Combinations problems and word problems
Question 1 - Question: Answer: As n represents all positive integers, we have Multiplying the above terms of both sides respectively, we get Multiplying both sides of inequality by n!, we g..
Question 1 - Question: Answer: As n represents all positive integers, we have Multiplying the above terms of both sides respectively, we get Multiplying both sides of inequality by n!, we g..Question 7
Question: Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Find the number of words which have atleast one letter repeated. Answer: Total number of 5 letter words from given 10 letters = 10 5 (if ..
Properties of Inverse of Matrix
In other words, a square matrix A is invertible if and only if A is a non-singular matrix. (c) If A and B are invertible square matrices, then (AB) - 1 = B - 1 A - 1 (d) If A and B are two non-singular square matrices of the same order, then AB and BA are also non-singular matr..
In other words, a square matrix A is invertible if and only if A is a non-singular matrix. (c) If A and B are invertible square matrices, then (AB) - 1 = B - 1 A - 1 (d) If A and B are two non-singular square matrices of the same order, then AB and BA are also non-singular matr..Summary
[A i j ] where A i j is the co-factor of the element a i j . Adjoint of A is denoted by Adj A. Note that the concept of adj is only for square matrix. A square matrix A is said to be non-singular if |A| 0. Let A be a square matrix of order n. If there exists a square matrix B of order n, such that ..
[A i j ] where A i j is the co-factor of the element a i j . Adjoint of A is denoted by Adj A. Note that the concept of adj is only for square matrix. A square matrix A is said to be non-singular if |A| 0. Let A be a square matrix of order n. If there exists a square matrix B of order n, such that ..About how many inches long is the key?
About how many inches long is the key? => 2 inches or 1 inch or 3 inches..
Identify the group that has fewer keys.
Identify the group that has fewer keys. => Group C or Group A or Group C & Group B or Group B..
Which tower has the same number of keys as one on the top?
Which tower has the same number of keys as one on the top? => Tower 2 or Tower 3 or Tower 1 or Tower 4..
Identify the object that can be used as a tool to measure the length ..
Identify the object that can be used as a tool to measure the length of the key. => Figure 2 or Figure 1 or Both of these or None of these..
The ruler is marked in sixteenths of an inch. Find the length of the k..
The ruler is marked in sixteenths of an inch. Find the length of the key. => 2 1 4 inches or 1 1 2 inches or 1 1 4 inches or 1 3 4 inches..
The word DICE has _________line of symmetry.
The word DICE has _________line of symmetry. => Vertical or Horizontal..
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