Class 10 · गणित · 182+ Q&A
Class 10 Mathematics Important Questions with Answers
Class 10 Mathematics is still the CBSE board paper that rewards NCERT exercise lines more than imported entrance tricks. Real numbers (Euclid, fundamental theorem), quadratic formula, similar triangles, trigonometry identities, circles and surface area are the high-search clusters. This hub writes 150+ important questions with a hidden key so you can run a 20-question mock without scrolling a 40-screen PDF. No invented board date — only rationalized 2023–26 chapter names.
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Class 10 Mathematics revision note
Class 10 Mathematics is still the CBSE board paper that rewards NCERT exercise lines more than imported entrance tricks. Real numbers (Euclid, fundamental theorem), quadratic formula, similar triangles, trigonometry identities, circles and surface area are the high-search clusters. This hub writes 150+ important questions with a hidden key so you can run a 20-question mock without scrolling a 40-screen PDF. No invented board date — only rationalized 2023–26 chapter names. You are on the full Class 10 Mathematics bank (All Q&A), page 1 of 10 — 182 questions in this filter. This page lists mixed MCQ, short and long items so a weekly test feels like the school paper. Reveal a key only after you have written your own line. High-search phrases such as class 10 mathematics important questions and कक्षा 10 गणित प्रश्न उत्तर are mapped to these chips, not to an empty database shell. Phone layout: chapter chips scroll sideways, answers stay inside a tap, and the next page is a numbered link so Google and students both get a short URL. Updated for 2026 classroom practice on the rationalized NCERT.
Chapter-wise unique notes — Class 10 Mathematics
1. Real Numbers वास्तविक संख्याएँ
Euclid’s division lemma and the Fundamental Theorem of Arithmetic are the two engines. HCF × LCM = product for two positives. Terminating versus non-terminating recurring decimals follow the prime factors of the denominator after the fraction is in lowest terms. Irrationals such as √2 stay irrational in the usual school proofs. Class 10 no longer dwells on the old “revisiting irrationality” extras that some reprints dropped — these questions follow the slim chapter.
Practice Real Numbers →
2. Polynomials बहुपद
Zeros and coefficients: for a quadratic, sum = −b/a, product = c/a. A linear polynomial has one zero; a cubic can have three. Graph-and-zero language is enough; do not import Class 11 remainder circus unless the item is a simple p(1)=0 check. Relationship questions are the board regulars.
Practice Polynomials →
3. Pair of Linear Equations in Two Variables दो चर वाले रैखिक समीकरण युग्म
a1/a2 versus b1/b2 versus c1/c2 decides unique, infinite or none. Graphical intersection is the picture; substitution, elimination and cross-multiplication are the algebra. A consistent pair can still be dependent. Word problems: age, digits, fractions, upstream-downstream. Write the pair before you solve.
Practice Pair of Linear Equations in Two Variables →
4. Quadratic Equations द्विघात समीकरण
ax²+bx+c=0, a≠0. Factor, complete the square, or formula. Discriminant D=b²−4ac: two real, one real, none real (in reals). Nature of roots is a two-mark gift if you remember the three cases. Word problems must end with the rejected root explained (negative age, etc.).
Practice Quadratic Equations →
5. Arithmetic Progressions समांतर श्रेणी
nth term an = a+(n−1)d, sum Sn = n/2[2a+(n−1)d]. Three terms in AP can be written a−d, a, a+d. Applications: instalments, logs in a pile. Do not use Class 11 GP formulas here.
Practice Arithmetic Progressions →
6. Triangles त्रिभुज
AAA similarity, Basic Proportionality (Thales), and the Pythagoras family including converse. Areas of similar triangles scale as the square of corresponding sides. Mid-point and right-triangle altitude-to-hypotenuse facts return every year. Draw, mark equal angles, then write the similarity statement in corresponding order.
Practice Triangles →
7. Coordinate Geometry निर्देशांक ज्यामिति
Distance, section (internal), and area of a triangle from vertices. Mid-point is section 1:1. Collinearity via area zero or equal slopes. Keep the formula card honest: no Class 11 straight-line intercept theory unless the school still prints it — this hub stays Class 10 NCERT.
Practice Coordinate Geometry →
8. Introduction to Trigonometry त्रिकोणमिति का परिचय
sin, cos, tan of 0°, 30°, 45°, 60°, 90° and identities sin²θ+cos²θ=1, 1+tan²=sec², 1+cot²=csc². Complementary relations: sin(90−θ)=cosθ. Do not invent 15° values unless an identity produces them. These MCQs are table-plus-identity, the board’s cheapest six marks if you are fluent.
Practice Introduction to Trigonometry →
9. Some Applications of Trigonometry त्रिकोणमिति के कुछ अनुप्रयोग
Line of sight, angle of elevation and depression. A two-position problem (walking towards a tower) is the standard long question. Draw; mark both angles; write two tan equations. Height and distance never need a 3D vector.
Practice Some Applications of Trigonometry →
10. Circles वृत्त
Tangent ⊥ radius at the point of contact; two tangents from an external point are equal. Alternate segment is often trimmed in rationalized lists — these questions stay on the two sure theorems plus a numerical. Do not quote intersecting-chord chapter if your book dropped it.
Practice Circles →
11. Areas Related to Circles वृत्तों से संबंधित क्षेत्रफल
Sector, segment, and a combination with a square or triangle. Area of sector = (θ/360)πr². A minor segment is sector minus triangle. π = 22/7 unless told. Keep the diagram’s angle in the formula, not a random 90°.
Practice Areas Related to Circles →
12. Surface Areas and Volumes पृष्ठीय क्षेत्रफल और आयतन
Combination of cube, cuboid, cylinder, cone, sphere, hemisphere. A capsule is cylinder plus two hemispheres. Convert units before you add volumes. Frustum appears only if your school still lists it; the core numericals here are the six solids in combination.
Practice Surface Areas and Volumes →
13. Statistics सांख्यिकी
Mean by direct, assumed-mean and step-deviation; median via cumulative frequency; mode via the modal-class formula. A frequency polygon is a graph, not a bar. Choose the average the question names. Ogive extras may be school-optional — this bank focuses on mean-median-mode.
Practice Statistics →
14. Probability प्रायिकता
P = favourable/total for equally likely outcomes. 0 ≤ P ≤ 1 and P(E)+P(not E)=1. Cards, coins, dice — write the sample space size first. A sure event is 1, an impossible 0. No Class 11 conditional probability.
Practice Probability →
People also ask — Class 10 Mathematics
Class 10 Mathematics में कितने प्रश्न हैं? 182 महत्वपूर्ण प्रश्न: 112 MCQ, 42 लघु, 28 दीर्घ। NCERT गणित के rationalized अध्याय।
उत्तर कहाँ हैं? हर प्रश्न के नीचे View the correct answer दबाएँ। पहले स्वयं लिखें, फिर मिलाएँ। MCQ में सही विकल्प और एक पंक्ति की व्याख्या है।
पेज क्यों बँटे हैं? एक स्क्रीन पर 20 प्रश्न। बाकी Page 2, 3 पर — फोन पर स्क्रॉल छोटा रहता है। यह पेज 1/10 है।
अध्याय कैसे चुनें? ऊपर chapter chips से एक पाठ खोलें। हर अध्याय का unique paragraph और उसी पाठ के प्रश्न मिलते हैं।
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