Ask & Answer Question

Maths NCERT Exemplar Solutions Class 12th Chapter Twelve Maths Class 12th Permutations and Combinations Maths NCERT Exemplar Solutions Class 12th Chapter Seven

A test consists of 6 multiple choice questions, each having 4 alternative answers of which only one is correct. The number of ways, in which a candidate answers all six questions such that exactly four of the answers are correct, is

3 Views | Posted 2 months ago

Asked by Shiksha User

1 Answer

Answered by

alok kumar singh | Contributor-Level 10

2 months ago

$\begin{array}{r} D_{1} = |\begin{matrix} - 7 & 4 & - 1 \\ 8 & 1 & 5 \\ 15 & b & 6 \end{matrix}| = 0 \Rightarrow b = - 3 \\ D = |\begin{matrix} 1 & 4 & - 1 \\ 3 & 1 & 5 \\ a & b & 6 \end{matrix}| = 0 \Rightarrow 21 a - 8 b - 66 = 0 \\ P : 2 x - 3 y + 6 z = 15 \end{array}$

so required distance $= \frac{21}{7} = 3$

0 Upvotes 0 Downvotes

Similar Questions for you

Let b₁ b₂ b₃ b₄be a 4-element permutation with $b_{i} \in {1, 2, 3, . . . ., 100} f o r 1 \leq i \leq 4 a n d b_{i} \neq b_{j}$ for $i \neq j,$ such that either b_1, b₂, b₃ are consecutive integers or b₂, b₃, b₄ are consecutive integers. Then the number of such permutations b₁ b₂b₃ b₄ is equal to……………

alok kumar singh

Three consecutive integers belong to 98 sets and four consecutive integers belongs to 97 sets.

Þ Number of permutations of b₁ b₂ b₃ b₄ = number of permutations when b₁ b₂ b₃ are consecutive + number of permutations when b₂, b₃, b₄are consecutive – b₁ b₂ b₃ b₄ are consecutive = 98 * 97 * 98 * 97 – 97 = 18915

Numbers are to be formed between 1000 and 3000, which are divisible by 4, using the digits 1,2,3,4,5 and 6 without repetition of digits. Then the total number of such numbers is………

alok kumar singh

Last two digit must be in form

$\begin{array}{l} 2 3, 4, 5 1 6 \\ 3 2 4 \\ 3 2 \\ 5 2 \end{array}} 3 \times 4 = 12$

Total number of required number = 12 + 18 = 30

A class contains b boys and g girls. If the number of ways of selecting 3 boys and 2 girls from the class is 168, then b + 3g is equal to…………..

Vishal Baghel

Kindly consider the following figure

The total number of 5-digit numbers, formed by using the digits 1, 2, 3, 5, 6, 7 without repetition, which are multiple of 6, is

Payal Gupta

Sum of digits

1 + 2 + 3 + 5 + 6 + 7 = 24

So, either 3 or 6 rejected at a time

Case 1 Last digit is 2

……….2

no. of cases = ²C₁ × 4! = 48

Case 2 Last digit is 6

……….6

= 4! = 24

Total cases = 72

The number of matrices of order 3 × 3, whose entries are either 0 or 1 and the sum of all the entries is a prime number, is……….

Vishal Baghel

$A = [\begin{matrix} a_{1} & a_{2} & a_{3} \\ b_{1} & b_{2} & b_{3} \\ c_{1} & c_{2} & c_{3} \end{matrix}], a_{2}, b_{2}, c_{2} \in {0, 1}$

S = $a_{1} + a_{2} + a_{3} + b_{1} + b_{2} + b_{3} + c_{1} + c_{2} + c_{3}$ is prime

$0 \leq s \leq 9$

Prime value = 2,3, 5, 7

$F o r S = 2, 1 + 1 + 0 + 0 + 0 + 0 + 0 + 0 + 0 \to \frac{9!}{2! 7!} = 36$

Total number of matrices

= 36 + 84 + 126 + 36 = 282

Get authentic answers from experts, students and alumni that you won't find anywhere else

On Shiksha, get access to

65k Colleges
1.2k Exams
688k Reviews
1800k Answers

Community GuidelinesUser Points System

QuestionsDiscussionsTags

A test consists of 6 multiple choice questions, each having 4 alternative answers of which only one is correct. The number of ways, in which a candidate answers all six questions such that exactly four of the answers are correct, is

1 Answer

Similar Questions for you

Learn more about...

Most viewed information

Most viewed information

Share Your College Life Experience

Didn't find the answer you were looking for?

Need guidance on career and education? Ask our experts

Your Question