🏔️ JAMMU AND KASHMIR BOARD

JKBOSE PREVIOUS YEAR SOLVED PAPER 2024

📘 CLASS 10 · MATHEMATICS · SET X
⏳ Time: 3 Hours
🎯 Max Marks: 80
📄 Questions: 40

Roll No. A-3-X · ARM(SZ)JKUT2024 1003-X

📋
GENERAL INSTRUCTIONS
  • ✓ Four sections A, B, C, D · 40 questions · 80 marks · All compulsory.
  • ✓ Section A: Q1–20 (1 mark each) · Section B: Q21–26 (2 marks each)
  • ✓ Section C: Q27–34 (3 marks each) · Section D: Q35–40 (4 marks each)
  • ✓ Internal choice in 2 questions of 1 mark, 2 of 2 marks, 2 of 3 marks, 4 of 4 marks.

📌 SECTION A · 1 × 20 = 20 MARKS

Q1.
🔢 Number Systems

Which is irrational?
(A) 0.101
(B) 0.202202220…
(C) 0.1011
(D) None

🔍 VIEW ANSWER

✅ ANSWER: (B)

0.202202220… is non-terminating non-repeating ⇒ irrational.

Q2.
🧮 Polynomials

Sum of zeroes of \(3x^2-8x+6\)?
(A) -4
(B) 3
(C) 4
(D) None

🔍 VIEW ANSWER

✅ ANSWER: (D) None

Sum = \(-b/a = -(-8)/3 = 8/3\), not in options.

Q3.
📈 Linear Equations

\(2x+3y-9=0\) and \(4x+6y-18=0\) are?
(A) Coincident
(B) Parallel
(C) Intersecting
(D) None

🔍 VIEW ANSWER

✅ ANSWER: (A) Coincident

\(\frac{a1}{a2}=\frac{b1}{b2}=\frac{c1}{c2}=1/2\) ⇒ coincident lines.

Q4.
📊 Arithmetic Progression

35th term of AP 21,18,15,…?
(A) -18
(B) -71
(C) -81
(D) None

🔍 VIEW ANSWER

✅ ANSWER: (C) -81

\(a=21, d=-3\), \(a_{35}=21+34(-3)\)\(=21-102=-81\).

Q5.
📐 Trigonometry

cot 30° = ?
(A) sec 30°
(B) cos 60°
(C) tan 60°
(D) None

🔍 VIEW ANSWER

✅ ANSWER: (C) tan 60°

cot 30° = √3 = tan 60°.

Q6.
📍 Coordinate Geometry

Distance from x‑axis is called?
(A) Abscissa
(B) Ordinate
(C) Coordinate
(D) None

🔍 VIEW ANSWER

✅ ANSWER: (B) Ordinate

Q7.
🔢 HCF

HCF of 7 and 28?
(A) 4
(B) 28
(C) 7
(D) None

🔍 VIEW ANSWER

✅ ANSWER: (C) 7

28 = 7×4 ⇒ HCF = 7.

Q8.
🎲 Probability

P(rain)=0.85, P(not rain)=?
(A) 0.25
(B) 0.15
(C) 0.05
(D) None

🔍 VIEW ANSWER

✅ ANSWER: (B) 0.15

1 – 0.85 = 0.15.

Q9.
📦 Mensuration

Volume of cone?
(A) πr²h
(B) ⅓πr²h
(C) 3πr²h
(D) None

🔍 VIEW ANSWER

✅ ANSWER: (B) ⅓πr²h

Q10.
🔢 Quadratic

Discriminant of \(x^2+5x+5=0\)?
(A) 25
(B) -5
(C) 5
(D) None

🔍 VIEW ANSWER

✅ ANSWER: (C) 5

\(D = 25 – 4×1×5 = 5\).

Q11.
✅ True/False

5313 = 3×7×11×23 ? (True/False)

🔍 VIEW ANSWER

✅ ANSWER: True

Q12.
➕ Sum of AP

Sum of first 100 positive integers?
(A) 5000
(B) 5050
(C) 5005
(D) None

🔍 VIEW ANSWER

✅ ANSWER: (B) 5050

\(S_n = n(n+1)/2\) \(= 100×101/2 = 5050\).

Q13.
❌ Probability

-0.5 can be probability of an event? (True/False)

🔍 VIEW ANSWER

✅ ANSWER: False

Probability ∈ [0,1]. Negative not allowed.

Q14.
⭕ Circles

All circles are (congruent / similar)

🔍 VIEW ANSWER

✅ ANSWER: similar

Q15.
🔵 Tangents

Number of tangents from a point outside the circle = ______

🔍 VIEW ANSWER

✅ ANSWER: two

Q16.
📈 AP Formula

Write formula for sum to n terms of an AP.

🔍 VIEW ANSWER

✅ ANSWER: \(S_n = \frac{n}{2}[2a+(n-1)d]\) or \(S_n = \frac{n}{2}[a+l]\)

Q17.
✅ True/False

\(x=0, y=2\) is a solution of \(y-2x=-2\) ? (True/False)

🔍 VIEW ANSWER

✅ ANSWER: False

LHS = 2 – 0 = 2, RHS = -2 ⇒ not equal.

Q18.
📐 Trigonometry

The value of cos A exceeds 1. (True/False)
OR \(\sin^2 A + \_\_\_\_\_ = 1\)

🔍 VIEW ANSWER

✅ ANSWER: False ; \(\cos^2 A\)

cos A ≤ 1; \(\sin^2 A + \cos^2 A = 1\).

Q19.
📊 Mean

Calculate mean of first 6 prime numbers.

🔍 VIEW ANSWER

✅ ANSWER: 6.833

(2+3+5+7+11+13)/6 = 41/6 ≈ 6.833.

Q20.
📊 Statistics

Write formula for class mark of grouped data.
OR If mean=15.6, median=15.73, then mode=?

🔍 VIEW ANSWER

✅ Class mark: (Upper + Lower)/2
OR Mode: 3×Median – 2×Mean = 3×15.73 – 2×15.6 = 47.19 – 31.2 = 15.99

🏁 END OF SECTION A · Q1–20 SOLVED 🏁
✅ JKBOSE Class 10 2024 · Set X · Section A

PreviousNext