Differentiation Test 47

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Differentiation Test 47

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Question 1
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 2
1 / -0

A
$$6$$

B
$$7$$

C
$$8$$

D
$$9$$

E
$$10$$

Solution
Question 3
1 / -0

Total number of ways of selecting two numbers from the set $${1,2,3,...90}$$ so that their sum is divisible by $$3$$ is

A
$$885$$

B
$$1335$$

C
$$1770$$

D
$$3670$$

Solution
Question 4
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
Question 5
1 / -0

The number of $$n$$ digit numbers which consists of the digits $$1$$ & $$2$$ only if each digits is to be used atleast once, is equal to $$510$$ then $$n$$ is equal to

A
$$7$$

B
$$8$$

C
$$9$$

D
$$10$$
Question 6
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 7
1 / -0

Find the missing number, if same rule is followed in all the three figures.

A
12

B
16

C
14

D
9

Solution

REF.Image.
Given

If we consider down two number of fig(i)

then their product is $$ \Rightarrow 4\times 16 = 64 $$

Now if we take square root then =$$ \sqrt{64}$$

$$ = 8 \to$$upper are we are getting.

similarly from fig (iii)

down number product $$ \Rightarrow 12 \times27 = 324$$

take square roots $$ = \sqrt{324} = 18 \to$$upper number.

So, similarly from fig(ii)

Down product = $$ 18 \times 8 = 144 $$

so square root = $$ \sqrt{144} = 12 \rightarrow $$ option A
Question 8
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 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

A student is to answer 10 out of 13 questions in an examination such that he must choose at least 4 from the first five questions. The number of choices available to him is

A
140

B
196

C
280

D
346

Solution

There would be two cases,

(1) When 4 is selected from first five and rest 6 from remaining 8.
This is done in $$^{5}C_{4}\times ^{8}C_{6}$$ ways.

(2) When all 5 are selected from first five and rest five from remaining 8.
This can be done in $$^{5}C_{5}\times ^{8}C_{5}$$ ways.

$$\therefore $$ A total of $$^{5}C_{4}\times ^{8}C_{6}+^{5}C_{5}\times ^{8}C_{5}$$

$$=5\times \cfrac{8!}{6!2!}+\cfrac{8!}{3!5!}$$

$$=\cfrac{5\times 8\times 7}{2}+\cfrac{8\times 7\times 8}{3\times 2}$$

$$=140+56=196\,ways$$