RRB NTPC CBT 2 Level 6 May-2-2022 Shift 1 Exam Previous Question Paper with Solutions

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96) If $\frac1{1+\tan\theta}+\frac1{1-\tan\theta}$ = 4, 0°< 0 < 90°, then what is the value of (cosec²θ+sec²θ)

A) $\frac92$
B) $\frac43$
C) $\frac83$
D) $\frac52$

View Answer

A) $\frac92$

Explanation:We are given the equation:
$\frac{1}{1 + \tan \theta} + \frac{1}{1 - \tan \theta} = 4$
We are asked to find the value of $( \csc^2 \theta + \sec^2 \theta ), where ( 0^\circ < \theta < 90^\circ )$ .
Step 1: Simplify the given expression
Let’s simplify the left-hand side of the given equation:
$\frac{1}{1 + \tan \theta} + \frac{1}{1 - \tan \theta}$
To add these fractions, we take the common denominator:
$= \frac{(1 - \tan \theta) + (1 + \tan \theta)}{(1 + \tan \theta)(1 - \tan \theta)}$
The numerator simplifies to:
$(1 - \tan \theta) + (1 + \tan \theta) = 1 - \tan \theta + 1 + \tan \theta = 2$
The denominator simplifies using the difference of squares:
$(1 + \tan \theta)(1 - \tan \theta) = 1^2 - (\tan \theta)^2 = 1 - \tan^2 \theta$
Thus, the equation becomes:
$\frac{2}{1 - \tan^2 \theta} = 4$
Step 2: Solve for $( \tan^2 \theta )$
Now, solve for $( \tan^2 \theta )$ by cross-multiplying:
$2 = 4(1 - \tan^2 \theta)$
$2 = 4 - 4 \tan^2 \theta$
$4 \tan^2 \theta = 4 - 2 = 2$
$\tan^2 \theta = \frac{1}{2}$
Step 3: Find $( \csc^2 \theta + \sec^2 \theta )$
We know the following identities:
$\csc^2 \theta = 1 + \cot^2 \theta$
$\sec^2 \theta = 1 + \tan^2 \theta$
Since we have $( \tan^2 \theta = \frac{1}{2} )$ , we can calculate $( \sec^2 \theta )$ :
$\sec^2 \theta = 1 + \frac{1}{2} = \frac{3}{2}$
Next, to find $( \csc^2 \theta )$ , we use the identity $( \cot^2 \theta = \frac{1}{\tan^2 \theta} )$ :
$\cot^2 \theta = \frac{1}{\frac{1}{2}} = 2$
Thus,
$\csc^2 \theta = 1 + 2 = 3$
Now, adding $( \csc^2 \theta )$ and $( \sec^2 \theta )$ :
$\csc^2 \theta + \sec^2 \theta = 3 + \frac{3}{2} = \frac{6}{2} + \frac{3}{2} = \frac{9}{2}$
Final Answer:
The value of $( \csc^2 \theta + \sec^2 \theta )$ is $( \frac{9}{2} )$ , so the correct answer is:
$\boxed{\frac{9}{2}}$

97) The marginal propensity to consume (MPC) refers to the:

A) rate of change of consumption as income changes
B) savings per unit of income
C) consumption per unit of income
D) change in savings per unit change in income

View Answer

A) rate of change of consumption as income changes

98) In a certain code language,
‘see their dresses’ is coded as ‘ti ve su”,
‘dresses we see’ is coded as ‘nx ti ve’,
‘we see their party’ is coded as ‘fs ve nx su
(Note: All codes are two letter codes only)
What is the probable code for ‘party dresses’ in the given code language?

A) ti ve
B) na ti
C) ti fs
D) su na

View Answer

C) ti fs

Explanation:Given:
→1. “see their dresses” → “ti ve su”
→2. “dresses we see” → “nx ti ve”
→3. “we see their party” → “fs ve nx su”
Step 1: Decode each word and its corresponding code:
“see their dresses” → “ti ve su”
– “see” → ve
– “their” → ti
– “dresses” → su
“dresses we see” → “nx ti ve”
– “dresses” → su (matches from the first sentence)
– “we” → nx
– “see” → ve (matches from the first sentence)
“we see their party” → “fs ve nx su”
– “we” → nx (matches from the second sentence)
– “see” → ve (matches from the first sentence)
– “their” → ti (matches from the first sentence)
– “party” → fs
Step 2: Identify the code for “party dresses”:
– “party” → fs (from the third sentence).
– “dresses” → su (from the first and second sentences).
So, the code for “party dresses” is “fs su”.
Step 3: Match with the options:
Unfortunately, “fs su” is not listed among the options. Let’s carefully consider the choices and see if any of them seem plausible:
→1. Option 1: ti ve — This corresponds to “see their”, not “party dresses.”
→2. Option 2: na ti — This does not match any words in the analysis.
→3. Option 3: ti fs — This is close, but “ti” corresponds to “their”, and “fs” corresponds to “party”.
→4. Option 4: su na — This doesn’t match any words in the analysis.
Upon reviewing, “ti fs” seems the most likely, as it contains “fs” (for party) and “ti” (for their). So, the probable code for “party dresses” based on the available choices is:
– ti fs.

99) Which of the following internet protocols allows us to access the data over the World Wide Web?

A) DNS
B) SNMP
C) HTTP
D) FTP

View Answer

C) HTTP

100) Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements.
Statements:
Some athletes are businessmen.
All businessmen are rich.
Conclusions:
I. Some athletes are rich.
II. No athlete is rich.

A) Neither conclusion I nor II follows.
B) Both conclusions I and II follow.
C) Only conclusion II follows.
D) Only conclusion I follows.

View Answer

D) Only conclusion I follows.

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