GATE AE 2022 • Q11 MCQ • 1 Mark Aerodynamics & Fluid Mechanics

Aerodynamics & Fluid Mechanics

Basic Fluid Mechanics

Subtopic: Conservation Equations of Mass, Momentum & Energy

Question Statement:

The equation of the straight line representing the tangent to the curve $y = x^2$ at the point $(1, 1)$ is:

Options:

  • (A) $y = 2x - 2$
  • (B) $x = 2y - 1$
  • (C) $y - 1 = 2(x - 1)$
  • (D) $x - 1 = 2(y - 1)$

Official Answer Key:

C

Step-by-Step Solution & Explanation

### **Detailed Step-by-Step Solution (GATE AE 2022 Q.11)** **1. Derivative and Tangent Slope**: For the parabola $y = x^2$: $$\frac{dy}{dx} = 2x$$ At the point of tangency $(x_0, y_0) = (1, 1)$: $$m = \left.\frac{dy}{dx}\right|_{x=1} = 2(1) = 2$$ **2. Point-Slope Form of Tangent Line**: $$y - y_0 = m(x - x_0) \implies y - 1 = 2(x - 1)$$ - **Official Answer Key**: **C**
← Previous (Q10) All 2022 Questions Next (Q12) →

Related Basic Fluid Mechanics Solved Questions

View All Basic Fluid Mechanics PYQs →
GATE AE 2026 Q13 MCQ • 1M

The following equation with respect to $\phi$(x, t), where a is a non-zero constant, represents ________. $\partial \phi \partial$t + a $\partial \phi \partial$x = 0

GATE AE 2026 Q15 MCQ • 1M

In fluid dynamics, d'Alembert's paradox refers to which one of the following?

GATE AE 2026 Q19 MCQ • 1M

The velocity potential function ($\phi$) given below represents which one of the following? $\phi$ = 5x - 12y

GATE AE 2026 Q47 MSQ • 2M

Consider the flow over an oval modeled using the elementary potential flows as shown below. U represents uniform flow velocity and $\Gamma$ represents circulation around an irrotational line vortex. Which of the following statements is/are TRUE for this model?

Practice This in Real CBT Exam Interface

Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.

Launch CBT Mock Test