TCS Ninja, Digital, NQT placement questions - 30

Star mark question:
1. 1. In particular language if A=0, B=1, C=2,…….. .. , Y=24, Z=25 then what is the value of ONE+ONE (in the form of alphabets only)
a. BDAI
b. ABDI
c. DABI
d. CIDA

2. 2. Find the number of perfect squares in the given series 2013, 2020, 2027,................, 2300 (Hint 44^2=1936)
a. 1
b. 2
c. 3
d. Can’t be determined

3. What is in the 200th position of 1234 12344 123444 1234444....?
a. 4
b. 3
c. 2
d. 1

4. 2345 23455 234555 234555........... what was last 2 numbers at 200th digit?
a. 23
b. 34
c. 45
d. 55


5. There are equal number of boys and girls in a class. If 12 girls entered out, twice the boys as girls remain. What was the total number of students in a class?
a. 36
b. 48
c. 64
d. 72


6. a bb ccc dddd eeeee .........What is the 120th letter?
a. M
b. N
c. O
d. P


7. There are 120 male and 100 female in a society. Out of 25% male and 20% female are rural. 20% of male and 25% of female rural people passed in the exam. What % of rural students have passed the exam?
a. 17
b. 20
c. 21
d. 22


8. 1/7 th of the tank contains fuel. If 22 litres of fuel is poured into the tank the indicator rests at 1/5th mark. What is the quantity of the tank?
a. 360
b. 385
c. 420
d. 455

9. What is the probability of getting sum 3 or 4 when 2 dice are rolled
a. 5/36
b. 1/6
c. 7/36
d. 1/9


10. On the fabled Island of Knights and Knaves, we meet three people, A, B, and C, one of whom is a knight, one a knave, and one a spy. The knight always tells the truth, the knave always lies, and the spy can either lie or tell the truth.A says: "C is a knave". B says: "A is a knight". C says: "I am the spy". Who is the knight?
a. A
b. B
c. C
d. B or C

TCS Ninja, Digital, NQT placement questions - 29

1. The perimeter of a equilateral triangle and regular hexagon are equal.  Find out the ratio of their areas?

a. 3:2

b. 2:3

c. 1:6

d. 6:1

Correct Option: b

Explanation:
Let the side of the equilateral triangle = $a$ units and side of the regular hexagon is $b$ units.
Given that,  $3a=6b$ $\Rightarrow \frac{a}{b}=\frac{2}{1}$
Now ratio of the areas of equilateral triangle and hexagon = $\frac{\sqrt{3}}{4}{a}^2:\frac{3\sqrt{3}}{2}{b}^2$
$\Rightarrow \frac{\sqrt{3}}{4}{\left(2\right)}^2:\frac{3\sqrt{3}}{2}{\left(1\right)}^2$
$\Rightarrow 2:3$

2. What is the remainder of (32^31^301) when it is divided by 9?

a. 3

b. 5

c. 2

d. 1

Correct option: b
Explanation:
See solved example 6 here
$\frac{{32}^{{31}^{301}}}{9}$ = $\frac{5^{{31}^{301}}}{9}$
Euler totient theorem says that ${\left[\frac{a^{\varphi \left(n\right)}}{n}\right]}_{\mathrm{Re}m}=1$
$\varphi \left(n\right)=n\left(1-\frac{1}{a}\right)\left(1-\frac{1}{b}\right)...$ here $n=a^p.b^q...$
Now $\varphi \left(9\right)=9\left(1-\frac{1}{3}\right)=6$
Therefore, $5^6$ when divided by 9 remainder 1.
Now $\frac{{31}^{301}}{6}=1^{301}=1$
So ${31}^{301}$ can be written as 6k + 1
$\Rightarrow 5^{{31}^{301}}={\left(5^6\right)}^K{.5}^1$
$\frac{5^{{31}^{301}}}{9}=\frac{{\left(5^6\right)}^K{.5}^1}{9}=\frac{1^K.5}{9}=5$

3. Which of the following numbers must be added to 5678 to give a reminder 35 when divided by 460?

a. 980
b. 797
c. 955
d. 618
Correct option: b
Explanation:
Let $x$ be the number to be added to 5678.
When you divide 5678 + $x$ by 460 the remainder = 35.
Therefore, 5678 + $x$ = 460k + 35 here $k$ is some quotient.
$\Rightarrow$ 5643 + $x$ should exactly divisible by 460.
Now from the given options x = 797.

4. A girl entered a store and bought x flowers for y dollars (x and y are integers). When she was about to leave, the clerk said, “If you buy 10 more flowers I will give you all for $\$$2, and you will save 80 cents a dozen”. The values of x and y are:

a. (15,1)
b. (10,1)
c. (5,1)
d. Cannot be determined from the given information.
Correct option: c
Explanation:
Given she bought $x$ flowers for $y$ dollars.
So 1 flower cost = $\frac{y}{x}$
12 flowers or 1 dozen cost = $\frac{12y}{x}$
Again, $x$+10 cost = 2 dollars
1 flower cost = $\frac{2}{10+x}$
12 flowers or 1 dozen cost = $\frac{2\times 12}{10+x}=\frac{24}{10+x}$
Given that this new dozen cost is 80 cents or 4/5 dollar less than original cost.
$\Rightarrow \frac{12y}{x}-\frac{24}{10+x}=\frac{4}{5}$
From the given options, c satisfies this.

5. If a number is divided by 357 the remainder is 5, what will be the remainder if the number is divided by 17?

a. 9
b. 3
c. 5
d. 7
Correct option: c
Explanation:
Let ${}^{\prime }{N}^{\prime }$ be the given number.
$N=357k+5$ = $17\times 21k+5$
If this number is divided by 17 remainder is 5 as 357k is exactly divided by 17.

6. In how many possible ways can write 3240 as a product of 3 positive integers a,b and c.

a. 450
b. 420
c. 350
d. 320
Correct option:
Explanation:
$3450=2^3\times 3^4\times 5^1=a\times b\times c$
We have to distribute three 2's to a, b, c in ${}^{3+3-1}{C}_{3-1}={}^5{C}_2=10$ ways
We have to distribute four 3's to a, b, c in ${}^{3+4-1}{C}_{3-1}={}^6{C}_2=15$ ways
We have to distribute one 5 to a, b, c in 3 ways.
Total ways = $10\times 15\times 3=450$ ways.

7. On door A - It leads to freedomOn door B - It leads to Ghost houseOn door C - door B leads to Ghost houseThe statement written on one of the doors is wrong.Identify which door leads to freedom.

a. A
b. B
c. C
d. None
Correct option: c
Explanation:
Case 1: A, B are true. In this case, Statement C also correct. So contradiction.
Case 2: B, C are true. In this case, B leads to ghost house and C confirms it. Now A is wrong. So door A does not lead to freedom. So Door C leads to freedom.

8. In the given figure, If the sum of the values along each side is equal. Find the possible values a, b, c, d, e, and f.

a. 9, 7, 20, 16, 6, 38
b. 4, 9, 10, 13, 16, 38
c. 4, 7, 20, 13, 6, 38
d. 4, 7, 20, 16, 6, 33
Correct option: c
Explanation:
From the above table, 42 + a + b = 47 + e.  Therefore,  a + b = 5 + e.  Option a, b ruled out.
47 + e = 15 + f.   Therefore, 32 + e = f. Option d ruled out.
4 men throw a die each simultaneously. Find the probability that at least 2 people get the same number
a. 5/18
b. 13/18
c. 1/36
d. 1/2

9. 70, 54, 45, 41……. What is the next number in the given series?

a. 35
b. 36
c. 38
d. 40
Correct option: d
Explanation:
Consecutive squares are subtracted from the numbers.
70 - 54 = 16
54 - 45 = 9
45 - 41 = 4
So next we have to subtract 1. So answer = 41 - 1 = 40

10. How many positive integers less than 500 can be formed using the numbers 1,2,3,and 5 for digits, each digit being used only once.

a. 52
b. 68
c. 66
d. 34
Correct option:
Explanation:
Single digit number = 4
Double digit number = 4$\times$3 = 12
Three digit numbers = 3$\times$3$\times$2= 18 ($\because$ If Hundred's place is 5, then the number is greater than 500)
Total = 34.