Straight Lines Test 14

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Straight Lines Test 14

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Question 1
1 / -0

There are $$10$$ trees between two stations $$A$$ and $$B$$. Three of them are to be cut down then the total number of ways so that no two trees are to be cut consecutively, is

A
$$^{8}C_{3}$$

B
$$^{7}C_{3}$$

C
$$^{10}C_{3}$$

D
$$^{9}C_{3}$$

Solution

$$3$$ trees to be cut $$7$$ left

Total no. of ways to cut $$3$$ trees $$=$$

Total no. of was to place $$3$$ trees

in the given gaps,
$$=$$ select $$3$$ gaps from $$8$$ $$=\, ^8C_3$$
Question 2
1 / -0

33, 43, 65, 99, 145 ?

A
201

B
203

C
205

D
211

E
none of these

Solution

REF.Image
So Correct Answer is $$145+58= 203$$
Question 3
1 / -0

If $$\left( {n + 1} \right)! = 12 \times (n - 1)!\;then\;n = $$

A
3

B
4

C
2

D
5

Solution

We have,
$$\left( {n + 1} \right)! = 12 \times (n - 1)!$$

$$(n + 1)\times n\times (n-1)! = 12 \times (n - 1)!$$

$$(n + 1)\times n = 12$$

$$n^2 +n- 12=0$$

$$n^2 +4n-3n- 12=0$$

$$(n+4)(n-3)=0$$

$$(n+4)\ne 0$$

So,
$$n-3=0$$
$$n=3$$

Hence, this is the answer.
Question 4
1 / -0

If D=4 and COVER = 63, then BASIC is equal to

A
49

B
50

C
34

D
55

Solution

In the alphabets D is 4th.
So, A = 1, B = 2 and C =3
So, COVER = 3+15+22+5+18 = 63
Therefore BASIC = 2+1+19+9+3 = 34
Question 5
1 / -0

If $$5\times 9=144; 7\times 8=151:4\times 6=102,$$ then $$2\times 5=?$$

A
$$73$$

B
$$77$$

C
$$37$$

D
$$97$$

Solution

$$5\times 9=\underset{(5+9)}{14}\underset{(9-5)}{4}$$ ; $$7\times 8=\underset{(7+8)}{15}\underset{(8-7)}{1}$$ So, $$2\times 5=\underset{(2+5)}{7}\underset{(5-3)}{3}$$
Question 6
1 / -0

The mid points of three sides of a triangle are (0, 1) (0, 2) and (0, 3). Area of this triangle.

A
3

B
0

C
1

D
None of these

Solution
Question 7
1 / -0

If P (n, n) denotes the number of permutations of n different things taken all at a time then P (n, n ) is also identical to:

A
$$

P ( n - 1 , n - 1 )

$$

B
$$

P ( n , n - 1 )

$$

C
$$

\mathrm { r } ! \mathrm { P } ( \mathrm { n } , \mathrm { n } - \mathrm { r } )

$$

D
$$

( n - r ) \cdot P ( n , r )

$$

Solution
Question 8
1 / -0

How many six letter words be made out of the letters of $$ASSIST$$ ? In how many words the alphabets $$S$$ alternates with other letters ?

A
$$120,6$$

B
$$720,\,12$$

C
$$120,\,12$$

D
$$720,\,24$$

Solution

The word ASSIST has 3 's' and 3 other characters (AIT).
Place the other 3 characters first. This can be done in 3! ways.
Now there are 4 spaces remaining (1234) mark as 1,2,3,4.
3 's' 5 can be placed at the spaces marked as 1,2,3 or at the spaces marked as 2,3,4 (2)was
Total no.of ways =3! .2$$=3\times 2\times 2=12$$
Total no.of ways =5!.$$=5\times 4\times 3\times 2=120.$$
$$\therefore$$ so, the answer is 120,12.
Question 9
1 / -0

Observe the given pattern
$$4\times 0+1=01$$
$$4\times1+2=06$$
$$4\times 2+3=11$$
$$4\times 3+4=16$$
Then the value of $$4\times8+9 $$ is -----

A
$$43$$

B
$$42$$

C
$$41$$

D
$$40$$

Solution

If we carefully observe the pattern
in first row it shows four multiply with zero addition one equals one
same for other pattern too
so answer of $$4\times 8+9 = 41$$
Question 10
1 / -0

When we realize a specific implementation of a pancake algorithm, every move when we find the greatest of the sized array and flipping can be modeled through ____________.

A
Combinations

B
Exponential functions

C
Logarithmic functions

D
Permutations

Solution

Unlike a traditional sorting algorithm, which attempts to sort with the fewest comparisons possible, the goal is to sort the sequence in as few reversals as possible.
Here when we flipping the array or stack, we have to take utmost priority to preserve the order of the list so that that sorting doesnt become invalid. Hence we use permutations, we are ensuring that order matters.

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Re-Attempt Weekly Quiz Competition

Straight Lines Test 14

Result

Straight Lines Test 14

Score

-

Rank

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SHARING IS CARING

Question 1

$$^{8}C_{3}$$

$$^{7}C_{3}$$

$$^{10}C_{3}$$

$$^{9}C_{3}$$

Solution

Question 2

201

203

205

211

none of these

Solution

Question 3

3

4

2

5

Solution

Question 4

49

50

34

55

Solution

Question 5

$$73$$

$$77$$

$$37$$

$$97$$

Solution

Question 6

3

0

1

None of these

Solution

Question 7

$$P ( n - 1 , n - 1 )$$

$$P ( n , n - 1 )$$

$$\mathrm { r } ! \mathrm { P } ( \mathrm { n } , \mathrm { n } - \mathrm { r } )$$

$$( n - r ) \cdot P ( n , r )$$

Solution

Question 8

$$120,6$$

$$720,\,12$$

$$120,\,12$$

$$720,\,24$$

Solution

Question 9

$$43$$

$$42$$

$$41$$

$$40$$

Solution

Question 10

Combinations

Exponential functions

Logarithmic functions

Permutations

Solution

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$$

P ( n - 1 , n - 1 )

$$

$$

P ( n , n - 1 )

$$

$$

\mathrm { r } ! \mathrm { P } ( \mathrm { n } , \mathrm { n } - \mathrm { r } )

$$

$$

( n - r ) \cdot P ( n , r )

$$