Sequences and Series Test 44

Result

Sequences and Series Test 44

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
1 / -0

The line $$\displaystyle 3x+2y=24$$ meets x-axis at A and y-axis at B. The perpendicular bisector of $$\displaystyle \overline { AB } $$ meets the line through (0, -1) and parallel to x-axis at C. Find the area of $$\displaystyle \Delta ABC$$.

A
85 $$\displaystyle { units }^{ 2 }$$

B
87 $$\displaystyle { units }^{ 2 }$$

C
90 $$\displaystyle { units }^{ 2 }$$

D
91 $$\displaystyle { units }^{ 2 }$$

Solution
Question 2
1 / -0

Two classrooms A and B having capacity of $$25$$ and $$(n-25)$$ seats respectively. $$A_n$$ denotes the number of possible seating arrangements of room $$'A'$$, when 'n' students are to be seated in these rooms, starting from room $$'A'$$ which is to be filled up to its capacity. If $$A_n-A_{n-1}=25!(^{49}C_{25})$$ then 'n' equals:

A
$$50$$

B
$$48$$

C
$$49$$

D
$$51$$

Solution

Given $$A_n=nC_{25} \cdot 25!$$

$$A_{n-1}={n-1}C_{25} \cdot 25!$$

Hence $$nC_{25} \cdot 25! - (n-1)C_{25} \cdot 25!=25! 49C_{25}$$

$$\Rightarrow (n-1)C_{25}+(n-1)C_{24}-(n-1)C_{25}=49C_{24}$$

$$\Rightarrow n-1=49$$

$$\Rightarrow n=50$$
Question 3
1 / -0

Consider the following statements:
$$S_1: \lim_\limits{x \to 0} \dfrac{[x]}{x}$$ is an indeterminate form (where [.] denotes greatest integer function).
$$S_2: \lim_\limits{x\to\infty}\dfrac{sin(3^x)}{3^x}=0$$
$$S_3: \lim_\limits{x \to \infty}\sqrt{\dfrac{x- sinx}{x+cos^2x}}$$ does not exist.
$$S_4: \lim_\limits{n\to \infty}\dfrac{(n+2)!+(n+1)!}{(n+3)! }(n \in N=0$$
State, in order, whether $$S_1, S_2, S_3, S_4$$ are true or false

A
FTFT

B
FTTT

C
FTFF

D
TTFT

Solution
Question 4
1 / -0

Observe the pattern carefully
$$11\times11=121$$
$$111\times111=12321$$
$$1111\times1111=\,?$$

A
$$12345321$$

B
$$123421$$

C
$$1234321$$

D
$$12468$$

Solution

$$11\times11=121$$
$$111\times111=12321$$
$$1111\times1111=1234321$$
Question 5
1 / -0

How many $$10-digit$$ numbers can be formed by using the digits $$1$$ and $$2$$?

A
$$^{10}{P}_{2}$$

B
$$^{10}{C}_{2}$$

C
$${2}^{10}$$

D
$$10\ !$$

Solution

Each place of a ten digit number can be fixed by any of the two digits. So, the number of ways to form a ten digit number is $${2^{10}}$$.
Question 6
1 / -0

There are infinite, alike, blue, red, green and yellow balls. Find the number of ways to select $$10$$ balls.

A
$$286$$

B
$$84$$

C
$$715$$

D
None of these.

Solution
Question 7
1 / -0

What is the value of $$^nC_n$$?

A
zero

B
$$1$$

C
$$n$$

D
$$n!$$

Solution
Question 8
1 / -0

A
$$6$$

B
$$7$$

C
$$8$$

D
$$9$$

E
$$10$$

Solution
Question 9
1 / -0

A library has $$'a'$$ copies of one book, $$'b'$$ copies of each of two books, $$'c'$$ copies of each of three books, and single copy each of $$'d'$$. The total number of ways in which these books can be arranged in a row is

A
$$\dfrac{(a+b+c+d)!}{a!b!c!}$$

B
$$\dfrac{(a+2b+3c+d)!}{a!(b!)^{2}(c!)^{3}}$$

C
$$\dfrac{(a+2b+3c+d)!}{a!b!c!}$$

D
none of these

Solution
Question 10
1 / -0

In a certain examination paper, there are $$n$$ question. For $$j = 1, 2....n$$, there are $$2^{n-j}$$ students who answered $$j$$ or more questions wrongly. If the total number of wrong answers is $$4095$$, then the value of $$n$$ is:

A
$$12$$

B
$$11$$

C
$$10$$

D
$$9$$

Solution