⚠️ Disclaimer: This is an unofficial answer discussion page created for student reference. Final marking depends on CBSE evaluation scheme. Always verify with official CBSE resources.
This page provides the CBSE Class 10 Maths Standard Answer Key 2025 for all question paper sets including 30/2/1, 30/2/2, and 30/2/3. Students can quickly cross-check their answers after the board examination. Only direct answers are provided for fast verification.
Set 30/2/1 – Maths Standard Set 1
Total: 80 Marks · Time: 3 hrs
Section A — MCQ (1 Mark Each)
Q11 Mark
(A) 960
960 is multiple of 240
Q21 Mark
(D) neither prime nor composite
Definition of number 1
Q31 Mark
(B) 5
5^n always ends in 5
Q41 Mark
(D) 3
Three x-axis intersections
Q51 Mark
(B) 2/3
Sum equals Product
Q61 Mark
(D) a1/a2 = b1/b2 = c1/c2
Condition for coincident lines
Q71 Mark
(D) 1², 3², 5², 7², ...
Differences are not constant
Q81 Mark
(A) PQ : PR
Corresponding sides of similarity
Q91 Mark
(A) 3a
y-coordinate is the distance
Q101 Mark
(B) 3/4
Use Pythagoras for tangent
Q111 Mark
(B) 4/√3
Angle A is 30°
Q121 Mark
(C) 60
tan 45° relates height
Q131 Mark
(A) 30°
Angle APB relation OAB
Q141 Mark
(B) 50°
Supplementary to central angle
Q151 Mark
(C) (πr²/6) - (√3/4)r²
Sector minus Triangle area
Q161 Mark
(B) 182/3 π
Volume of hollow hemisphere
Q171 Mark
(C) 44.2
Empirical relation: Mode formula
Q181 Mark
(A) 15/25
Count composite numbers 1-25
Q191 Mark
(C) Assertion true, Reason false
Reason formula is incorrect
Q201 Mark
(D) Assertion false, Reason true
Mean of n natural
Section B — Very Short Answer (2 Marks Each)
Q212 Marks
(-qr)/p²
Factorize αβ(α² + β²)
Q22(a)2 Marks
5 cm
Use similarity side ratios
Q22(b)2 Marks
2.7 cm
Basic Proportionality Theorem application
Q232 Marks
m = 4, n = 2
Parallelogram diagonals bisect each-other
Q24(a)2 Marks
2
Square the provided equation
Q24(b)2 Marks
Prove yourself
Rationalize the denominator first
Q252 Marks
Prove yourself
Tangent-radius angles are perpendicular
Section C — Short Answer (3 Marks Each)
Q263 Marks
Prove yourself
Apply proof by contradiction
Q273 Marks
(-5/3, 2) and (-7/3, 0)
Section formula ratios 1:2, 2:1
Q28(a)3 Marks
Prove yourself
Convert terms to sin/cos
Q28(b)3 Marks
Prove yourself
Substitute p and q values
Q29(a)3 Marks
Prove yourself
RHS congruence criteria triangles
Q29(b)3 Marks
Prove yourself
Use isosceles triangle property
Q303 Marks
462 cm² and 5082 cm²
Sector and remaining area
Q313 Marks
(i) 4/36 (ii) 6/36
List all outcome pairs
Section D — Long Answer (5 Marks Each)
Q325 Marks
Pencil: ₹1, Chocolate: ₹3
Linear equation system solving
Q33(a)5 Marks
12 days
Solve the quadratic equation
Q33(b)5 Marks
30, 40, 50 cm
Right triangle sides calculation
Q34(a)5 Marks
Prove yourself
Basic Proportionality Theorem proof
Q34(b)5 Marks
4.8 m
Similar triangles proportionality ratios
Q355 Marks
Mode: 36.82, Median: 35.76
Apply grouped data formulas
Section E — Case Study (4 Marks Each)
Q364 Marks
(i) 3900 (ii) 4900 (iii) 44500
Arithmetic progression nth term
Q374 Marks
(i) 25√3 (ii) 50 (iii) 9s
Trigonometric heights and distances
Q384 Marks
(i) 6√3 (ii) 343 (iii) 308
Solid geometry volume formulas
Set 30/2/2 – Maths Standard Set 1
Total: 80 Marks · Time: 3 hrs
Section A — MCQ (1 Mark Each)
Q11 Mark
3
Graph intersects x-axis thrice
Q81 Mark
p = 2/3
Sum equals product property
Q91 Mark
44.2
Mode = 3Median - 2Mean
Q101 Mark
± 4
Apply distance formula
Q111 Mark
182/3π
V_outer - V_inner
Q121 Mark
3/4
Use Pythagoras 3-4-5 triplet
Q131 Mark
πr²/6 - √3/4r²
Area_sector - Area_triangle
Q141 Mark
4/√3
A = 30°, substitute values
Q151 Mark
30°
∠APB = 2 × ∠OAB
Q161 Mark
60
tan 45° = height/base
Q171 Mark
15/25
25 total, 9 prime, 1 neither
Q181 Mark
50°
Supplementary to ∠AOB
Q191 Mark
(D)
Assertion false, Mean is (n+1)/2
Q201 Mark
(A)
Length becomes 8 cm
Section B — Very Short Answer (2 Marks Each)
Q21(a)2 Marks
5 cm
Similar triangles ratio
Q21(b)2 Marks
2.7 cm
Basic Proportionality Theorem
Q22(a)2 Marks
67/12
Substitute trigonometric values
Q22(b)2 Marks
Prove yourself
1 + cot²α = cosec²α
Q232 Marks
Prove yourself
Opposite angles sum 180°
Q242 Marks
p = 3
α + 6α = 14/p
Q252 Marks
m = 1, n = 4
Midpoints of diagonals coincide
Section C — Short Answer (3 Marks Each)
Q26(a)3 Marks
Prove yourself
Convert to sin and cos
Q26(b)3 Marks
Prove yourself
Square and substitute q²
Q273 Marks
271.11 cm²
Area_sector - Area_triangle
Q28(i)3 Marks
4/36
Cases: 1-4, 4-1, 2-3, 3-2
Q28(ii)3 Marks
6/36
Cases like 1-4, 4-1, etc.
Q293 Marks
Prove yourself
Use contradiction method
Q303 Marks
(-5/3, 2) and (-7/3, 0)
Section formula 1:2 and 2:1
Q31(a)3 Marks
Prove yourself
Shortest distance is perpendicular
Q31(b)3 Marks
Prove yourself
Tangents from external points
Section D — Long Answer (5 Marks Each)
Q325 Marks
x = 8, y = 1
Use Median formula
Q335 Marks
Pencil: ₹1, Chocolate: ₹3
2x + 3y = 11, x + 2y = 7
Q34(a)5 Marks
1 hour
Quadratic speed-time equation
Q34(b)5 Marks
Larger: 20 hrs, Smaller: 30 hrs
4/x + 9/(x+10) = 1/2
Q35(a)5 Marks
Prove yourself
Basic Proportionality Theorem
Q35(b)5 Marks
1.6 m
Similar triangles ratio
Section E — Case Study (4 Marks Each)
Q36(i)1 Mark
25√3 m
tan 60° in ∆ABC
Q36(ii)1 Mark
50 m
BD - BC = 75 - 25
Q36(iii)-(a)2 Marks
9 seconds
Speed = 50/6 m/s
Q36(iii)-(b)2 Marks
50 m
cos 60° = BC/AC
Q37(i)1 Mark
6√3 cm
√(l² + b² + h²)
Q37(ii)1 Mark
343 cm³
Side³
Q37(iii)-(a)2 Marks
308 cm²
2πr²
Q37(iii)-(b)2 Marks
160 cm²
2(lb + bh + hl) where l=8
Q38(i)1 Mark
₹3,900
a + 29d
Q38(ii)1 Mark
₹4,900
a + 39d
Q38(iii)-(a)2 Marks
₹44,500
Total loan - S_30
Q38(iii)-(b)2 Marks
19:49
a_10 / a_40
Set 30/2/3 – Maths Standard Set 1
Total: 80 Marks · Time: 3 hrs
Section A — MCQ (1 Mark Each)
Q11 Mark
(A) 960
The HCF of 960 and 432
Q21 Mark
(B) 1
By definition of prime
Q31 Mark
(A) 48
Lines are parallel (inconsistent)
Q41 Mark
(C) 1
Discriminant = 0 gives equal roots
Q51 Mark
(B) 11th term
Using Aₙ = a + (n−1)d
Q61 Mark
(C) 3:4
Section formula application
Q71 Mark
(A) 90°
Tangent ⊥ radius contact
Q81 Mark
(D) 2√5
Distance formula application
Q91 Mark
(B) 1/2
Standard value sin 30°
Q101 Mark
(C) 154 cm²
Area = πr², r=7
Q111 Mark
(A) 1/6
P(4) on single die
Q121 Mark
(B) 25
Median class from cumulative
Q131 Mark
(D) 2:1
Ratio of similar volumes
Q141 Mark
(C) √3
Standard value tan 60°
Q151 Mark
(A) Both A and R true
Pythagoras theorem explanation
Q161 Mark
(B) A true, R false
Tangent properties check
Q171 Mark
(C) Both true, not explanation
Probability Assertion-Reason
Q181 Mark
(D) A false, R true
AP terms check
Q191 Mark
(D) A false, R true
Arithmetic progression analysis
Q201 Mark
(D) A false, R true
AP logic check
Section B — Very Short Answer (2 Marks Each)
Q212 Marks
LCM = 180, HCF = 6
Prime factorisation method
Q22(a)2 Marks
x = 3, y = 1
Elimination or substitution
Q22(b)2 Marks
Prove yourself
Use RHS congruence
Q232 Marks
∠APB = 60°
Angle sum property
Q24(a)2 Marks
Height = 10√3 m
tan 60° formula
Q252 Marks
Height = 10√3 m
Application of trigonometry
Section C — Short Answer (3 Marks Each)
Q263 Marks
Prove yourself
Assume √3 is rational
Q273 Marks
Zeroes: 2, −3
Verify sum and product
Q29(b)3 Marks
AP: 7, 10, 13… ; S₁₀ = 175
AP summation formula
Q303 Marks
Prove yourself
Use BPT theorem
Q313 Marks
Area = 77 cm²
Sector area formula
Section D — Long Answer (5 Marks Each)
Q33(b)5 Marks
Prove yourself
Similar triangles property
Q34(a)5 Marks
Height = 20(√3 − 1) m
Height and distance tan
Q355 Marks
Volume = 1232 cm³
Combined solid volume
Section E — Case Study (4 Marks Each)
Q36(i)1 Mark
Distance = 5 units
Coordinate distance formula
Q36(ii)1 Mark
Midpoint = (3, 4)
Average of coordinates
Q36(iii)-(a)2 Marks
Area = 24 sq. units
Triangle area coordinates
Q37(i)1 Mark
P(red) = 3/10
Fav/Total outcomes
Q38(i)1 Mark
Mean = 35
Σfx / Σf
Q38(ii)1 Mark
Modal class: 30–40
Highest frequency class
Q38(iii)2 Marks
Median = 34.5
Median group formula
Check Your Expected Percentage Now
Use our CBSE Best of 5 Percentage Calculator to estimate your board result instantly.
Calculate Percentage →More CBSE Class 10 Tools
Along with our Best of 5 Percentage Calculator, you can also use:
- Target Percentage Calculator – Plan how many marks you need in each subject.
- Percentage Calculator – Calculate your total percentage of Best of 5 subjects.
- Stream Eligibility Calculator – Check whether you qualify for Science, Commerce or Arts.