The degree of the differential equation (1 - (dy/dx)^2)^(3/2) = k (d^2 y)/dx^2 is : Option 1: 1 Option 2: 2 Option 3: 3 Option 4: 3/2

Answer: 2. Solution: Squaring both sides to remove the fractional exponent: (1 - (dy/dx)^2)^3 = k^2 ((d^2 y)/dx^2)^2. The highest order derivative now appears with power 2, so degree = 2.

Applied Mathematics

Calculus

Medium

The degree of the differential equation $\left(1 - \left(\frac{dy}{dx}\right)^2\right)^{3/2} = k \frac{d^2 y}{dx^2}$ is :

$\frac{3}{2}$

✅ Correct Option: 2

Squaring both sides to remove the fractional exponent: $\left(1 - \left(\frac{dy}{dx}\right)^2\right)^3 = k^2 \left(\frac{d^2 y}{dx^2}\right)^2$ . The highest order derivative now appears with power 2, so degree $= 2$ .

2023: 30 May Shift 3

If $x^3 + y^3 = xy$ , then $\frac{dy}{dx}$ is equal to :

2026: 14 May Shift 2

$\int_1^4 x^3\log x\, dx$ is equal to:

2023: 23 May Shift 3

If $y = \frac{\log x}{x^2}$ , then $\frac{d^2y}{dx^2}$ is equal to

2023: 22 May Shift 3

Match List - I with List - II.

	List - I		List - II
(A)	For break-even point	(I)	$< 0$
(B)	For maxima $\frac{d^2y}{dx^2}$	(II)	$\frac{dy}{dx} = 0$
(C)	For points of maxima/minima	(III)	$R(x) - C(x)$
(D)	$P(x) =$ Profit function	(IV)	$R(x) = C(x)$

Choose the correct answer from the options given below :

2026: 21 May Shift 2

The demand function for a commodity is $p = 45 + x - x^2$ , then the consumer's surplus at equilibrium price $p_0 = 25$ will be:

2023: 22 May Shift 3

Match List - I with List - II.

	List - I		List - II
(A)	If $y = x^2 - 8$ and $\frac{dy}{dx} = 0$ , then $x = ?$	(I)	1
(B)	If $p(x) = 3x + 1$ , then $R(x)$ at $x = 2$	(II)	0
(C)	If $y = x^3$ , then $\frac{dy}{dx}$ at $x = -1$	(III)	14
(D)	If $C(x) = 100 + 5x$ , $R(x) = 102 + 3x$ , then break-even point	(IV)	3

Choose the correct answer from the options given below :

The degree of the differential equation (1−(dydx)2)3/2=kd2ydx2\left(1 - \left(\frac{dy}{dx}\right)^2\right)^{3/2} = k \frac{d^2 y}{dx^2}(1−(dxdy​)2)3/2=kdx2d2y​ is :

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

The degree of the differential equation $\left(1 - \left(\frac{dy}{dx}\right)^2\right)^{3/2} = k \frac{d^2 y}{dx^2}$ is :