NCERT Class 10 Maths – Full Syllabus Online Test
Complete Course Coverage | Board Exam 2026
Q1. HCF of 306 and 657 is:
9
3
6
18
Using Euclid’s division algorithm, HCF = 3.
Q2. Fundamental Theorem of Arithmetic states that every integer greater than 1:
Has a unique prime factorisation
Is prime
Is composite
Is even
Each integer has a unique prime factorisation.
Q3. If α and β are zeros of x²−5x+6, then α+β equals:
6
-5
5
-6
α+β = coefficient of x with sign changed = 5.
Q4. Product of zeros of 2x²−7x+3 is:
3/2
-3/2
7/2
-7/2
Product = constant/coefficient of x² = 3/2.
Q5. The pair of equations x−y=2 and 2x−2y=4 has:
No solution
Infinitely many solutions
Unique solution
Two solutions
Both equations represent same line.
Q6. Roots of x²−4x+4=0 are:
2,−2
−2,−2
2,−2
2,2
Discriminant = 0, equal roots 2 and 2.
Q7. The 10th term of AP: 2,5,8,… is:
29
30
32
35
a₁=2,d=3 ⇒ a₁₀=2+9×3=29.
Q8. If two triangles are similar, then the ratio of their areas is equal to:
Ratio of heights
Ratio of medians
Square of ratio of corresponding sides
Ratio of angles
Area ratio equals square of side ratio.
Q9. Distance between (0,0) and (3,4) is:
3
5
4
6
Distance = √(3²+4²)=5.
Q10. sin30° equals:
1/2
√3/2
1
0
sin30° = 1/2.
Q11. Value of tan45° is:
0
√3
1
1/√3
tan45° = 1.
Q12. Angle of elevation is the angle between:
Line of sight and horizontal below eye
Line of sight and horizontal through eye
Vertical and horizontal
Object and observer
Defined with horizontal through observer’s eye.
Q13. Tangent to a circle is perpendicular to the radius at the point of:
Contact
Centre
Diameter
Chord
Property of tangents.
Q14. Area of a circle of radius r is:
2πr
πr
πr
πr²
Area = πr².
Q15. Volume of a sphere of radius r is:
πr³
4/3πr³
2πr³
3πr³
Volume = 4/3πr³.
Q16. Mean of 2,4,6,8 is:
4
6
5
8
Mean = 20/4 = 5.
Q17. Probability of getting head when tossing a fair coin is:
1/2
1
0
2
Two equally likely outcomes.
Q18. LCM of 6 and 8 is:
12
24
48
16
LCM = 24.
Q19. Zero of polynomial x−5 is:
5
-5
0
1
x−5=0 ⇒ x=5.
Q20. Solution of 2x=10 is:
2
10
5
0
x=5.
Q21. Discriminant of x²+4x+4 is:
16
-16
8
0
D=b²−4ac=0.
Q22. Common difference of AP 7,10,13,… is:
7
3
10
13
d=3.
Q23. Sum of angles of a triangle is:
180°
90°
360°
270°
Triangle angle sum = 180°.
Q24. Coordinates of origin are:
(1,0)
(0,1)
(0,0)
(1,1)
Origin is (0,0).
Q25. cos60° equals:
√3/2
1/2
1
0
cos60°=1/2.
Q26. Radius drawn to the point of contact of a tangent is:
Perpendicular
Parallel
Equal
Inclined
Property of tangent.
Q27. Area of a semicircle of radius r is:
πr²
2πr
πr
1/2πr²
Half of πr².
Q28. Curved surface area of cylinder is:
πr²
2πrh
πrh
2πr²
CSA = 2πrh.
Q29. Mode of data is:
Average
Middle value
Most frequent value
Lowest value
Mode = highest frequency value.
Q30. Probability of sure event is:
1
0
1/2
-1
Sure event probability is 1.
Q31. Graph of linear equation in two variables is a:
Curve
Straight line
Circle
Parabola
Linear equation gives straight line.
Q32. Roots of x²−9=0 are:
±3
3,9
0,9
-3,9
x=±3.
Q33. 5th term of AP: 3,7,11,… is:
19
23
19
21
a₅=3+4×4=19.
Q34. If two triangles are similar, their corresponding angles are:
Unequal
Equal
Right angles
Acute
Similar triangles have equal angles.
Q35. Distance between (1,2) and (4,6) is:
5
4
3
6
√[(3)²+(4)²]=5.
Q36. Value of sin²45°+cos²45° is:
0
1/2
1
2
Identity equals 1.
Q37. Angle of depression is measured from:
Vertical
Horizontal
Object
Ground
From horizontal through observer.
Q38. Number of tangents from an external point to a circle are:
2
1
3
0
Two tangents possible.
Q39. Area of sector of angle θ and radius r is:
πr²
2πr
πr
(θ/360)πr²
Sector area formula.
Q40. Volume of a cone is:
πr²h
1/3πr²h
2πr²h
πrh
Volume = 1/3πr²h.
Q41. Mean of 1,2,3 is:
1
3
2
4
Mean=6/3=2.
Q42. Probability of impossible event is:
0
1
1/2
-1
Impossible event probability is 0.
Q43. HCF of two consecutive natural numbers is:
2
1
0
Same number
Consecutive numbers are coprime.
Q44. Number of zeros of polynomial represented by graph touching x-axis is:
1
2
0
Infinite
Touching implies one zero.
Q45. If discriminant < 0, roots are:
Real and equal
Real and unequal
No real roots
Rational
Negative discriminant gives no real roots.
Q46. First term of AP is 5 and d=0, then AP is:
Increasing
Constant
Decreasing
None
All terms equal.
Q47. In similar triangles, ratio of perimeters equals:
Ratio of corresponding sides
Square of sides
Cube of sides
Inverse ratio
Perimeter ratio equals side ratio.
Q48. Distance formula is derived from:
Trigonometry
Algebra
Mensuration
Pythagoras theorem
Based on Pythagoras theorem.
Q49. tan45°×cos30° equals:
√3
√3/2
1
1/2
1×√3/2=√3/2.
Q50. Total number of outcomes when a die is thrown is:
6
3
12
36
Sample space has 6 outcomes.
📘 NCERT Class 10 Maths – Chapter-wise Online Tests
- Chapter 1: Real Numbers – Online Test
- Chapter 2: Polynomials – Online Test
- Chapter 3: Pair of Linear Equations in Two Variables – Online Test
- Chapter 4: Quadratic Equations – Online Test
- Chapter 5: Arithmetic Progressions – Online Test
- Chapter 6: Triangles – Online Test
- Chapter 7: Coordinate Geometry – Online Test
- Chapter 8: Introduction to Trigonometry – Online Test
- Chapter 9: Applications of Trigonometry – Online Test
- Chapter 10: Circles – Online Test
- Chapter 11: Areas Related to Circles – Online Test
- Chapter 12: Surface Areas and Volumes – Online Test
- Chapter 13: Statistics – Online Test
- Chapter 14: Probability – Online Test
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