Mathematics
Permutations-and-Combinations
Easy

Question

The number of numbers that can be formed with the help of the digits 1,2,3,4,3,2,1, so that odd digits always occupy odd places is

  1. 24
  2. 18
  3. 12
  4. 30

The correct answer is: 18

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Related Questions to study

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If 5(x - 8) + 3(x - 8) = 80, what is the value of X - 8 ?

8(x – 8) = 80
(x – 8) = 10
Option (D)

If 5(x - 8) + 3(x - 8) = 80, what is the value of X - 8 ?

mathematicsgrand-tests
8(x – 8) = 80
(x – 8) = 10
Option (D)
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x is 63% of y. If x > 0, which expression represents y in terms of x ?

table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell x equals 63 over 100 cross times y end cell row cell y equals 100 over 62 cross times x end cell end table
Option (B)

x is 63% of y. If x > 0, which expression represents y in terms of x ?

mathematicsgrand-tests
table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell x equals 63 over 100 cross times y end cell row cell y equals 100 over 62 cross times x end cell end table
Option (B)
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Which of the following linear equations has no solution?

No solution occurs when:
Xa1 + b1 = xa2 + b2
Where a1 = a2 and b1  b2
The only option that conforms to this is option (C).

Which of the following linear equations has no solution?

mathematicsgrand-tests
No solution occurs when:
Xa1 + b1 = xa2 + b2
Where a1 = a2 and b1  b2
The only option that conforms to this is option (C).
grand-tests
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Which quadratic equation has exactly one distinct real solution?

One solution occurs when
b2 = 4ac = 0.
The only option that asrees to this is option (D).

Which quadratic equation has exactly one distinct real solution?

mathematicsgrand-tests
One solution occurs when
b2 = 4ac = 0.
The only option that asrees to this is option (D).
grand-tests
mathematics

The number of employees in Jorge's business can be modeled by the equation E(t) = 4(1.2)t, where t is the number of years since the business opened. Which of the following is the best interpretation of the number 4 in this context?

According to exponential formula
Y = a(b) x
Where a = initial value
Hence option (c).

The number of employees in Jorge's business can be modeled by the equation E(t) = 4(1.2)t, where t is the number of years since the business opened. Which of the following is the best interpretation of the number 4 in this context?

mathematicsgrand-tests
According to exponential formula
Y = a(b) x
Where a = initial value
Hence option (c).
grand-tests
mathematics

The graph shows the mass, in kilograms, of an African elephant from birth to age 20 years.

What was the average rate of change in mass, in kilograms per year, of the elephant from age 6 years to age 10 years?

From graph and using slope formula, option D.

The graph shows the mass, in kilograms, of an African elephant from birth to age 20 years.

What was the average rate of change in mass, in kilograms per year, of the elephant from age 6 years to age 10 years?

mathematicsgrand-tests
From graph and using slope formula, option D.
grand-tests
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The shaded region shown represents the solutions to which inequality?

From substituting the y and x values from x, option A.


The shaded region shown represents the solutions to which inequality?

mathematicsgrand-tests
From substituting the y and x values from x, option A.
grand-tests
mathematics


Some values of x and their corresponding values of f(x) for the linear function fare shown in the table. What is the value of f (-6) ?

Linear function form not stretchy rightwards double arrow y equals m x plus c
C = - 1 Since [x = 0 means y – intercept]
fraction numerator negative 2 plus 5 over denominator 3 minus 12 end fraction equals fraction numerator plus 3 over denominator negative 9 end fraction equals negative 1 third equals m
y equals fraction numerator negative 1 over denominator 3 end fraction x minus 1
y equals negative 1 third left parenthesis negative 6 right parenthesis minus 1
= 2 - 1
y = 1
Option A


Some values of x and their corresponding values of f(x) for the linear function fare shown in the table. What is the value of f (-6) ?

mathematicsgrand-tests
Linear function form not stretchy rightwards double arrow y equals m x plus c
C = - 1 Since [x = 0 means y – intercept]
fraction numerator negative 2 plus 5 over denominator 3 minus 12 end fraction equals fraction numerator plus 3 over denominator negative 9 end fraction equals negative 1 third equals m
y equals fraction numerator negative 1 over denominator 3 end fraction x minus 1
y equals negative 1 third left parenthesis negative 6 right parenthesis minus 1
= 2 - 1
y = 1
Option A
grand-tests
mathematics


The average amount spent, in dollars, by each attendee at a conference from 2008 to 2010 is shown in the table. Which of the following quadratic functions best models the average amount spent f(x), by attendees at the conference from 2008 to 2010, where xis the number of years after 2008?

From substitution option B


The average amount spent, in dollars, by each attendee at a conference from 2008 to 2010 is shown in the table. Which of the following quadratic functions best models the average amount spent f(x), by attendees at the conference from 2008 to 2010, where xis the number of years after 2008?

mathematicsgrand-tests
From substitution option B
grand-tests
mathematics

A landscape-supply company sells mulch at a rate of $30 per cubic yard. What price does the company charge for 54 cubic feet of mulch? (1 yard= 3 feet)

table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell 54 left parenthesis tt right parenthesis cubed cross times fraction numerator 1 straight y cubed over denominator 27 ft cubed end fraction end cell row cell 2 cross times straight $ 30 equals 60 straight $ end cell end table
Option B.

A landscape-supply company sells mulch at a rate of $30 per cubic yard. What price does the company charge for 54 cubic feet of mulch? (1 yard= 3 feet)

mathematicsgrand-tests
table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell 54 left parenthesis tt right parenthesis cubed cross times fraction numerator 1 straight y cubed over denominator 27 ft cubed end fraction end cell row cell 2 cross times straight $ 30 equals 60 straight $ end cell end table
Option B.
grand-tests
mathematics


The graph of y = f(x) - 2 is shown. Which equation defines function f ?

When subtracted by (-2) the graph is translated down by 2 units. So f(x) intersects origin so option A


The graph of y = f(x) - 2 is shown. Which equation defines function f ?

mathematicsgrand-tests
When subtracted by (-2) the graph is translated down by 2 units. So f(x) intersects origin so option A
grand-tests
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The mean score of a basketball team for its last 8 games was 64.5. If the highest score of these games is removed, the mean score of the remaining games becomes 63. What was the highest score of the last 8 games?

straight n over 8 equals 64.5
N= 516
fraction numerator 516 minus y over denominator 7 end fraction equals 63
516 – y = 441
75 = y
Option (A)

The mean score of a basketball team for its last 8 games was 64.5. If the highest score of these games is removed, the mean score of the remaining games becomes 63. What was the highest score of the last 8 games?

mathematicsgrand-tests
straight n over 8 equals 64.5
N= 516
fraction numerator 516 minus y over denominator 7 end fraction equals 63
516 – y = 441
75 = y
Option (A)
grand-tests
mathematics

28 is p% of 35. What is the value of p ?

table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell 28 equals p over 100 cross times 35 end cell row cell 28 cross times 100 over 35 end cell row cell p equals 80 end cell end table 

28 is p% of 35. What is the value of p ?

mathematicsgrand-tests
table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell 28 equals p over 100 cross times 35 end cell row cell 28 cross times 100 over 35 end cell row cell p equals 80 end cell end table 
grand-tests
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The scatterplot shows the relationship between two variables, x and y. A line of best fit for the data is also shown.

For how many data points does the line of best fit predict a y-value greater than they-value of the actual data point?

According to information from graph.
Answer = 3.

The scatterplot shows the relationship between two variables, x and y. A line of best fit for the data is also shown.

For how many data points does the line of best fit predict a y-value greater than they-value of the actual data point?

mathematicsgrand-tests
According to information from graph.
Answer = 3.
grand-tests
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What is the x-coordinate of the x-intercept of the line with equation 2 over 3 x plus 1 third y equals 1  when it is  graphed in the xy-plane?

On substituting y =0,  x equals 3 over 2

What is the x-coordinate of the x-intercept of the line with equation 2 over 3 x plus 1 third y equals 1  when it is  graphed in the xy-plane?

mathematicsgrand-tests
On substituting y =0,  x equals 3 over 2