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JEE • MATHEMATICS • COMBINATIONS

Combinations practice · Hard

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Practice format and chapter quiz

These sets use single-correct-answer MCQs. They do not cover every JEE Main or JEE Advanced question format and are not full-length mock papers.

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1 Hard

1 of 5

Application +4 | -1

A rectangle of dimension

m \times n

(

m

and

n

being odd) is divided into square of unit length by drawing horizontal and vertical lines. The number of rectangles having side of odd unit length is

View answer and explanation

Correct option: B

\left(\frac{(m+1)(n+1)}{4}\right)^{2}

Option B (

\left(\frac{(m+1)(n+1)}{4}\right)^{2}

) is correct because it represents the number of rectangles with odd side lengths within the given rectangle.

2 Hard

2 of 5

Application +4 | -1

There are two bags each of which contains '

n

' balls. A man has to select an equal number of balls from both the bags. The number of ways in which a man can choose at least one ball from each bag is

View answer and explanation

Correct option: D

{ }^{2 n} C_n-1

Option D (

{}^{2 n} C_n-1

) is correct because it represents the number of ways to select an equal number of balls from two bags, each containing 'n' balls, with at least one ball selected from each bag.

3 Hard

3 of 5

Application +4 | -1

The number of solutions of

x_{1}+x_{2}+x_{3}=51\left(x_{1}, x_{2}, x_{3}\right.

being odd natural numbers) is

View answer and explanation

Correct option: B

325

Option B (325) is correct because it represents the number of solutions to the equation with odd natural numbers, transformed into a simpler equation.

4 Hard

4 of 5

Application +4 | -1

Number of positive unequal integral solutions of the equation

x+y+z=12

View answer and explanation

Correct option: B

Option B (42) is correct because it enumerates the unique sets of three unequal positive integers that sum to 12, and then accounts for the permutations of each set.

5 Hard

5 of 5

Analyzing +4 | -1

\sum_{i=1}^{20}\left(\frac{{ }^{20} \mathrm{C}_{i-1}}{{ }^{20} \mathrm{C}_{i}+{ }^{20} \mathrm{C}_{i-1}}\right)^{3}=\frac{k}{21}

, then

k

equals:

View answer and explanation

Correct option: D

100

The correct answer is D (100) because after simplifying the expression inside the summation and using the formula for the sum of cubes of first n natural numbers, we get k = 100.

Revision notes and key takeaways

Review COMBINATIONS in your textbook or class notes, then use this set to check your understanding.

Key Takeaways

✓ This set contains 5 single-correct-answer MCQs on COMBINATIONS.
✓ Try each question before opening its answer. Read the explanation where one is available.
✓ Sign in to save submitted answers. Revisit incorrect answers alongside your textbook or class notes.

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