NIMCET 2021 Question Paper with solutions

Question : 4 of 120

Marks: +1, -0

There are 50 questions in a paper. Find the number of ways in which a student can attempt one or more questions:

Solution:

Total no. of questions

=50

To choose one or more questions,

{ }^{50} {C}_{1}+{ }^{50} {C}_{2}+{ }^{50} {C}_{3} ......+{ }^{50} {C}_{50}

.......(1)

{ }^{50} {C}_{0}+{ }^{50} {C}_{1}+{ }^{50} {C}_{2} .....+{ }^{50} {C}_{50}=2^{50}

{ }^{50} {C}_{1}+{ }^{50} {C}_{2}+{ }^{50} {C}_{3} ......+{ }^{50} {C}_{50}

=2^{50}-{ }^{50} {C}_{0}

{ }^{50} {C}_{1}+{ }^{50} {C}_{2}+{ }^{50} {C}_{3}+.....+{ }^{50} {C}_{50}

=2^{50}-1

Put in equation (1)

{ }^{50} {C}_{1}+{ }^{50} {C}_{2}+{ }^{50} {C}_{3}+.......+{ }^{50} {C}_{50}

=2^{50}-1

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