JKBOSE Class 11 Mathematics

JKBOSE Class 11 Maths: 50 Most Repeated Questions to Score Full Marks!

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JKBOSE Class 11 Mathematics

The Ultimate 50 Most Repeated Questions (2025-26)

Sets, Relations & Functions

  1. In a group of 65 people, 40 like cricket, 10 like both cricket and tennis. How many like tennis only and not cricket? Use the formula:
    \[ n(A \cup B) = n(A) + n(B) – n(A \cap B) \]
  2. Let \( A = \{1, 2, 3, 4, 6\} \). Let \( R \) be the relation on \( A \) defined by \( \{(a, b) : a, b \in A, b \text{ is exactly divisible by } a\} \). Write in roster form.
  3. Find the Domain and Range of the real function:
    \[ f(x) = \sqrt{9 – x^2} \]
    Most Repeated
  4. If \( f(x) = x^2 \) and \( g(x) = 2x + 1 \), find:
    \( (f+g)(x), (f-g)(x), (fg)(x), \text{ and } \left(\frac{f}{g}\right)(x) \)
  5. Prove De Morgan’s Laws using Venn Diagram:
    \[ (A \cup B)’ = A’ \cap B’ \]

Trigonometric Functions

  1. Prove that:
    \[ \frac{\sin 5x + \sin 3x}{\cos 5x + \cos 3x} = \tan 4x \]
  2. Prove:
    \[ \frac{\cos 4x + \cos 3x + \cos 2x}{\sin 4x + \sin 3x + \sin 2x} = \cot 3x \]
    Long Answer
  3. Find the value of:
    \( \sin 75^\circ \text{ and } \tan 15^\circ \)
  4. Prove that:
    \[ \cos^2 x + \cos^2\left(x + \frac{\pi}{3}\right) + \cos^2\left(x – \frac{\pi}{3}\right) = \frac{3}{2} \]

Algebra (Complex No, P&C, Binomial, Sequence)

  1. Express in form \( a + ib \):
    \[ \frac{5 + \sqrt{2}i}{1 – \sqrt{2}i} \]
  2. Solve graphically:
    \[ x + y \leq 5, \quad 4x + y \geq 4, \quad x \leq 5, \quad y \leq 3, \quad x, y \geq 0 \]
  3. Find the term independent of \( x \) in:
    \[ \left(x^2 + \frac{1}{x}\right)^{12} \]
  4. Insert 3 numbers between 1 and 256 so that the resulting sequence is a G.P.
  5. Find the sum to \( n \) terms:
    \( 8, 88, 888, 8888, \dots \)
    Classic

Coordinate Geometry & Conic Sections

  1. Find the angle between lines:
    \( y – \sqrt{3}x – 5 = 0 \text{ and } \sqrt{3}y – x + 6 = 0 \)
  2. Find coordinates of focus and directrix for:
    \[ y^2 = 12x \]
  3. Find the equation of ellipse with vertices \( (\pm 13, 0) \) and foci \( (\pm 5, 0) \).

Calculus (High Weightage)

  1. Evaluate:
    \[ \lim_{x \to 0} \frac{\sqrt{1+x} – 1}{x} \]
  2. First Principle: Find the derivative of \( \sin x \) from first principle. 5 Marks
  3. Differentiate using Quotient Rule:
    \[ f(x) = \frac{x + \cos x}{\tan x} \]

Statistics & Probability

  1. Calculate Variance and Standard Deviation for:
    Class: 30-40, 40-50, 50-60, 60-70, 70-80, 80-90, 90-100
    Freq: 3, 7, 12, 15, 8, 3, 2
  2. If \( P(E) = \frac{1}{4}, P(F) = \frac{1}{2}, P(E \cap F) = \frac{1}{8} \), find \( P(\text{not } E \text{ and not } F) \).

Asterisk Classes Strategy

Focus on the First Principle and Linear Inequalities. These are guaranteed long-answer questions. For statistics, always draw the table clearly to avoid calculation errors!

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