Permutations and Combinations Test 40

Result

Permutations and Combinations Test 40

Score
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Weekly Quiz Competition

Question 1
1 / -0

7, 11, 23, 51, 103 ?

A
186

B
188

C
185

D
187

E
none of these

Solution

$$7,11,23,51,103,?$$
$$7+4\times 1= 11 $$
$$11+4\times 3=23$$ $$\leftarrow $$ difference of 2
$$23+4\times 7=51$$ $$\leftarrow $$ difference of 4
$$51+4\times 13= 103$$ $$\leftarrow $$ difference of 6
$$103+4\times 21= 187$$ $$\leftarrow $$ difference will be of 8
Question 2
1 / -0

The number of words which can be made out of the letters of the word $$'MOBILE'$$ when consonants always occupy odd places is _______.

A
$$20$$

B
$$36$$

C
$$30$$

D
$$720$$

Solution
Question 3
1 / -0

13, 16, 22, 33, 51 ?

A
89

B
78

C
102

D
69

E
none of these

Solution

REF.Image
$$ 13,16,22,33,51, ?$$
Question 4
1 / -0

655, 439, 314, 250, 223 ?

A
215

B
210

C
195

D
190

E
none of these

Solution

Solution $$\rightarrow $$ Given terms are 655,439,314,250,223,?
As $$a_{1}=655$$
$$a_{2}= 439$$
$$a_{3}=314$$
$$a_{4}= 250$$
$$a_{5}= 223$$
$$a_{6}=?$$
So, $$a_{1}-a_{2}=655- 439= 216=6^{3}$$
$$a_{3}-a_{2}= 439- 314= 125=5^{3}$$
$$a_{3}-a_{4}= -250+314= 64=4^{3}$$
$$a_{4}-a_{5}=-223+250= 27=3^{3}$$
So, we can observe difference b/w terms are cubes
of 6,5,4,3 so, is similar way
$$a_{5}-a_{6}=2^{3}$$
$$223-a_{6}= 8$$
$$a_{6} = 215$$
So, we find next term is 215
Question 5
1 / -0

Using all digits $$2,3,4,5,6$$ how many even number can be formed

A
$$24$$

B
$$48$$

C
$$72$$

D
$$120$$

Solution

$$2,3,4,5,6$$
(Ref Image)
$$\Rightarrow 4!\times 3=24\times 3=72$$
Question 6
1 / -0

$$1+1.1!+2.2!+3.3!+...+n.n!$$ is equal to

A
$$n!$$

B
$$(n-1)!$$

C
$$(n+1)!$$

D
$$n$$

Solution

given,

$$1+1.1!+2.2!+3.3!+......+n.n!$$

$$=1+(2-1).1!+(3-1)!.2!+.......+(n+1-1).n!$$

$$=1+2.1!-1.1!+3.2!-1.2!+...+(n+1)n!-1n!$$

$$=1+2!-1!+3!-2!+4!-3!+......(n+1)!-n!$$

$$=1+(n+1)!-1$$

$$=(n+1)!$$
Question 7
1 / -0

Find the next term
$$210,209,205,196,180,?$$

A
$$138$$

B
$$77$$

C
$$155$$

D
$$327$$

Solution

$$T_1=210$$ $$,T_2=209,$$ $$T_3=205,$$ $$T_4=196,$$ $$T_5=180,$$ $$T_6=?$$

$$T_1-T_2=1^2\\$$
$$T_2-T_3=2^2\\$$
$$T_3-T_4=3^2\\$$
$$T_4-T_5=4^2\\$$
$$T_5-T_6=5^2\\$$
$$\implies T_6=T_5 - 5^2=180-25=155$$
Question 8
1 / -0

The number of was dividing $$52$$ cards amongst four players equally, are

A
$$\dfrac {52!}{(13!)^{4}}$$

B
$$\dfrac {52!}{(13!)^{4}4!}$$

C
$$\dfrac {52!}{(12!)^{4}4!}$$

D
None of these
Question 9
1 / -0

Find the next term
$$7,20,46,98,202,?$$

A
$$420$$

B
$$410$$

C
$$310$$

D
$$320$$

Solution
Question 10
1 / -0

The area of the triangle vertices $$(1,0),(7,0)$$ and $$(4,4)$$ is ___ square units.

A
$$8$$

B
$$10$$

C
$$12$$

D
$$14$$

Solution