Chapter 1,2,3,4

Kalaimagal Academy

Mid-Term Assessment (Mathematics)

Time: 1 Hr 30 Mins	Max. Marks: 50
Class: 10th Standard	Portion: Chapters 1, 2, 3 & 4
Student Name: _______________________	Roll No: ____________
Date: ____________

PART - I: CHOOSE THE CORRECT ANSWER 10 × 1 = 10 Marks

1. 1. If \( n(A \times B) = 6 \) and \( A = \{1, 3\} \), then \( n(B) \) is:
   (a) 1

   (b) 2

   (c) 3

   (d) 6
2. 2. If \( f(x) = 2x^2 \) and \( g(x) = \frac{1}{3x} \), then \( f \circ g \) is:
   (a) \(\frac{3}{2x^2}\)

   (b) \(\frac{2}{3x^2}\)

   (c) \(\frac{2}{9x^2}\)

   (d) \(\frac{1}{6x^2}\)
3. 3. Euclid's division lemma states that for positive integers \( a \) and \( b \), there exist unique integers \( q \) and \( r \) such that \( a = bq + r \), where \( r \) must satisfy:
   (a) \( 1 < r < b \)

   (b) \( 0 < r < b \)

   (c) \( 0 \le r < b \)

   (d) \( 0 < r \le b \)
4. 4. The sum of the exponents of the prime factors in the prime factorization of 1729 is:
   (a) 1

   (b) 2

   (c) 3

   (d) 4
5. 5. The GCD of \( 6x^2 y, 9x^3 y^2, 12x^2 y^2 \) is:
   (a) \( 36 x^3 y^2 \)

   (b) \( 3 x^2 y \)

   (c) \( 3 x y \)

   (d) \( 36 x^2 y \)
6. 6. Graph of a linear polynomial is a:
   (a) Straight line

   (b) Circle

   (c) Parabola

   (d) Hyperbola
7. 7. If a polynomial \( x^3 - 3x^2 + 5x - 3 \) is divided by \( x - 2 \), the remainder is:
   (a) 1

   (b) 3

   (c) -1

   (d) 0
8. 8. If in \( \Delta ABC \), \( DE \parallel BC \), \( AD = 4\text{ cm} \), \( DB = 6\text{ cm} \), and \( AE = 5\text{ cm} \), then \( EC \) is:
   (a) \( 6.5\text{ cm} \)

   (b) \( 7.5\text{ cm} \)

   (c) \( 8\text{ cm} \)

   (d) \( 9\text{ cm} \)
9. 9. How many tangents can be drawn to a circle from an exterior point?
   (a) One

   (b) Two

   (c) Infinite

   (d) Zero
10. 10. The ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding:
    (a) Medians

    (b) Altitudes

    (c) Sides

    (d) All of these

PART - II: SHORT ANSWER QUESTIONS 10 × 2 = 20 Marks

11. 11. Let \( A = \{1, 2, 3\} \) and \( B = \{x \mid x \text{ is a prime number less than } 10\} \). Find \( A \times B \).
12. 12. If \( f(x) = 2x + 1 \) and \( g(x) = x^2 - 2 \), find \( f \circ g \).
13. 13. Find the HCF of 252 and 105 using Euclid's Division Algorithm.
14. 14. Solve: \( 8x \equiv 1 \pmod{11} \).
15. 15. Find the general term of the Arithmetic Progression (A.P.): \( 3, 15, 27, 39, \dots \)
16. 16. Reduce the rational expression to its lowest form: \( \frac{x^2 - 11x + 18}{x^2 - 4} \).
17. 17. Find the square root of \( \frac{400 x^4 y^{12}}{100 x^2 y^4} \).
18. 18. Determine the nature of roots for the quadratic equation \( 2x^2 - x - 1 = 0 \).
19. 19. State **Thales Theorem** (Basic Proportionality Theorem).
20. 20. In \( \Delta ABC \), \( D \) and \( E \) are points on the sides \( AB \) and \( AC \) respectively such that \( DE \parallel BC \). If \( \frac{AD}{DB} = \frac{3}{4} \) and \( AC = 15\text{ cm} \), find \( AE \).

PART - III: DETAILED ANSWER QUESTIONS 4 × 5 = 20 Marks

21. 21. Let \( A = \{x \in \mathbb{W} \mid x < 2\} \), \( B = \{x \in \mathbb{N} \mid 1 < x \le 4\} \), and \( C = \{3, 5\} \). Verify that:
    

    \( A \times (B \cup C) = (A \times B) \cup (A \times C) \)
22. 22. Find the sum to $n$ terms of the series \( 5 + 55 + 555 + \dots \)
23. 23. Find the square root of the polynomial \( 64x^4 - 16x^3 + 17x^2 - 2x + 1 \) by division method.
24. 24. State and prove **Pythagoras Theorem**.

*** ALL THE BEST ***