {x, x^{2}, x < 0 x \geq 0$ . Then area bounded by the curve $y = (f \circ g) (x)$ and the lines $y = 0, 2 y - x = 15$ is equal to …2023 · 31 Jan · Shift 1 · Q46 · Numerical
Let the area of the region ${(x, y) : ∣2 x - 1∣ \leq y \leq x^{2} - x, 0 \leq x \leq 1}$ be $A$ . Then $(6 A + 11)^{2}$ is equal to2023 · 31 Jan · Shift 2 · Q38 · Numerical
Let S be the region bounded by the curves y = x3 and y2 = x. The curve y = 2|x| divides S into two regions of areas R1, R2. If max {R1, R2} = R2, then $\frac{R _{2}}{R _{1}}$ is equal to .2022 · 24 Jun · Shift 1 · Q42 · Numerical
The area (in sq. units) of the region enclosed between the parabola y2 = 2x and the line x + y = 4 is .2022 · 24 Jun · Shift 2 · Q42 · Numerical
The area of the region given by $A = {(x, y) : x^{2} \leq y \leq min {x + 2, 4 - 3 x}}$ is :2022 · 25 Jul · Shift 1 · Q28 · MCQ
Let the locus of the centre $(α, β), β > 0$ , of the circle which touches the circle $x^{2} + (y - 1)^{2} = 1$ externally and also touches the $x$ -axis be $L$ . Then the area bounded by $L$ and the line $y = 4$ is:2022 · 25 Jul · Shift 1 · Q33 · MCQ
Let the area enclosed by the x-axis, and the tangent and normal drawn to the curve $4 x^{3} - 3 x y^{2} + 6 x^{2} - 5 x y - 8 y^{2} + 9 x + 14 = 0$ at the point ( $-$ 2, 3) be A. Then 8A is equal to .2022 · 25 Jul · Shift 2 · Q44 · Numerical
The area of the region enclosed between the parabolas y2 = 2x $-$ 1 and y2 = 4x $-$ 3 is2022 · 25 Jun · Shift 2 · Q28 · MCQ
The odd natural number a, such that the area of the region bounded by y = 1, y = 3, x = 0, x = ya is $\frac{364}{3}$ , is equal to :2022 · 26 Jul · Shift 1 · Q28 · MCQ
The area bounded by the curves $y = x^{2} - 1$ and $y = 1$ is2022 · 26 Jul · Shift 2 · Q33 · MCQ
The area bounded by the curve y = |x2 $-$ 9| and the line y = 3 is :2022 · 26 Jun · Shift 1 · Q28 · MCQ
The area of the region bounded by y2 = 8x and y2 = 16(3 $-$ x) is equal to:2022 · 26 Jun · Shift 2 · Q30 · MCQ
The area of the smaller region enclosed by the curves $y^{2} = 8 x + 4$ and $x^{2} + y^{2} + 43 x - 4 = 0$ is equal to2022 · 27 Jul · Shift 1 · Q32 · MCQ
The area of the region enclosed by $y \leq 4 x^{2}, x^{2} \leq 9 y$ and $y \leq 4$ , is equal to :2022 · 27 Jul · Shift 2 · Q28 · MCQ
Consider a curve $y = y (x)$ in the first quadrant as shown in the figure. Let the area $A_{1}$ is twice the area $A_{2}$ . Then the normal to the curve perpendicular to the line $2 x - 12 y = 15$ does NOT pass through the point. Includes diagram2022 · 27 Jul · Shift 2 · Q30 · MCQ
Let $A_{1} = {(x, y) : ∣ x ∣ \leq y^{2}, ∣ x ∣ + 2 y \leq 8}$ and $A_{2} = {(x, y) : ∣ x ∣ + ∣ y ∣ \leq k}$ . If 27 (Area A1) = 5 (Area A2), then k is equal to :2022 · 27 Jun · Shift 1 · Q40 · Numerical
If the area of the region ${(x, y) : x^{\frac{2}{3}} + y^{\frac{2}{3}} \leq 1, x + y \geq 0, y \geq 0}$ is A, then $\frac{256 A}{π}$ is equal to .2022 · 27 Jun · Shift 2 · Q42 · Numerical
The area enclosed by the curves $y = lo g_{e} (x + e^{2}), x = lo g_{e} (\frac{2}{y})$ and $x = lo g_{e} 2$ , above the line $y = 1$ is:2022 · 28 Jul · Shift 2 · Q30 · MCQ
The area of the region S = {(x, y) : y2 $\leq$ 8x, y $\geq 2$ x, x $\geq$ 1} is2022 · 28 Jun · Shift 1 · Q30 · MCQ
The area of the bounded region enclosed by the curve $y = 3 - x - \frac{1}{2} - ∣ x + 1∣$ and the x-axis is :2022 · 28 Jun · Shift 2 · Q30 · MCQ
The area of the region ${(x, y) : ∣ x - 1∣ \leq y \leq 5 - x^{2}}$ is equal to :2022 · 29 Jul · Shift 1 · Q36 · MCQ
The area enclosed by y2 = 8x and y = $2$ x that lies outside the triangle formed by y = $2$ x, x = 1, y = 2 $2$ , is equal to:2022 · 29 Jun · Shift 1 · Q24 · MCQ
For real numbers a, b (a > b > 0), let Area ${(x, y) : x^{2} + y^{2} \leq a^{2} an d \frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} \geq 1} = 30 π$ and Area ${(x, y) : x^{2} + y^{2} \leq b^{2} an d \frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} \leq 1} = 18 π$ …2022 · 29 Jun · Shift 2 · Q38 · Numerical
If for some $α$ > 0, the area of the region ${(x, y) : ∣ x + α ∣ \leq y \leq 2 - ∣ x ∣}$ is equal to $\frac{3}{2}$ , then the area of the region ${(x, y) : 0 \leq y \leq x + 2 α, ∣ x ∣ \leq 1}$ is equal to .2022 · 30 Jun · Shift 1 · Q36 · Numerical
The area, enclosed by the curves $y = sin x + cos x$ and $y = ∣ cos x - sin x ∣$ and the lines $x = 0, x = \frac{π}{2}$ , is :2021 · 1 Sep · Shift 2 · Q31 · MCQ
Let $f : [- 3, 1] \to R$ be given as $f (x) = {min {(x + 6), x^{2}} max {x, x^{2}} - 3 \leq x \leq 0 0 \leq x \leq 1$ If the area bounded by $y = f (x)$ and $x$ -axis is $A$ …2021 · 17 Mar · Shift 2 · Q42 · Numerical
The area bounded by the curve 4y2 = x2(4 $-$ x)(x $-$ 2) is equal to :2021 · 18 Mar · Shift 2 · Q25 · MCQ
Let T be the tangent to the ellipse E : x2 + 4y2 = 5 at the point P(1, 1). If the area of the region bounded by the tangent T, ellipse E, lines x = 1 and x = $5$ is $α 5$ + $β$ + $γ$ cos $-$ 1 $(\frac{1}{5})$ …2021 · 20 Jul · Shift 1 · Q41 · Numerical
The area (in sq. units) of the region bounded by the curves x2 + 2y $-$ 1 = 0, y2 + 4x $-$ 4 = 0 and y2 $-$ 4x $-$ 4 = 0, in the upper half plane is .2021 · 22 Jul · Shift 2 · Q43 · Numerical
The area (in sq. units) of the part of the circle x2 + y2 = 36, which is outside the parabola y2 = 9x, is :2021 · 24 Feb · Shift 1 · Q32 · MCQ
The area of the region : $R = {(x, y) : 5 x^{2} \leq y \leq 2 x^{2} + 9}$ is :2021 · 24 Feb · Shift 2 · Q33 · MCQ
The graphs of sine and cosine functions, intersect each other at a number of points and between two consecutive points of intersection, the two graphs enclose the same area A. Then A4 is equal to .2021 · 25 Feb · Shift 1 · Q38 · Numerical
The area (in sq. units) of the region, given by the set ${(x, y) \in R \times R ∣ x \geq 0, 2 x^{2} \leq y \leq 4 - 2 x}$ is :2021 · 25 Jul · Shift 1 · Q31 · MCQ
The area of the region $S = {(x, y) : 3 x^{2} \leq 4 y \leq 6 x + 24}$ is .2021 · 26 Aug · Shift 1 · Q38 · Numerical
Let a and b respectively be the points of local maximum and local minimum of the function f(x) = 2x3 $-$ 3x2 $-$ 12x. If A is the total area of the region bounded by y = f(x), the x-axis and the lines x = a and x = b, then 4A is equal to …2021 · 26 Aug · Shift 2 · Q40 · Numerical
The area bounded by the lines y = || x $-$ 1 | $-$ 2 | is .2021 · 26 Feb · Shift 1 · Q40 · Numerical
Let A1 be the area of the region bounded by the curves y = sinx, y = cosx and y-axis in the first quadrant. Also, let A2 be the area of the region bounded by the curves y = sinx, y = cosx, x-axis and x = $\frac{π}{2}$ in the first…2021 · 26 Feb · Shift 2 · Q34 · MCQ
The area of the region bounded by the parabola (y $-$ 2)2 = (x $-$ 1), the tangent to it at the point whose ordinate is 3 and the x-axis is :2021 · 27 Aug · Shift 2 · Q32 · MCQ
If the area of the bounded region $R = {(x, y) : max {0, lo g_{e} x} \leq y \leq 2^{x}, \frac{1}{2} \leq x \leq 2}$ is , $α (lo g_{e} 2)^{- 1} + β (lo g_{e} 2) + γ$ , then the value of $(α + β - 2 λ)^{2}$ …2021 · 27 Jul · Shift 1 · Q27 · MCQ
The area of the region bounded by y $-$ x = 2 and x2 = y is equal to :2021 · 27 Jul · Shift 2 · Q29 · MCQ
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 + 4x $-$ x2, then 12 m is equal to .2021 · 31 Aug · Shift 2 · Q41 · Numerical
Area (in sq. units) of the region outside $\frac{∣ x ∣}{2} + \frac{∣ y ∣}{3} = 1$ and inside the ellipse $\frac{x ^{2}}{4} + \frac{y ^{2}}{9} = 1$ is :2020 · 2 Sep · Shift 1 · Q21 · MCQ
Consider a region R = {(x, y) $\in$ R : x2 $\leq$ y $\leq$ 2x}. if a line y = $α$ divides the area of region R into two equal parts, then which of the following is true?2020 · 2 Sep · Shift 2 · Q37 · MCQ
The area (in sq. units) of the region { (x, y) : 0 $\leq$ y $\leq$ x2 + 1, 0 $\leq$ y $\leq$ x + 1, $\frac{1}{2} \leq$ x $\leq$ 2 } is :2020 · 3 Sep · Shift 1 · Q32 · MCQ
The area (in sq. units) of the region A = {(x, y) : (x – 1)[x] $\leq$ y $\leq$ 2 $x$ , 0 $\leq$ x $\leq$ 2}, where [t] denotes the greatest integer function, is :2020 · 5 Sep · Shift 2 · Q27 · MCQ
The area (in sq. units) of the region A = {(x, y) : |x| + |y| $\leq$ 1, 2y2 $\geq$ |x|}2020 · 6 Sep · Shift 1 · Q20 · MCQ
The area (in sq. units) of the region enclosed by the curves y = x2 – 1 and y = 1 – x2 is equal to :2020 · 6 Sep · Shift 2 · Q20 · MCQ
The area of the region, enclosed by the circle x2 + y2 = 2 which is not common to the region bounded by the parabola y2 = x and the straight line y = x, is:2020 · 7 Jan · Shift 1 · Q42 · MCQ
The area (in sq. units) of the region {(x, y) $\in$ R2 | 4x2 $\leq$ y $\leq$ 8x + 12} is :2020 · 7 Jan · Shift 2 · Q36 · MCQ
For a > 0, let the curves C1 : y2 = ax and C2 : x2 = ay intersect at origin O and a point P. Let the line x = b (0 < b < a) intersect the chord OP and the x-axis at points Q and R, respectively. If the line x = b bisects the area…2020 · 8 Jan · Shift 1 · Q32 · MCQ
The area (in sq. units) of the region {(x,y) $\in$ R2 : x2 $\leq$ y $\leq$ 3 – 2x}, is :2020 · 8 Jan · Shift 2 · Q35 · MCQ
Given : $f (x) = ⎩ ⎨ ⎧ x, \frac{1}{2}, 1 - x, 0 \leq x < \frac{1}{2} x = \frac{1}{2} \frac{1}{2} < x \leq 1$ and $g (x) = (x - \frac{1}{2})^{2}, x \in R$ …2020 · 9 Jan · Shift 2 · Q32 · MCQ
The area (in sq. units) of the region A = { (x, y) $\in$ R × R| 0 $\leq$ x $\leq$ 3, 0 $\leq$ y $\leq$ 4, y $\leq$ x2 + 3x} is :2019 · 8 Apr · Shift 1 · Q24 · MCQ
Let S( $α$ ) = {(x, y) : y2 $\leq$ x, 0 $\leq$ x $\leq α$ } and A( $α$ ) is area of the region S( $α$ ). If for a $λ$ , 0 < $λ$ < 4, A( $λ$ ) : A(4) = 2 : 5, then $λ$ equals2019 · 8 Apr · Shift 2 · Q36 · MCQ
The area (in sq. units) of the region A = {(x, y) : x2 $\leq$ y $\leq$ x + 2} is2019 · 9 Apr · Shift 1 · Q38 · MCQ
The area (in sq. units) of the region A = {(x, y) : $\frac{y ^{2}}{2} \leq$ x $\leq$ y + 4} is :-2019 · 9 Apr · Shift 2 · Q28 · MCQ
The area (in sq. units) bounded by the parabolae y = x2 – 1, the tangent at the point (2, 3) to it and the y-axis is :2019 · 9 Jan · Shift 1 · Q43 · MCQ
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 :2019 · 9 Jan · Shift 2 · Q40 · MCQ
The area (in sq.units) of the region bounded by the curves y = 2x and y = |x + 1|, in the first quadrant is :2019 · 10 Apr · Shift 2 · Q38 · MCQ
If the area enclosed between the curves y = kx2 and x = ky2, (k > 0), is 1 square unit. Then k is -2019 · 10 Jan · Shift 1 · Q35 · MCQ
The area (in sq. units) of the region bounded by the curve x2 = 4y and the straight line x = 4y – 2 is :2019 · 11 Jan · Shift 1 · Q41 · MCQ
The area (in sq. units) in the first quadrant bounded by the parabola, y = x2 + 1, the tangent to it at the point (2, 5) and the coordinate axes is :2019 · 11 Jan · Shift 2 · Q29 · MCQ
If the area (in sq. units) of the region {(x, y) : y2 $\leq$ 4x, x + y $\leq$ 1, x $\geq$ 0, y $\geq$ 0} is a $2$ + b, then a – b is equal to :2019 · 12 Apr · Shift 1 · Q40 · MCQ
If the area (in sq. units) bounded by the parabola y2 = 4 $λ$ x and the line y = $λ$ x, $λ$ > 0, is $\frac{1}{9}$ , then $λ$ is equal to :2019 · 12 Apr · Shift 2 · Q24 · MCQ
The area (in sq. units) of the region bounded by the parabola, y = x2 + 2 and the lines, y = x + 1, x = 0 and x = 3, is2019 · 12 Jan · Shift 1 · Q40 · MCQ
The area (in sq. units) of the region {x $\in$ R : x $\geq$ 0, y $\geq$ 0, y $\geq$ x $-$ 2 and y $\leq x$ }, is :2018 · 15 Apr · Shift 1 · Q42 · MCQ
If the area of the region bounded by the curves, $y = x^{2}, y = \frac{1}{x}$ and the lines y = 0 and x= t (t >1) is 1 sq. unit, then t is equal to :2018 · 16 Apr · Shift 1 · Q35 · MCQ
Let g(x) = cosx2, f(x) = $x$ and $α, β (α < β)$ be the roots of the quadratic equation 18x2 - 9 $π$ x + $π^{2}$ = 0. Then the area (in sq. units) bounded by the curve y = (gof)(x) and the…2018 · Shift 0 · Q41 · MCQ
The area (in sq. units) of the smaller portion enclosed between the curves, x2 + y2 = 4 and y2 = 3x, is :2017 · 8 Apr · Shift 1 · Q42 · MCQ
The area (in sq. units) of the region ${(x, y) : x \geq 0, x + y \leq 3, x^{2} \leq 4 y an d y \leq 1 + x}$ is2017 · Shift 0 · Q38 · MCQ
The area (in sq. units) of the region described by A= {(x, y) $∣$ y $\geq$ x2 $-$ 5x + 4, x + y $\geq$ 1, y $\leq$ 0} is :2016 · 9 Apr · Shift 1 · Q39 · MCQ
The area (in sq. units) of the region ${(x, y) : y^{2} \geq 2 x an d x^{2} + y^{2} \leq 4 x, x \geq 0, y \geq 0}$ is :2016 · Shift 0 · Q26 · MCQ
The area (in sq. units) of the region described by ${(x, y) : y^{2} \leq 2 x$ and $y \geq 4 x - 1}$ is :2015 · Shift 0 · Q29 · MCQ
The area of the region described by $A = {(x, y) : x^{2} + y^{2} \leq 1$ and $y^{2} \leq 1 - x}$ is :2014 · Shift 0 · Q29 · MCQ
The area (in square units) bounded by the curves $y = x, 2 y - x + 3 = 0, x$ -axis, and lying in the first quadrant is :2013 · Shift 0 · Q31 · MCQ
The area between the parabolas $x^{2} = \frac{y}{4}$ and $x^{2} = 9 y$ and the straight line $y = 2$ is :2012 · Shift 0 · Q32 · MCQ
The area of the region enclosed by the curves $y = x, x = e, y = \frac{1}{x}$ and the positive $x$ -axis is :2011 · Shift 0 · Q39 · MCQ
The area bounded by the curves $y = cos x$ and $y = sin x$ between the ordinates $x = 0$ and $x = \frac{3 π}{2}$ is2010 · Shift 0 · Q35 · MCQ
The area of the region bounded by the parabola $(y - 2)^{2} = x - 1,$ the tangent of the parabola at the point $(2, 3)$ and the $x$ -axis is :2009 · Shift 0 · Q34 · MCQ
The area of the plane region bounded by the curves $x + 2 y^{2} = 0$ and $x + 3 y^{2} = 1$ is equal to :2008 · Shift 0 · Q36 · MCQ
The area enclosed between the curves $y^{2} = x$ and $y = ∣ x ∣$ is :2007 · Shift 0 · Q47 · MCQ
The area enclosed between the curve $y = lo g_{e} (x + e)$ and the coordinate axes is :2005 · Shift 0 · Q80 · MCQ
The parabolas $y^{2} = 4 x$ and $x^{2} = 4 y$ 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 ; then $S_{1}, S_{2}, S_{3}$ …2005 · Shift 0 · Q81 · MCQ
Let $f (x)$ be a non - negative continuous function such that the area bounded by the curve $y = f (x), x$ -axis and the ordinates $x = \frac{π}{4}$ and $x = β > \frac{π}{4}$ is $(β sin β + \frac{π}{4} cos β + 2 β) .$ …2005 · Shift 0 · Q82 · MCQ
The area of the region bounded by the curves $y = ∣ x - 2 ∣, x = 1, x = 3$ and the $x$ -axis is :2004 · Shift 0 · Q88 · MCQ
The area of the region bounded by the curves $y = ∣ x - 1 ∣$ and $y = 3 - ∣ x ∣$ is :2003 · Shift 0 · Q82 · MCQ
The area bounded by the curves $y = ln x, y = ln ∣ x ∣, y = ∣ ln x ∣$ and $y = ∣ ln ∣ x ∣ ∣$ is :2002 · Shift 0 · Q84 · MCQ