Permutations and Combinations Test 50

Result

Permutations and Combinations Test 50

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Weekly Quiz Competition

Question 1
1 / -0

If $$\displaystyle\sum^m_{k=1}(k^2+1)k!=1999(2000!)$$, then m is?

A
$$1999$$

B
$$2000$$

C
$$2001$$

D
$$2002$$

Solution
Question 2
1 / -0

If $$24 + 37 = 7,12 + 18 = 3$$, then 54+21=?

A
11

B
9

C
12

D
3

Solution
Question 3
1 / -0

In the following number series,one number is wrong.find out the ?

1,2,8,33,149,765,4626

A
$$33$$

B
$$8$$

C
$$149$$

D
$$0$$

Solution

1,2,8,33,149,765,4626
Carefully analyzing the series, we can see the following pattern
$$1\times 1+(1)^{2}=2$$
$$2\times 2+(2)^{2}=8$$
$$8\times 3+(3)^{2}=33$$
$$33\times 4+(4)^{2}=148$$
$$148\times 5+(5)^{2}=765$$
$$765\times 6+(6)^{2}=4626$$
So, we can clearly see that 149 is the wrong entry in the series.
Question 4
1 / -0

How many Pythagorean triangles are there with integer sides and one leg is Ramanujan Number 1729 .

A
$$10$$

B
$$11$$

C
$$12$$

D
$$13$$

E
None
Question 5
1 / -0

The number of the three digits numbers having only two consecutive digits identical is:

A
153

B
160

C
180

D
161

Solution
Question 6
1 / -0

$$10$$ IIT and $$2$$ NIT students sit at random in a row, and then number of ways in which exactly $$3$$ IIT students sit between $$2$$ NIT students is

A
$$16\times 10!$$

B
$$15\times 10!$$

C
$$10\times 16!$$

D
$$None\ of\ these$$

Solution
Question 7
1 / -0

The number of 5 letter words formed using letters of word "CALCULUS" is

A
$$280$$

B
$$15$$

C
$$1110$$

D
$$56$$

Solution
Question 8
1 / -0

Find the missing number, if a certain rule is followed
$$1$$ $$9$$ ?
$$2$$ $$12$$ $$14$$
$$3$$ $$117$$ $$105$$
either row-wise or column-wise.

A
$$7$$

B
$$8$$

C
$$11$$

D
$$9$$

Solution
Question 9
1 / -0

Direction: In a given question, one number is missing in the series. you have to understand the pattern of the series and insert the number
JN 28 27 GP
CE 12 45 TU
LR ? ? MS

A
$$34, 36$$

B
$$35, 35$$

C
$$30, 32$$

D
$$30, 41$$
Question 10
1 / -0

The area of the triangle whose co-ordinates are $$(2012, 7), (2014, 7)$$ and $$(2014, a)$$ is $$1 \,sq$$ unit. The sum of possible values of $$a$$ is

A
$$6$$

B
$$8$$

C
$$14$$

D
$$16$$

Solution