Question
If r, s, t are prime numbers and p, q are the positive integers such that the LCM of p, q is r2t4s2, then the number of ordered pair (p, q) is –
- 224
- 225
- 252
- 256
Hint:
Natural numbers known as prime numbers can only be divided by one (1) and by the number itself. In other terms, prime numbers are positive integers greater than one that only have the number itself and the number's first digit as factors. Here we have given r, s, t are prime numbers and p, q are the positive integers such that the LCM of p, q is r2t4s2, then what is the number of ordered pair (p, q).
The correct answer is: 225
An ordered pair is made up of the ordinate and the abscissa of the x coordinate, with two values given in parenthesis in a certain sequence.
Now we have given the LCM as: r2t4s2
Consider following cases:
Case 1: if p contains r2 then q will have rk, for the value k=0,1.
So 2 ways.
Case 2: if q contains r2 then p will have rk, for the value k=0,1.
So 2 ways.
Case 3:Both p and q contain r2
So 1way.
So after this we can say that:
exponent of r=2+2+1 = 5 ways.
Similarly
exponent of t=4+4+1=9 ways.
exponent of s=2+2+1 = 5 ways.
So total ways will be:
5 x 5 x 9 = 225 ways.
Finding the smallest common multiple between any two or more numbers is done using the least common multiple (LCM) approach. A number that is a multiple of two or more other numbers is said to be a common multiple. Here we understood the concept of LCM and the pairs, so the total pairs can be 225.
Related Questions to study
A rectangle has sides of (2m – 1) & (2n – 1) units as shown in the figure composed of squares having edge length one unit then no. of rectangles which have odd unit length
![](data:image/png;base64,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)
Here we used the concept of number system and the rectangle, we can also solve it by permutation and combination. herefore, we get the number of rectangles possible with odd side length = m2n2.
A rectangle has sides of (2m – 1) & (2n – 1) units as shown in the figure composed of squares having edge length one unit then no. of rectangles which have odd unit length
![](data:image/png;base64,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)
Here we used the concept of number system and the rectangle, we can also solve it by permutation and combination. herefore, we get the number of rectangles possible with odd side length = m2n2.
nCr + 2nCr+1 + nCr+2 is equal to (2
r
n)
nCr + 2nCr+1 + nCr+2 is equal to (2
r
n)
The coefficient of in
is
The coefficient of in
is
How many different words can be formed by jumbling the letters in the word MISSISSIPPI in which not two S are adjacent ?
The different ways in which items from a set may be chosen, usually without replacement, to construct subsets, are called permutations and combinations. When the order of the selection is a consideration, this selection of subsets is referred to as a permutation; when it is not, it is referred to as a combination. So the final answer is .
How many different words can be formed by jumbling the letters in the word MISSISSIPPI in which not two S are adjacent ?
The different ways in which items from a set may be chosen, usually without replacement, to construct subsets, are called permutations and combinations. When the order of the selection is a consideration, this selection of subsets is referred to as a permutation; when it is not, it is referred to as a combination. So the final answer is .
The value of 50C4 +
is -
The different ways in which items from a set may be chosen, usually without replacement, to construct subsets, are called permutations and combinations. When the order of the selection is a consideration, this selection of subsets is referred to as a permutation; when it is not, it is referred to as a combination. So the final answer is .
The value of 50C4 +
is -
The different ways in which items from a set may be chosen, usually without replacement, to construct subsets, are called permutations and combinations. When the order of the selection is a consideration, this selection of subsets is referred to as a permutation; when it is not, it is referred to as a combination. So the final answer is .
The number of ways of distributing 8 identical balls in 3 distinct boxes so that none of the boxes is empty is-
The different ways in which items from a set may be chosen, usually without replacement, to construct subsets, are called permutations and combinations. When the order of the selection is a consideration, this selection of subsets is referred to as a permutation; when it is not, it is referred to as a combination. So the final answer is 21.
The number of ways of distributing 8 identical balls in 3 distinct boxes so that none of the boxes is empty is-
The different ways in which items from a set may be chosen, usually without replacement, to construct subsets, are called permutations and combinations. When the order of the selection is a consideration, this selection of subsets is referred to as a permutation; when it is not, it is referred to as a combination. So the final answer is 21.
A mass of
strikes the wall with speed
at an angle as shown in figure and it rebounds with the same speed. If the contact time is
, what is the force applied on the mass by the wall
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)
A mass of
strikes the wall with speed
at an angle as shown in figure and it rebounds with the same speed. If the contact time is
, what is the force applied on the mass by the wall
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)
If the locus of the mid points of the chords of the ellipse
, drawn parallel to
is
then ![m subscript 1 end subscript m subscript 2 end subscript equals](data:image/png;base64,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)
If the locus of the mid points of the chords of the ellipse
, drawn parallel to
is
then ![m subscript 1 end subscript m subscript 2 end subscript equals](data:image/png;base64,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)
If nCr denotes the number of combinations of n things taken r at a time, then the expression nCr+1 + nCr –1 + 2 × nCr equals-
The different ways in which items from a set may be chosen, usually without replacement, to construct subsets, are called permutations and combinations. When the order of the selection is a consideration, this selection of subsets is referred to as a permutation; when it is not, it is referred to as a combination. So the final answer is .
If nCr denotes the number of combinations of n things taken r at a time, then the expression nCr+1 + nCr –1 + 2 × nCr equals-
The different ways in which items from a set may be chosen, usually without replacement, to construct subsets, are called permutations and combinations. When the order of the selection is a consideration, this selection of subsets is referred to as a permutation; when it is not, it is referred to as a combination. So the final answer is .