Class 11 Applied Mathematics Half-Yearly Exam 2026: Important Questions & Revision

Preparing for the Class 11 Applied Mathematics half-yearly examination can be challenging when multiple topics require formula revision, calculation practice and conceptual understanding. Areas such as number systems, logarithms, permutations, combinations and geometric progressions involve different methods, making it important to practise a variety of question types before the exam.

The Class 11 Applied Mathematics Half-Yearly Exam 2026 Important Questions cover key concepts with answers and step-by-step solutions. These worked examples help revise important topics, understand calculation methods and identify areas that need further practice before the examination.

Class 11 Applied Mathematics Half-Yearly Exam 2026: Important Topics

The supplied questions cover several areas of Applied Mathematics. Revising the underlying concepts and practising calculations can help improve accuracy.

For broader syllabus planning, the CBSE Class 11 Applied Maths syllabus outlines the subject areas to revise. 

Class 11 Applied Mathematics Important Questions 2026 with Solutions

Understanding the Class 11 Applied Mathematics Important Questions 2026 with Solutions helps strengthen conceptual clarity, improve calculation skills and revise important formulas through step-by-step explanations and exam-focused practice questions.

Question 1: Convert Decimal to Binary

Convert the decimal number 963 into binary.

• A) ((111000010)_2)

• B) ((1111000011)_2)

• C) ((1110100101)_2)

• D) None of these

Answer: B) ((1111000011)_2)

Solution: Repeatedly divide the decimal number by 2 and record the remainders. Reading the remainders from bottom to top gives the binary number.

[
963=512+256+128+64+2+1
]

Therefore, ((963)_{10}=(1111000011)_2).

Question 2: Convert Binary to Decimal

Convert ((1010101010)_2) into decimal.

• A) 286

• B) 786

• C) 682

• D) None of these

Answer: C) 682

Solution: Multiply each bit by its corresponding power of 2 and add the results.

[
\begin{aligned}
(1010101010)_2
&=2^9+2^7+2^5+2^3+2^1\
&=512+128+32+8+2\
&=\boxed{682}
\end{aligned}
]

Question 3: Simplify Using Exponents

Simplify:

[
\sqrt{\frac14}+(0.01)^{-1/2}-27^{2/3}
]

• A) (\frac12)

• B) (\frac23)

• C) (\frac32)

• D) None of these

Answer: C) (\frac32)

Solution:

[
\sqrt{\frac14}=\frac12
]

[
(0.01)^{-1/2}=100^{1/2}=10
]

[
27^{2/3}=(3^3)^{2/3}=3^2=9
]

Therefore,

[
\frac12+10-9=\boxed{\frac32}
]

Question 4: Solve an Equation Using Exponent Rules

If

[
\left(\frac xy\right)^{a^2+4}
=\left(x^{-1}y\right)^{-5a},
]

find the possible values of (a).

• A) (-4,1)

• B) (4,-1)

• C) (-4,-1)

• D) (4,1)

Answer: D) (4,1)

Solution: Since (x^{-1}y=y/x),

[
\left(\frac yx\right)^{-5a}
=\left(\frac xy\right)^{5a}
]

Equating the exponents gives

[
a^2+4=5a
]

[
a^2-5a+4=0
]

[
(a-1)(a-4)=0
]

Hence, (a=1) or (a=4).

Question 5: Evaluate a Logarithm

If (\log_{\frac13}(27\sqrt3)=x), find (x).

• A) (-7)

• B) (7)

• C) (-\frac72)

• D) (\frac72)

Answer: C) (-\frac72)

Solution:

[
27\sqrt3=3^3\times3^{1/2}=3^{7/2}
]

Since (\frac13=3^{-1}),

[
(3^{-1})^x=3^{7/2}
]

Comparing the exponents gives

[
-x=\frac72
]

Therefore, (x=-\frac72).

Question 6: Apply Logarithm Properties

If

[
\frac{\log243}{\log27}=x,
]

find (x).

• A) (\frac53)

• B) (\frac35)

• C) (3)

• D) (5)

Answer: A) (\frac53)

Solution: Express both numbers as powers of 3.

[
243=3^5,\qquad27=3^3
]

Therefore,

[
x=\frac{\log3^5}{\log3^3}
=\frac{5\log3}{3\log3}
=\boxed{\frac53}
]

Question 7: Simplify a Logarithmic Expression

Evaluate (\log5+2\log0.5+3\log2).

• A) 3

• B) 1

• C) 10

• D) 2

Answer: B) 1

Solution: Using (n\log a=\log(a^n)) and the product rule,

[
\begin{aligned}
&\log5+2\log0.5+3\log2\
&=\log5+\log(0.5)^2+\log2^3\
&=\log(5\times0.25\times8)\
&=\log10=\boxed{1}
\end{aligned}
]

This answer assumes common logarithms, with base 10.

Question 8: Find the Angle Between Clock Hands

What is the smaller angle between the hands of a clock at 10:25 PM?

• A) (120^\circ)

• B) (146.5^\circ)

• C) (162.5^\circ)

• D) None of these

Answer: C) (162.5^\circ)

Solution: Use the formula

[
\theta=\left|30H-\frac{11}{2}M\right|
]

Here, (H=10) and (M=25).

[
\begin{aligned}
\theta&=\left|30(10)-\frac{11}{2}(25)\right|\
&=|300-137.5|\
&=\boxed{162.5^\circ}
\end{aligned}
]

Question 9: Solve a Time and Work Problem

Reena completes a painting in 4 days, while Mihir completes the same painting in 5 days. How long will they take to finish it together?

• A) (\frac9{20}) days

• B) (\frac{20}{9}) days

• C) (\frac{20}{7}) days

• D) None of these

Answer: B) (\frac{20}{9}) days

Solution: Reena's one-day work is (1/4), and Mihir's one-day work is (1/5).

Their combined one-day work is

[
\frac14+\frac15=\frac9{20}
]

Hence, the time required is

[
\frac{1}{9/20}=\boxed{\frac{20}{9}\text{ days}}
]

Question 10: List the Elements of a Set

List all elements of the set

[
S=\left{x\text{ is an integer},-\frac12<x<\frac92\right}.
]

• A) ({-1,0,1,2,3})

• B) ({0,1,2,3,4})

• C) ({0,2,3,4})

• D) None of these

Answer: B) ({0,1,2,3,4})

Solution: The inequality becomes

[
-0.5<x<4.5
]

The integers strictly between (-0.5) and (4.5) are (0,1,2,3,4).

Therefore,

[
S=\boxed{{0,1,2,3,4}}
]

• B) 27

Class 11 Applied Mathematics Half-Yearly Exam 2026 PDF

Keeping the important questions and their solutions together can make revision easier. Use the PDF of the half-yearly revision material to review the MCQs, check the correct options and revisit the calculations before the examination.

How to Revise for the Class 11 Applied Maths Half-Yearly Exam 2026

Effective revision involves reviewing formulas, practising different question types and understanding the steps used to solve each problem. The following tips can help organise preparation for the Class 11 Applied Maths Half-Yearly Exam 2026.

• Revise Important Formulas: Review exponent rules, logarithmic properties, time and work calculations, permutations and combinations, and geometric progression formulas.

• Practise Number System Conversions: Solve decimal-to-binary and binary-to-decimal questions using place values and powers of 2.

• Follow Step-by-Step Calculations: Write the relevant formula, substitute the given values and simplify the expression carefully to minimise calculation errors.

• Understand Question Conditions: Check specific requirements, such as avoiding repeated digits, identifying integers within a given interval and ensuring that (|r|<1) when calculating the sum to infinity of a GP.

• Review Mistakes and Difficult Topics: Revisit the worked solutions, identify errors and practise similar questions to improve accuracy and build confidence.

For additional practice, check the Class 11 Applied Maths Calculus resource to review calculus concepts and the Sequence and Series resource to strengthen understanding of geometric progressions and related formulas.

Understanding key concepts, revising formulas and practising different question types are essential for the Class 11 Applied Mathematics half-yearly examination. These solved important questions cover number systems, logarithms, counting techniques, time and work, and geometric progressions, helping students revise important topics, follow solution methods and improve calculation accuracy.