अवकल समीकरण 3e^x y\, dx + (1 - e^x)² y\, dy = 0 का हल ज्ञात... | Agrigyan

सभी विषय सामान्य कृषि, कृषि अर्थशास्त्र एवं प्रसार शिक्षा उच्च गणित: बीजगणित, कलन एवं अवकल समीकरण सांख्यिकीय विधियां, प्रायिकता एवं प्रायोगिक अभिकल्पनाएं कंप्यूटर अनुप्रयोग, प्रोग्रामिंग एवं जैव सूचना विज्ञान

Q.106

ICAR AIEEA PG 2024 - Statistical Sciences

MCQ (Single Correct) +4 −1

Evaluate $\int_0^1 \frac{1}{\sqrt{-\log_e x}}\, dx$:

$\int_0^1 \frac{1}{\sqrt{-\log_e x}}\, dx$ का मान ज्ञात कीजिए:

$\sqrt{\frac{\pi}{2}}$ $\sqrt{\frac{\pi}{2}}$ $2\pi^2$ $2\pi^2$ $\frac{\sqrt{\pi}}{2}$ $\frac{\sqrt{\pi}}{2}$ $\sqrt{\pi}$ $\sqrt{\pi}$

Q.107

ICAR AIEEA PG 2024 - Statistical Sciences

MCQ (Single Correct) +4 −1

Solve the differential equation $3e^x \tan y\, dx + (1 - e^x)\sec^2 y\, dy = 0$:

अवकल समीकरण $3e^x \tan y\, dx + (1 - e^x)\sec^2 y\, dy = 0$ का हल ज्ञात कीजिए:

$\frac{\cos y}{(1 - e^x)^3} = c$ $\frac{\cos y}{(1 - e^x)^3} = c$ $\frac{\tan y}{(1 - e^x)^3} = c$ $\frac{\tan y}{(1 - e^x)^3} = c$ $\frac{\sin y}{(1 - e^x)^3} = c$ $\frac{\sin y}{(1 - e^x)^3} = c$ $\frac{\sin y}{(1 - e^x)^5} = c$ $\frac{\sin y}{(1 - e^x)^5} = c$

Q.108

ICAR AIEEA PG 2024 - Statistical Sciences

MCQ (Single Correct) +4 −1

Find the solution of the differential equation $\frac{dx}{dy} + \frac{x}{y} = y^2$:

अवकल समीकरण $\frac{dx}{dy} + \frac{x}{y} = y^2$ का हल ज्ञात कीजिए:

$x = \frac{1}{4}x^3 + \frac{c}{y}$ $x = \frac{1}{4}x^3 + \frac{c}{y}$ $y = \frac{1}{4}x^3 + \frac{c}{x}$ $y = \frac{1}{4}x^3 + \frac{c}{x}$ $x = \frac{1}{4}y^3 + \frac{c}{x}$ $x = \frac{1}{4}y^3 + \frac{c}{x}$ $x = \frac{1}{4}y^3 + \frac{c}{y}$ $x = \frac{1}{4}y^3 + \frac{c}{y}$

Q.109

ICAR AIEEA PG 2024 - Statistical Sciences

MCQ (Single Correct) +4 −1

Find the solution of the differential equation $\frac{d^2 y}{dx^2} + 2\frac{dy}{dx} + 4y = 2x^2 + 3e^{-x}$:

अवकल समीकरण $\frac{d^2 y}{dx^2} + 2\frac{dy}{dx} + 4y = 2x^2 + 3e^{-x}$ का हल ज्ञात कीजिए:

$y = e^{-x}[C_1 \cos \sqrt{3}x + C_2 \sin \sqrt{3}x] + \frac{1}{2}x^2 - \frac{1}{2}x + e^{-x}$ $y = e^{-x}[C_1 \cos \sqrt{3}x + C_2 \sin \sqrt{3}x] + \frac{1}{2}x^2 - \frac{1}{2}x + e^{-x}$ $y = 4[C_1 \cos \sqrt{3}x + C_2 \sin \sqrt{3}x] + \frac{1}{2}x^2 + \frac{1}{2}x - e^{-x}$ $y = 4[C_1 \cos \sqrt{3}x + C_2 \sin \sqrt{3}x] + \frac{1}{2}x^2 + \frac{1}{2}x - e^{-x}$ $y = e^x[C_1 \cos \sqrt{3}x + C_2 \sin \sqrt{3}x] - \frac{1}{2}x^2 + \frac{1}{2}x - e^{-x}$ $y = e^x[C_1 \cos \sqrt{3}x + C_2 \sin \sqrt{3}x] - \frac{1}{2}x^2 + \frac{1}{2}x - e^{-x}$ $y = e^x[C_1 \cos \sqrt{3}x + C_2 \sin \sqrt{3}x]$ $y = e^x[C_1 \cos \sqrt{3}x + C_2 \sin \sqrt{3}x]$

Q.110

ICAR AIEEA PG 2024 - Statistical Sciences

MCQ (Single Correct) +4 −1

The value of the constant $a, b$ and $c$ which guarantee that the graph of $f(x) = x^3 + ax^2 + bx + c$ will have a relative maximum at $(-3, 18)$ and a relative minimum at $(1, -14)$ is given by:

अचर $a, b$ और $c$ के मान जो यह सुनिश्चित करते हैं कि $f(x) = x^3 + ax^2 + bx + c$ के आलेख का $(-3, 18)$ पर एक स्थानीय उच्चिष्ठ (relative maximum) और $(1, -14)$ पर एक स्थानीय निम्निष्ठ (relative minimum) होगा, दिए गए हैं:

$a = -3, b = 9, c = 9$ $a = -3, b = 9, c = 9$ $a = -3, b = -9, c = 9$ $a = -3, b = -9, c = 9$ $a = 3, b = 9, c = -9$ $a = 3, b = 9, c = -9$ $a = 3, b = -9, c = -9$ $a = 3, b = -9, c = -9$

सामान्य कृषि, कृषि अर्थशास्त्र एवं प्रसार शिक्षा 12
उच्च गणित: बीजगणित, कलन एवं अवकल समीकरण 48
सांख्यिकीय विधियां, प्रायिकता एवं प्रायोगिक अभिकल्पनाएं 46
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