Sequences and Series Test

Result

Sequences and Series Test - 66

Score
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Rank
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TIME Taken - -

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Weekly Quiz Competition

Question 1
1 / -0

Let three matrices are $$A=\left[ \begin{matrix} 2 & 1 \\ 4 & 1 \end{matrix} \right] ;A=\left[ \begin{matrix} 2 & 4 \\ 2 & 3 \end{matrix} \right] $$ and $$C=\left[ \begin{matrix} 3 & -4 \\ -2 & 3 \end{matrix} \right] $$, then $${ t }_{ r }(A)+{ t }_{ r }\left( \frac { ABC }{ 2 } \right) +{ t }_{ r }\left( \frac { A{ (BC) }^{ 2 } }{ 4 } \right) +{ t }_{ r }\left( \frac { A{ (BC) }^{ 3 } }{ 8 } \right) +.......+\infty $$ is equal to -

A
6

B
9

C
12

D
None

Solution
Question 2
1 / -0

The average expenditure of Sharma for the January to June is Rs. 4200 and he spent Rs. 1200 in January and Rs.1500 in July. The average expenditure for the months of February to July is:

A
4250

B
6520

C
2320

D
9999
Question 3
1 / -0

The value of $$\cot { \left( \sum _{ n=1 }^{ 23 }{ \cot { ^{ -1 } } } \left( 1+\sum _{ k=1 }^{ n }{ 2k } \right) \right) } $$ is

A
$$\dfrac { 23 }{ 25 } $$

B
$$\dfrac { 25 }{ 23 } $$

C
$$\dfrac { 23 }{ 24 } $$

D
$$\dfrac { 24 }{ 23 } $$

Solution
Question 4
1 / -0

The sum of the series (1 + 2)+(1+2+$${ 2 }^{ 2 }$$)+$$(1+2+{ 2 }^{ 2 }+{ 2 }^{ 3 })+.....$$ up to n terms is

A
$${ 2 }^{ n+2 }-n-4$$

B
$$2({ 2 }^{ n }-1)-n$$

C
$${ 2 }^{ n+1 }-n$$

D
$${ 2 }^{ n+1 }-1$$

Solution
Question 5
1 / -0

There are n A.M.'s between 3 and 29 such that $$6^{th} mean:(n-1)^{th} mean = 3:5$$, then the value of n, is

A
10

B
11

C
12

D
none of these

Solution
Question 6
1 / -0

If first and $$( 2 n - 1 )^{th}$$ terms of an $$A . P , G . P .$$ and $$H . P$$ . are equal and their $$n th$$ terms are $$a , b , c$$ respectively , then

A
$$a = b = c$$

B
$$a + c = b$$

C
$$a > b > c$$ and $$ac - b^2 = 0$$

D
none of these

Solution
Question 7
1 / -0

The $$20^{th}$$ term of the series $$2\frac{1}{2}+1\frac{7}{13}+1\frac{1}{9}+\frac{20}{23}+......$$ is

A
20/103

B
20/97

C
10/113

D
none of these
Question 8
1 / -0

21,25,52,68,193,?

A
229

B
242

C
257

D
409

Solution
Question 9
1 / -0

49,64,?,100,121

A
74

B
80

C
75

D
81

Solution
Question 10
1 / -0

1001,1004,1012,1027,?

A
1051

B
1050

C
259

D
269

Solution