CBSE & State Board Question Bank | 9th - 12th

Chapter: Triangles & Quadratic Equations - Ultimate Question Bank

Comprehensive Practice Questions (Parts I & II) with Step-by-Step Answers

1-Mark Questions: Part I (Q1 - Q50)

• 1 Mark Q1. In $\triangle ABC$, $DE \parallel BC$ such that $AD = x$, $DB = x - 2$, $AE = x + 2$, and $EC = x - 1$. The value of $x$ is:
  (a) $4$

  (b) $3$

  (c) $5$

  (d) $2.5$
  Answer: (a) $4$
  Explanation: By Thales's Theorem, $\frac{AD}{DB} = \frac{AE}{EC} \implies \frac{x}{x-2} = \frac{x+2}{x-1} \implies x(x-1) = (x+2)(x-2) \implies x^2 - x = x^2 - 4 \implies x = 4$.

1-Mark Questions: Part II (Q51 - Q100)

• 1 Mark Q51. [Placeholder for Question 51]
  Answer: Solution details for Q51.

2-Mark Questions: Part I (Q1 - Q25)

• 2 Marks Q1. In $\triangle ABC$, $DE \parallel BC$ such that $AD = 2.5\text{ cm}$, $DB = 5\text{ cm}$, and $AE = 3\text{ cm}$. Find $EC$.
  Answer: $EC = 6\text{ cm}$

2-Mark Questions: Part II (Q26 - Q50)

• 2 Marks Q26. [Placeholder for Question 26]
  Answer: Solution for Q26.

3-Mark Questions: Part I (Q1 - Q25)

• 3 Marks Q1. State and prove the Basic Proportionality Theorem.
  Answer: Proof steps included. Result: Proved.

3-Mark Questions: Part II (Q26 - Q50)

• 3 Marks Q26. [Placeholder for Question 26]
  Answer: Solution for Q26.

Case Study Questions

Q1. Case Study: Travel Speed & Relative Motion

Raj and Ajay decide to drive to a destination $400\text{ km}$ away. Raj's car travels at an average speed of $x\text{ km/h}$, while Ajay's car travels $5\text{ km/h}$ faster.

1 Mark (a) Expression for distance covered in $2\text{ hours}$.

Answer: $2(x + 5)\text{ km}$

5-Mark Essay / Long Answer Questions

• 5 Marks Q1. Comprehensive proof of Thales Theorem with application examples.
  Answer: Complete proof steps and detailed workings provided.

Assertion & Reasoning Questions

• Q1. Assertion (A): All congruent triangles are similar.
  Reason (R): Two triangles are similar if corresponding angles are equal.
  Answer: (b) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).

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