JKBOSE Class 10 Mathematics

The Ultimate 50 Most Important Questions (2025-26)

Real Numbers

Use Euclid’s Division Lemma to find the HCF of 135 and 225.
Prove that \( \sqrt{3} \) is an irrational number. Most Repeated
Given that HCF(306, 657) = 9, find the LCM using:
\[ \text{HCF} \times \text{LCM} = a \times b \]

Find the zeroes of \( x^2 – 2x – 8 \) and verify the relationship between zeroes and coefficients.
Age Problem: Jacob’s age will be three times his son’s in 5 years. Five years ago, it was seven times. Find their present ages.
Find roots of \( 2x^2 – 7x + 3 = 0 \) using the Quadratic Formula:
\[ x = \frac{-b \pm \sqrt{b^2 – 4ac}}{2a} \]
Find the 31st term of an AP whose 11th term is 38 and 16th term is 73.
Find the sum of the first 40 positive integers divisible by 6.

Basic Proportionality Theorem (Thales): State and Prove. Guaranteed
Tangent Theorem: Prove that lengths of tangents from an external point are equal. Theorem
Two concentric circles have radii 5 cm and 3 cm. Find the length of the chord of the larger circle that touches the smaller circle.

If \( \tan(A+B) = \sqrt{3} \) and \( \tan(A-B) = \frac{1}{\sqrt{3}} \), find A and B.
Prove the identity:
\[ \frac{\cos A}{1 + \sin A} + \frac{1 + \sin A}{\cos A} = 2\sec A \]
Must Do
A circus artist climbs a 20m rope tied from the top of a vertical pole to the ground. If the angle is \( 30^\circ \), find the pole height.

A toy is a cone of radius 3.5 cm mounted on a hemisphere. Total height is 15.5 cm. Find the Total Surface Area.
A metallic sphere (r=4.2 cm) is melted and recast into a cylinder (r=6 cm). Find the cylinder’s height.

Missing Frequency: If the median is 28.5 and total frequency is 60, find \( x \) and \( y \). Very Important
Find the Mode for: family size (1-3, 3-5, 5-7…) and families (7, 8, 2…).
One card is drawn from a deck of 52. Find the probability of getting a king of red color.

1. Theorems: BPT and the Circle Tangent theorem are your best friends. Practice them 5 times each.

2. Formula Sheet: Write down all Mensuration formulas (\( \pi r^2 h \), etc.) and paste them on your study wall.

3. Steps: In JKBOSE marking, you get marks for writing the “Given” and “To Prove” sections. Never leave a question blank!