Functions

Q.

A father told his son, “I was as old as you are at present at the time of your birth”. If the father’s age is 38 years now, the son’s age five years back was:

1. 14 years

2. 19 years

3. 33 years

4. 38 years

5. 46 years

Q.

If $R=\left\{(x,y)|x,y\in Z,x^2+3y^2\le 8\right\}$ is a relation on the set of integers $Z$, then the domain of $R^{-1}$ is

1. $\{-1,0,1\}$

2. $\{-2,-1,1,2\}$

3. $\{0,1\}$

4. $\{-2,-1,0,1,2\}$

Q.

In 10 years, A will be twice as old as B was 10 years. ago. If A is now 9 years older than B, the present age of B is:

1. 19 years

2. 39 years

3. 49 years

4. 29 years

5. 59 years

Q. If f(x + y) = f(x) + f(y) - xy - 1 for all $x,yϵR$ and f(1) = 1 then $f\left(n\right)=n,nϵN$ is true if?

1. n = 1
2. n = 1 and n = 2
3. n is odd
4. any value of n

Q. Which of the following is an even function?

1. f(x)=
2. 
3. f(x)=
4. 

Q.

X can do a piece of work in 40 days. He works at it for 8 days and then Y finishes it in 16 days. How long will they together take to complete the work?

1. $\frac{40}{3}$ days

2. $20$ days

3. $56$ days

4. None of these

5. $15$ days

Q.

If the letters of the word `MATHS` are rearranged to form 5 letter words such that none of the words repeat and the results are arranged in ascending order as in a dictionary, then what is the rank of the word `MATHS'?

1. 53

2. 48

3. None of these

4. 52

Q. The numerator of a fraction is increased by 300% and the denominator is increased by 500%, the resultant fraction is $\frac{5}{12}$. What was the original fraction?

1. $\frac{12}{5}$
2. $\frac{5}{7}$
3. $\frac{8}{5}$
4. None of these
5. $\frac{5}{11}$

Q.

Given that ${10}^{0.48}=x,{10}^{0.70}=yand{x}^z=y^2,$then the value of z is close to :

1. 1.45

2. 1.88

3. 3.7

4. 2.9

Q. The age of the father is 30 years more than the son’s age. Ten years hence, the father’s age will become three times the son’s age that time. What is the son’s present age?

1. Seven
2. Five
3. Six
4. Eight
5. None of these

Q.

If $f\left(x\right)$ = $\frac{9^x}{9^x+3}$, find the value of $f\left(\frac{1}{50}\right)$ + $f\left(\frac{2}{50}\right)$ + ...... + $f\left(\frac{48}{50}\right)$ + $f\left(\frac{49}{50}\right)$

1. 25

2. 25.5

3. 24

4. 24.5

Q. How many pairs of positive integers m, n satisfy $\left(\frac{1}{m}\right)+\left(\frac{4}{n}\right)=\left(\frac{1}{12}\right)$, where n is an odd integer less than 60?

1. 7
2. 5
3. 4
4. 3

Q.

If $f$ is a real valued function such that $f\left(x+y\right)=f\left(x\right)+f\left(y\right)$ and $f\left(1\right)=5$, then the value of $f\left(100\right)$ is

1. $200$

2. $300$

3. $350$

4. $400$

5. $500$

Q. Read the information given below and answer the questions that follow:
A, S, M and D are functions of x and y, and they are defined as follows:
A (x, y) = x + y
S (x, y) = x – y
M (x, y) = xy
D (x, y) = $\frac{x}{y}$ where y is not equal to 0.

What is the value of M(M(A(M(x, y), S(y, x)), x), A(y, x)) for x = 2, y = 3?

1. 50
2. 140
3. 25
4. 70

Q.

The difference between a two - digit number and the number obtained by interchanging the position of both the digits is 63. Which is the smallest two digit number that satisfies the above condition ?

1. 70

2. 49

3. 56

4. 81

5. 29

Q.

The denominator of a fraction is 3 more than the numerator. If the numerator as well as the denominator is increased by 4, the fraction becomes$\frac{4}{5}$. What was the original fraction?

1. 

2. 

3. 

4. 

5. 

Q.

The $9$th term of the series $27+9+5\frac{2}{5}+3\frac{6}{7}+...$ will be:

1. $1\frac{10}{17}$

2. $\frac{10}{17}$

3. $\frac{16}{27}$

4. $\frac{17}{27}$

Q. 6 16 57 244 1245 7506
4 (a) (b) (c) (d) (e)
What will come in place of (d)?

1. 985
2. 980
3. 1004
4. 1015
5. None of these

Q.

A function ' f ' from integers to integers is defined as follows: f(x) = n+3 if n is odd and n/2 if n is even. Suppose k is odd and f(f(f(k))) = 27. What is the sum of the digits of k?

1. 6
2. 9
3. 8
4. 3

Q. For two positive integers a and b, define the function h (a, b) as the greatest common factor (GCF) of a, b. Let A be a set of n positive integers G(A), the GCF of the elements of set A is computed by repeatedly using the function h. The minimum number of times h is required to be used to compute G is : (CAT 1999)

1. n
2. (n - 1)
3. n
4. None of these

Q. There are 8 students appearing in an examination of which 3 have to appear in a Mathematics paper and the remaining 5 in different subjects. In how many ways can they be made to sit in a row if the candidates In Mathematics cannot sit next to each other?

1. 14400
2. 15400
3. 17400
4. 16400

Q.

If a number is divided by 6 after being decreased by 4, the result is 8. What would be the result if it is divided by 5 after 2 is subtracted from it?

1. 10

2. 

3. 

4. 

5. 9

Q. The value of x, for which the functions f(x) = x, g(x) = $(\sqrt{x}{)}^2$ and h(x) $=\frac{x^2}{x}$ are identical, is

1. 0 < x
2. All real values
3. All real values except 0
4. 0 $\le$ x

Q.

If $2^{x+4}-2^{x+2}=3$, then x is equal to

1. – 2

2. 1

3. 0

4. 2

5. – 1

Q.

If $x^2+px+q=0$ has the roots $\alpha \mathrm{and}\beta$, then the value of ${(\alpha -\beta )}^2$ is

1. $p^2-4q$

2. ${\left(p^2-4q\right)}^2$

3. $p^2+4q$

4. ${\left(p^2+4q\right)}^2$

Q. Let g(x) be a function such that g(x + 1) + g(x - 1) = g(x) for every real x. Then for what value of p is the relation g(x + p) = g(x) necessarily true for every real x?

1. 5
2. 2
3. 6
4. 3

Q. Let f be a function with domain [-3, 5] and let g(x) = |3x + 4|, Then the domain of (fog)(x) is?

1. $[-3,\frac{1}{3}]$
2. $[-3,\frac{1}{3})$
3. $(-3,\frac{1}{3})$
4. $Noneofthese$

Q. If [X] is the greatest integer less than or equal to x, then find the value of the following series $\left[\sqrt{1}\right]+\left[\sqrt{2}\right]+\left[\sqrt{3}\right]+\left[\sqrt{4}\right]+...+\left[\sqrt{323}\right]$

1. 3723
2. None of these
3. 2373
4. 3237

Q. Each section in the first year of plus 2 courses has exactly 40 students. If there are 5 sections, in how many ways can a set of 4 student representatives be selected, 1 from each section?

1. 2560000
2. 246500
3. 2240000
4. 2360000
5. None of these

Q. Consider a sequence where the $n^{th}$ term
$t_n=\frac{n}{(n+2)},$ n = 1, 2, 3...
The value of $t_3\times t_4\times t_5\times ...\times t_{53}$ equals:

1. $\frac{2}{495}$
2. $\frac{2}{477}$
3. $\frac{12}{55}$
4. $\frac{1}{1485}$