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Class 10 Maths exam preparation works best when you focus on the right questions - that’s where CBSE Important Questions Class 10 Maths come in. They show you which chapters and types of problems to prioritize.
It’s not just about memorizing formulas. These questions include chapter-wise problems, MCQs, case study questions, and long-answer problems from your Class 10 Maths Question Bank, covering everything from Real Numbers important questions Class 10 to Trigonometry important questions Class 10.
Think of these important questions as doing two things:
Without them, you could waste time on low-priority topics or miss the problems that appear most often.
Think of it as your ultimate shortcut to mastering 2025-26 CBSE Class 10 Maths Important Questions - without skipping anything important!
Here are chapter-wise important questions that can make your life way easier. From Real Numbers to Statistics & Probability, these questions help you focus on what really shows up in exams.
Grab a Class 10 Maths Important Questions PDF or a Class 10 Sample Paper, pick a chapter, and start solving. It’s a smart way to practice without wasting time on every single exercise in the textbook.
Think of these important questions as your exam survival kit. Here’s why they really help:
Bottom line: these questions aren’t just practice- they’re your shortcut to smarter preparation, higher scores, and less stress.
Think of your Class 10 Maths Important Questions PDF as a secret weapon - not just extra exercises. Here’s what it does for you:
Tackling Real Numbers, Polynomials, or Quadratic Equations questions helps you actually understand formulas instead of just memorizing.
From short and long answers to MCQs, case studies, or assertion-reasoning questions, you get prepared for everything the exam can throw at you.
Practicing Chapter-wise Important Questions under time limits trains you to solve faster and cut down mistakes.
Familiarity with patterns from a Class 10 Maths Question Bank or your PDF makes exam day feel predictable - and way less stressful.
Here are some tips for you to score for Class 10 Maths Exam Preparation. Think of it as a combo of smart practice and exam strategy rather than just solving sums.
Make sure topics like Real Numbers important questions Class 10, Polynomials, and Quadratic Equations important questions Class 10 are solid. Weak basics = weak marks.
Tackle one topic at a time using your Chapter-wise Important Questions Class 10 Maths. It keeps revision structured and stress-free.
Solve a variety of problems - MCQs, Assertion-Reasoning questions Class 10 Maths, and Case Study Questions. The more formats you practice, the less surprises in the exam.
Check out Class 10 Maths previous year questions to spot repeated patterns. Focus especially on Coordinate Geometry important questions Class 10 and Trigonometry important questions Class 10.
Try a mini mock test weekly. Practicing under timed conditions improves speed and accuracy, which is key for Class 10 Maths Important Questions PDF prep.
Keep a mistake log. Revisit tough questions until you can solve them confidently. This applies to everything from Circles important questions Class 10 to Statistics & Probability important questions Class 10.
Here’s a complete set of Class 10 Maths Important Questions with detailed answers, covering all topics and question types - short answer, long answer, and case studies - so you can revise smartly and confidently before your exams.
Q1. Prove that square root of 3 is irrational
Ans.
Assume the square root of 3 is rational, so it can be written as p/q in lowest terms (p and q are integers with no common factor).
square root of 3 = p/q → 3 = p^2 / q^2 → p^2 = 3 q^2
This means p^2 is divisible by 3, so p is divisible by 3 → p = 3k
Substitute: (3k)^2 = 9k^2 = 3 q^2 → q^2 = 3 k^2
So q is also divisible by 3. Contradiction!
Hence, the square root of 3 is irrational.
Q2. Find HCF of 56 and 72 using Euclid’s division method
Ans.
72 = 56 × 1 + 16
56 = 16 × 3 + 8
16 = 8 × 2 + 0
Remainder is 0, so HCF = 8
Q3. Case Study: Number divisible by 6 if divisible by 2 and 3. Verify
Ans.
Example: 12 is divisible by 2 (12 ÷ 2 = 6) and divisible by 3 (12 ÷ 3 = 4). So it is divisible by 6.
Another example: 18 is divisible by 2 and 3 → divisible by 6.
Hence the statement is verified.
Q4. Find zeroes of 2x^2 - 5x + 3
Ans.
Use formula x = (-b plus or minus square root of (b^2 - 4ac)) / 2a
Here, a=2, b=-5, c=3
Discriminant = (-5)^2 - 4×2×3 = 25 - 24 = 1
x = (5 plus or minus 1)/4 → x = 6/4 = 3/2 or x = 4/4 = 1
Zeroes are 1 and 3/2
Q5. Divide x^3 - 2x^2 + 3x - 4 by x - 1
Ans.
Long division:
Q6. Case Study: p(x) = x^3 - 6x^2 + 11x - 6, find zeroes
Ans.
Try factors of 6 (constant term): ±1, ±2, ±3, ±6
p(1) = 1 - 6 + 11 - 6 = 0 → x-1 is factor
Divide by (x-1): x^2 - 5x + 6 → factor = (x-2)(x-3)
Zeroes: 1, 2, 3
Q7. Solve 3x + 2y = 5 and 4x - y = 3
Ans.
From 2nd equation: y = 4x - 3
Substitute in 1st: 3x + 2(4x - 3) = 5 → 3x + 8x - 6 = 5 → 11x = 11 → x = 1
y = 4×1 - 3 = 1
Solution: x = 1, y = 1
Q8. Solve x + y = 10 and 2x - y = 3 using substitution
Ans.
y = 10 - x → 2x - (10 - x) = 3 → 2x - 10 + x = 3 → 3x = 13 → x = 13/3
y = 10 - 13/3 = 30/3 - 13/3 = 17/3
Solution: x = 13/3, y = 17/3
Q9. Case Study: Cost of pencils and erasers
Ans. Let the cost of a pencil = x and an eraser = y. We are given:
Step 1: Solve the equations
Multiply the first equation by 2 to make the y-coefficient the same:
6x + 4y = 40
Subtract the second equation:
(6x + 4y) - (5x + 4y) = 40 - 36 → x = 4
Step 2: Find y
Substitute x = 4 into the first equation:
3×4 + 2y = 20 → 12 + 2y = 20 → 2y = 8 → y = 4
Answer: Cost of a pencil = 4, cost of an eraser = 4
Q10. Find roots of x^2 - 5x + 6 = 0
Ans.
Factor the equation: x^2 - 5x + 6 = (x - 2)(x - 3) = 0
So, x - 2 = 0 → x = 2, x - 3 = 0 → x = 3
Roots are 2 and 3
Q11. Solve 2x^2 - 3x - 2 = 0 using quadratic formula
Ans.
Quadratic formula: x = (-b plus or minus square root of (b^2 - 4ac)) / 2a
Here, a=2, b=-3, c=-2
Discriminant = (-3)^2 - 4×2×(-2) = 9 + 16 = 25
x = (3 plus or minus 5)/4 → x = 8/4 = 2, x = -2/4 = -0.5
Roots are 2 and -0.5
Q12. Case Study: Rectangle area 60 cm^2, length 5 cm more than width
Ans.
Let width = x → length = x + 5
Area = length × width → x(x + 5) = 60 → x^2 + 5x - 60 = 0
Factor: (x + 12)(x - 5) = 0 → x = 5 (width) [ignore negative]
Length = 5 + 5 = 10
Dimensions: width = 5 cm, length = 10 cm
Q13. Find 10th term of AP 3, 7, 11, 15 …
Ans.
nth term formula: an = a + (n-1)d
a = 3, d = 4, n = 10
a10 = 3 + (10-1)×4 = 3 + 36 = 39
10th term = 39
Q14. Sum of first 20 terms of AP = 400, find first term and common difference
Ans.
Sum formula: Sn = n/2 × [2a + (n-1)d]
20/2 × [2a + 19d] = 400 → 10 × (2a + 19d) = 400 → 2a + 19d = 40
We need more info to find exact values; assume first term = 2 → 2×2 +19d=40 → 19d=36 → d=36/19
Q15. Case Study: Staircase 15 steps, increase by 2 each rise
Ans.
AP with 1st term a = 1, d = 2, n = 15
Sum = n/2 × [2a + (n-1)d] = 15/2 × [2×1 +14×2] = 7.5 × (2 + 28) = 7.5 ×30 = 225
Total steps = 225
Q16. State and prove Pythagoras theorem
Ans.
In a right triangle, square of hypotenuse = sum of squares of other two sides
Proof: Using a triangle with sides a, b, c (c hypotenuse), area method or algebra → a^2 + b^2 = c^2
This is Pythagoras theorem
Q17. Right triangle perpendicular = 6 cm, base = 8 cm, find hypotenuse
Ans.
Hypotenuse^2 = 6^2 + 8^2 = 36 + 64 = 100 → hypotenuse = 10 cm
Q18. Case Study: Triangles congruent by SSS criterion
Ans.
If all three sides of one triangle equal corresponding sides of another, triangles are congruent
Example: Triangle ABC sides = 3, 4, 5; Triangle DEF sides = 3, 4, 5 → triangles are congruent
Q19. Distance between points (1,2) and (4,6)
Ans.
Distance formula: √[(x2-x1)^2 + (y2-y1)^2] → √[(4-1)^2 + (6-2)^2] = √[9+16] = √25 = 5
Q20. Midpoint of line joining (2,3) and (4,7)
Ans.
Midpoint = ((x1+x2)/2, (y1+y2)/2) = ((2+4)/2, (3+7)/2) = (6/2, 10/2) = (3,5)
Q21. Case Study: Quadrilateral ABCD, find fourth vertex
Ans.
If ABCD is parallelogram, D = A + C - B
D = (1,2) + (5,6) - (3,4) = (6-3, 8-4) = (3,4)
Fourth vertex = (3,4)
Q22. Define sine, cosine, and tangent ratios for an acute angle in a right triangle
Ans.
For angle θ in a right triangle:
Q23. Right triangle: hypotenuse = 10 cm, opposite side = 6 cm. Find sin, cos, tan
Ans.
Q24. Case Study: Ladder leans against wall, angle with ground 60°, ladder = 5 m. Find height
Ans.
Height = ladder × sin 60° = 5 × 0.866 = 4.33 m
Height where ladder touches wall = 4.33 m
Q25. Find height of tree if angle of elevation = 45° from 30 m away
Ans.
tan 45° = height / distance → height = distance × tan 45° = 30 × 1 = 30 m
Height of tree = 30 m
Q26. Person 50 m away from tower, angle of elevation = 30°, find height
Ans.
tan 30° = height / 50 → height = 50 × 1/√3 ≈ 50 × 0.577 ≈ 28.85 m
Height of tower ≈ 28.85 m
Q27. Case Study: Kite flying at 60 m height, angle of elevation = 30°. Find distance from point to base
Ans.
tan 30° = 60 / distance → distance = 60 / 0.577 ≈ 104 m
Distance from point to base ≈ 104 m
Q28. Define a tangent to a circle
Ans.
A tangent is a straight line that touches the circle at exactly one point. The line does not cross the circle.
Q29. Chord = 12 cm, perpendicular distance from center = 5 cm. Find radius
Ans.
Radius^2 = (chord/2)^2 + perpendicular distance^2 = (6)^2 + 5^2 = 36 + 25 = 61
Radius = √61 ≈ 7.81 cm
Q30. Case Study: Two tangents from external point = 8 cm and 10 cm. Find distance between tangents
Ans.
Distance between tangents = √(length1 × length2) (using formula for tangents from same external point)
Distance = √(8 × 10) = √80 ≈ 8.94 cm
Q1. How often should I practice from my Class 10 Maths Important Questions PDF?
Ans. Aim for daily practice or at least 4–5 times a week. Mix short, long, and MCQs for balanced prep. Timed practice also improves speed and accuracy.
Q2. Can these questions improve my problem-solving skills?
Ans. Absolutely. Working through Real Numbers, Coordinate Geometry, and Similar Triangles important questions teaches you formulas, tricks, and exam strategies.
Q3. Where can I find a reliable Class 10 Maths Important Questions PDF?
Ans. You can download a Chapter-wise Important Questions Class 10 Maths PDF from trusted CBSE resources, sample papers, or reputable educational blogs.
Q4. Do these questions help with previous year exam patterns?
Ans. Yes! Practicing Class 10 Maths previous year questions makes you familiar with recurring question types and reduces surprises on exam day.
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