Applied Mathematics

Calculus

Medium

applied

The point on the straight line $3x + 4y = 8$ , which is closest to the origin is:

$\left(\frac{13}{24}, \frac{17}{24}\right)$

$\left(\frac{24}{25}, \frac{32}{25}\right)$

$\left(\frac{5}{24}, \frac{7}{24}\right)$

$\left(1, \frac{5}{4}\right)$

✅ Correct Option: 2

The closest point is the foot of the perpendicular from the origin to $3x + 4y - 8 = 0$ . Using formula: $x = 0 - \frac{3(-8)}{25} = \frac{24}{25}$ , $y = 0 - \frac{4(-8)}{25} = \frac{32}{25}$ . Point: $\left(\frac{24}{25}, \frac{32}{25}\right)$ .

2022: 25 May Shift 1

If the sum of two positive numbers is 25 and their product is maximum when divided in the ratio of cubes of one and squares of the other, then the numbers are:

2024: 16 May Shift 1

A company is selling a certain commodity $x$ . The demand function for the commodity is linear. The company can sell $2000$ units when the price is ₹ $8$ per unit and it can sell $3000$ units when the price is ₹ $4$ per unit. The Marginal revenue at $x=5$ is:

2025: 29 May Shift 2

The supply function of a commodity is P = $x^3+2x+18$ . When 4 units of commodity are sold , then producer surplus is:

2023: 30 May Shift 3

If $x = 6t^2$ , $y = \frac{6}{t^2}$ , then $\frac{d^2 y}{dx^2}$ is equal to :

2023: 11 Aug Shift 1

the general solution of the differential equation $(1 + y) dx - 2x dy = 0$ is :

2023: 11 Aug Shift 1

If $y = x^3 \log x$ , then $\frac{d^2 y}{dx^2}$ is equal to :

The point on the straight line 3x+4y=83x + 4y = 83x+4y=8, which is closest to the origin is:

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

The point on the straight line $3x + 4y = 8$ , which is closest to the origin is: