There are 3 sections in a question paper and | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Let the number of questions chosen from the three sections be $(n_1, n_2, n_3)$ such that $n_1 + n_2 + n_3 = 5$ and $n_i \ge 1$ for $i = 1, 2, 3$.

Vedclass · Accepted Answer

$2250$

Vedclass · Answer

(D) Let the number of questions chosen from the three sections be $(n_1, n_2, n_3)$ such that $n_1 + n_2 + n_3 = 5$ and $n_i \ge 1$ for $i = 1, 2, 3$.The possible combinations of $(n_1, n_2, n_3)$ are $(3, 1, 1), (1, 3, 1), (1, 1, 3), (2, 2, 1), (2, 1, 2), (1, 2, 2)$.The number of ways to choose the questions is given by the sum of products of combinations:$= ({ }^5C_3 	imes { }^5C_1 	imes { }^5C_1) + ({ }^5C_1 	imes { }^5C_3 	imes { }^5C_1) + ({ }^5C_1 	imes { }^5C_1 	imes { }^5C_3) + ({ }^5C_2 	imes { }^5C_2 	imes { }^5C_1) + ({ }^5C_2 	imes { }^5C_1 	imes { }^5C_2) + ({ }^5C_1 	imes { }^5C_2 	imes { }^5C_2)$$= (10 	imes 5 	imes 5) + (5 	imes 10 	imes 5) + (5 	imes 5 	imes 10) + (10 	imes 10 	imes 5) + (10 	imes 5 	imes 10) + (5 	imes 10 	imes 10)$$= 250 + 250 + 250 + 500 + 500 + 500$$= 2250$

There are $3$ sections in a question paper and each section contains $5$ questions. $A$ candidate has to answer a total of $5$ questions,choosing at least one question from each section. Then the number of ways,in which the candidate can choose the questions,is

Similar Questions

$A$ molecule $M$ associates in a given solvent according to the equation $nM \rightleftharpoons (M)_n$. For a certain concentration of $M$,the van't Hoff factor was found to be $0.9$ and the fraction of associated molecules was $0.2$. The value of $n$ is:

What is the reduction electrode potential (in volts) of a copper electrode when $[Cu^{2+}] = 0.01 \ M$ is in a solution at $25^{\circ} C$? ($E^{\circ}$ of $Cu^{2+}/Cu$ electrode is $+0.34 \ V$)

$A$ thin wire of length $l$ and mass $M$ is bent in the form of a semicircle. What is its moment of inertia about an axis passing through the ends of the wire?

If one were to apply the Bohr model to a particle of mass $m$ and charge $q$ moving in a plane under the influence of a magnetic field $B$,the energy of the charged particle in the $n^{th}$ level will be:

Which one of the following pairs is incorrectly matched?

Vedclass Test Series

Exam Paper Generator

Online Exam Module