New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Differential Equations question

2024 · 31 Jan · Shift 2 · Q42

Guest · try one question or challengeGuest · try one question or challenge

PYQ Library
JEE Main
Mathematics
Differential Equations
2024 · 31 Jan · Shift 2 · Q42

Differential Equations question

2024 · 31 Jan · Shift 2 · Q42

JEE MainMathematicsDifferential EquationsMCQ+4 / −1

The temperature

T(t)

of a body at time

t=0

is

160^{\circ} \mathrm{F}

and it decreases continuously as per the differential equation

\frac{d T}{d t}=-K(T-80)

, where

K

is a positive constant. If

T(15)=120^{\circ} \mathrm{F}

, then

T(45)

is equal to

A
90 $^\circ$ F
B
85 $^\circ$ F
C
80 $^\circ$ F
D
95 $^\circ$ F

More from Differential Equations

Let $y = y (x)$ be the solution of the differential equation $sec^{2} x d x + (e^{2 y} tan^{2} x + tan x) d y = 0, 0 < x < \frac{π}{2}, y (π /4) = 0$ . If $y (π /6) = α$ , then $e^{8 α}$ is equal to …2024 · Numerical
The area enclosed by the closed curve $C$ given by the differential equation $\frac{d y}{d x} + \frac{x + a}{y - 2} = 0, y (1) = 0$ is $Q$ . Let $P$ and $Q$ be the points of intersection of the curve $C$ and the $y$ -axis. If…2023 · MCQ
If $y = y (x)$ is the solution curve of the differential equation $\frac{d y}{d x} + y tan x = x sec x, 0 \leq x \leq \frac{π}{3}, y (0) = 1$ , then $y (\frac{π}{6})$ is equal to2023 · MCQ
Let $α x = exp (x^{β} y^{γ})$ be the solution of the differential equation $2 x^{2} y d y - (1 - x y^{2}) d x = 0, x > 0, y (2) = lo g_{e} 2$ . Then $α + β - γ$ equals :2023 · MCQ
Let $y = y (x)$ be a solution of the differential equation $(x cos x) d y + (x y sin x + y cos x - 1) d x = 0, 0 < x < \frac{π}{2}$ . If $\frac{π}{3} y (\frac{π}{3}) = 3$ , then $\frac{π}{6} y^{''} (\frac{π}{6}) + 2 y^{'} (\frac{π}{6})$ …2023 · Numerical
If the solution curve $f (x, y) = 0$ of the differential equation $(1 + lo g_{e} x) \frac{d x}{d y} - x lo g_{e} x = e^{y}, x > 0$ , passes through the points $(α, 2)$ and $α^{α}$ , then $α^{α}$ is equal to :2023 · MCQ
If the solution curve of the differential equation $(y - 2 lo g_{e} x) d x + (x lo g_{e} x^{2}) d y = 0, x > 1$ passes through the points $(e, \frac{4}{3})$ and $(e^{4}, α)$ , then $α$ …2023 · Numerical
Let the solution curve $x = x (y), 0 < y < \frac{π}{2}$ , of the differential equation $(lo g_{e} (cos y))^{2} cos y d x - (1 + 3 x lo g_{e} (cos y)) sin y d y = 0$ satisfy $x (\frac{π}{3}) = \frac{1}{2 l o g _{e} 2}$ …2023 · Numerical