MCJ Sample Paper Mathematics – 1
(For Entry Test Class 1st Year)
1. Which of the following is not a valid element of a matrix?
A) Scalar
B) Vector
C) Entry
D) Element
2. The determinant of a 2×2 matrix is calculated as:
A) ad – bc
B) ac – bd
C) ab + cd
D) None of the above
3. Real numbers include which of the following?
A) Integers
B) Fractions
C) Irrational numbers
D) All of the above
4. What is the value of log₁₀ 1000?
A) 1
B) 2
C) 3
D) 4
5. Which of the following is an algebraic expression?
A) 3x + 5
B) √4
C) π
D) 2 + 2
6. (x + 3)(x – 4) can be expanded as:
A) x² + 7x + 12
B) x² – x – 12
C) x² – x + 12
D) x² – 7x – 12
7. Which of the following is a linear equation?
A) y = x²
B) 3x + 2y = 8
C) xy = 10
D) (x + 2)(y – 3) = 0
8. The slope of a line perpendicular to another line with slope m is:
A) m
B) -m
C) 1/m
D) -1/m
9. Which of the following is not a congruence criterion for triangles?
A) SSS
B) SAS
C) SSA
D) AAA
10. The sum of the angles of a triangle is:
A) 90°
B) 180°
C) 270°
D) 360°
11. If two sides of a triangle are equal, then the angles opposite to them are:
A) Acute
B) Right
C) Obtuse
D) All are possible
12. The ratio of the areas of two similar triangles is equal to the ratio of the:
A) Perimeters
B) Angles
C) Sides
D) Squares of the corresponding sides
13. In a parallelogram, opposite sides are:
A) Congruent
B) Parallel
C) Equal
D) Perpendicular
14. If the lengths of two sides of a right-angled triangle are 3 and 4, the length of the third side is:
A) 5
B) 6
C) 7
D) 8
15. The area of a triangle with base 6 and height 8 is:
A) 12
B) 24
C) 36
D) 48
16. Which of the following is a theorem related to the area of a triangle?
A) Pythagoras theorem
B) Heron’s formula
C) Midpoint theorem
D) AAA similarity criterion
17. Which of the following is not a practical geometric construction?
A) Constructing a perpendicular bisector
B) Constructing an angle bisector
C) Constructing a line parallel to a given line
D) Constructing a circle with a given radius
18. The matrix [3 2] represents:
A) A 2×2 matrix
B) A 2×3 matrix
C) A 3×2 matrix
D) A 3×3 matrix
19. What is the value of log₁₀ 1?
A) 0
B) 1
C) -1
D) Undefined
20. The expansion of (a + b)² is:
A) a² + b
B) a² + 2ab + b²
C) a³ + b³
D) a² – 2ab + b²
21. The sum of the squares of two consecutive integers is 365. What are the integers?
A) 13, 14
B) 18, 19
C) 19, 20
D) 20, 21
22. Which of the following is not a property of a parallelogram?
A) Opposite sides are equal
B) Opposite angles are equal
C) Diagonals bisect each other
D) Diagonals are equal
23. The midpoint of a line segment with endpoints (3, 4) and (7, 2) is:
A) (5, 3)
B) (5, 5)
C) (10, 6)
D) (2, 1)
24. In a right-angled triangle, the side opposite the right angle is called the:
A) Hypotenuse
B) Adjacent side
C) Opposite side
D) None of the above
25. The ratio of corresponding sides of similar triangles is equal to the ratio of their:
A) Perimeters
B) Areas
C) Angles
D) None of the above
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