The two curves x^3 - 3xy^2 + 15 = 0 and 3x^2 y - y^3 + 17 = 0 : Option 1: cut at right angles Option 2: touch each other Option 3: cut at an angle ()/4 Option 4: cut at an angle ()/3

Answer: cut at right angles. Solution: From curve 1: dy/dx = (x^2 - y^2)/2xy = m_1. From curve 2: dy/dx = (-2xy)/(x^2 - y^2) = m_2. Then m_1 * m_2 = -1, so curves cut at right angles.

Calculus

Application of Derivatives

Hard

core

The two curves $x^3 - 3xy^2 + 15 = 0$ and $3x^2 y - y^3 + 17 = 0$ :

cut at right angles

touch each other

cut at an angle $\frac{\pi}{4}$

cut at an angle $\frac{\pi}{3}$

✅ Correct Option: 1

From curve 1: $\frac{dy}{dx} = \frac{x^2 - y^2}{2xy} = m_1$ . From curve 2: $\frac{dy}{dx} = \frac{-2xy}{x^2 - y^2} = m_2$ . Then $m_1 \cdot m_2 = -1$ , so curves cut at right angles.

2023: 22 May Shift 3

The maximum value of $2x^3 - 24x + 107$ in the interval $[1, 3]$ is :

2022: 6 Aug Shift 2

The line $ax + by = 7$ is a tangent to the curve $y = \frac{x-7}{(x-2)(x-3)}$ at the point where it cuts the x-axis

A. The y-intercept of the line is $-0.7$

B. $b = -7$

C. $a = 1$

D. the line passes through the point $(-13, -1)$

E. $b = -20$

Choose the correct answer from the options given below:

2025: 15 May Shift 1

Which of the following are correct?

(A) The function $f(x) = 3x+12$ is increasing on R.

(B) The function $f(x) = e^{2x}$ is decreasing on R.

(D) The function $f(x) = x^3-3x^2+4x$ is increasing on R.

Choose the correct answer from the options given below:

2026: 15 May Shift 1

The demand function for a monopolist is given by $x = 100 - 4p$ , then the marginal revenue, when $x=6$ is (where $x$ is the number of units and $p$ is the price per unit)

2025: 13 May Shift 2

The function $f(x) = \frac{x}{2} + \frac{2}{x}, x \neq 0$ is increasing on

(A) $(-\infty, -2)$

(B) $(-2, 2)$

(D) $(-1, 1)$

Choose the correct answer from the options given below:

2026: 15 May Shift 1

Match the LIST-I with LIST-II

	LIST-I		LIST-II
A.	$y = x^2$	I.	decreasing on $(0, \infty)$
B.	$y = -x^2$	II.	increasing on $(0, \infty)$
C.	$y = x$	III.	decreasing on $(-\infty, \infty)$
D.	$y = -x$	IV.	increasing on $(-\infty, \infty)$

Choose the correct answer from the options given below:

The two curves x3−3xy2+15=0x^3 - 3xy^2 + 15 = 0x3−3xy2+15=0 and 3x2y−y3+17=03x^2 y - y^3 + 17 = 03x2y−y3+17=0 :

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

The two curves $x^3 - 3xy^2 + 15 = 0$ and $3x^2 y - y^3 + 17 = 0$ :