NIMCET Critical Thinking FLCD Previous Year Questions (PYQs) – Page 1 of 2

Let

$\sqrt{x+y}=a$

and

$\sqrt{y+z}=b$

Given,

$2\sqrt{x+y}-3\sqrt{y+z}=2$

So,

$2a-3b=2$

Also,

$x=a^2-y$

and

$z=b^2-y$

Now use the second condition:

$4x-5y-9z=8$

$4(a^2-y)-5y-9(b^2-y)=8$

$4a^2-4y-5y-9b^2+9y=8$

$4a^2-9b^2=8$

So,

$(2a-3b)(2a+3b)=8$

Since $2a-3b=2$,

$2(2a+3b)=8$

$2a+3b=4$

Now solve:

$2a-3b=2$

$2a+3b=4$

Adding both equations,

$4a=6$

$a=\frac{3}{2}$

Now,

$2a+3b=4$

$3+3b=4$

$3b=1$

$b=\frac{1}{3}$

Now,

$20x+38y+18z+1$

$=20(a^2-y)+38y+18(b^2-y)+1$

$=20a^2+18b^2+1$

Also,

$9y+9z+2=9(y+z)+2=9b^2+2$

Now substitute $a=\frac{3}{2}$ and $b=\frac{1}{3}$.

Numerator:

$20a^2+18b^2+1=20\left(\frac{3}{2}\right)^2+18\left(\frac{1}{3}\right)^2+1$

$=20\cdot \frac{9}{4}+18\cdot \frac{1}{9}+1$

$=45+2+1$

$=48$

Denominator:

$9b^2+2=9\left(\frac{1}{3}\right)^2+2$

$=1+2$

$=3$

Therefore,

$\sqrt{\frac{20x+38y+18z+1}{9y+9z+2}}=\sqrt{\frac{48}{3}}$

$=\sqrt{16}$

$=4$

Mira's mother-in-law means the mother of Mira's husband.

So, Mira's mother-in-law's mother means the grandmother of Mira's husband.

It is given that Mira's mother-in-law's mother is my grandmother.

So, Mira's husband's mother can be my aunt.

That means Mira's husband is my aunt's son.

Also, all my mother's offsprings are unmarried, so Mira cannot be my brother's wife.

Therefore, Mira is the wife of my aunt's son.

It is given that $C$ and $B$ must be on the same team.

Also, $C$ cannot be in Tech, so $B$ and $C$ must be either in Travel or Beauty.

Since $G$ must be in Travel and $F$ cannot be in Travel, $F$ must be in Beauty or Tech.

Also, $F$ must be with either $A$ or $B$, but not both.

Since $A$ cannot be in Beauty, if Beauty contains $F$, then $F$ must be with $B$.

So, the Beauty team becomes:

$B,F,C$

This satisfies all conditions.

The statement says that Indian children are talented, but they are weak in Science and Mathematics.

Course I talks about teaching and textbooks not being available in mother language. This may be a possible reason, but it is not directly connected to weakness in Science and Mathematics.

Course II says that education based on experiments in both subjects is lacking. Since Science and Mathematics require conceptual and experimental understanding, this course of action is more directly related.

Therefore, only II follows.

Given,

First : Second $=2:3$

Second : Third $=5:8$

Make the second term common.

LCM of $3$ and $5$ is $15$.

So,

First : Second $=10:15$

Second : Third $=15:24$

Therefore,

First : Second : Third $=10:15:24$

Sum of ratios:

$10+15+24=49$

Given sum of numbers is $98$.

So, one part is:

$\frac{98}{49}=2$

Second number is:

$15\times 2=30$

Let the balls faced by Lara be $x$.

Runs scored by Sachin are $10$ more than balls faced by Lara.

So,

Sachin's runs $=x+10$

Sachin faced $10$ balls less than Lara.

So,

Sachin's balls $=x-10$

Also, Sachin's balls are $5$ less than Lara's runs.

So,

Lara's runs $=x-5$

Together they scored $105$ runs.

Therefore,

$(x+10)+(x-5)=105$

$2x+5=105$

$2x=100$

$x=50$

So, Sachin's runs are:

$x+10=50+10=60$

Let the number of correct answers be $C$, wrong answers be $W$, and unanswered questions be $U$.

Total questions:

$C+W+U=160$ .....$(1)$

According to the first condition:

$C-\frac{W}{4}-\frac{U}{2}=79$ .....$(2)$

According to the second condition:

$C-\frac{W}{2}-\frac{U}{4}=76$ .....$(3)$

Subtract $(3)$ from $(2)$:

$\left(C-\frac{W}{4}-\frac{U}{2}\right)-\left(C-\frac{W}{2}-\frac{U}{4}\right)=79-76$

$-\frac{W}{4}+\frac{W}{2}-\frac{U}{2}+\frac{U}{4}=3$

$\frac{W}{4}-\frac{U}{4}=3$

$W-U=12$ .....$(4)$

From $(1)$,

$C=160-W-U$

Put this in $(2)$:

$160-W-U-\frac{W}{4}-\frac{U}{2}=79$

$160-\frac{5W}{4}-\frac{3U}{2}=79$

$\frac{5W}{4}+\frac{3U}{2}=81$

Multiply by $4$:

$5W+6U=324$ .....$(5)$

From $(4)$,

$W=U+12$

Put in $(5)$:

$5(U+12)+6U=324$

$5U+60+6U=324$

$11U=264$

$U=24$

So,

$W=24+12=36$

Now,

$C=160-36-24$

$C=100$

The word is:

$LOGIC$

Alphabet positions are:

$L=12,\ O=15,\ G=7,\ I=9,\ C=3$

Now, according to the new rule, every vowel is shifted by $+2$ before converting to its numerical position.

Vowels in $LOGIC$ are $O$ and $I$.

So,

$O+2=Q$

Position of $Q$ is $17$.

Also,

$I+2=K$

Position of $K$ is $11$.

Consonants remain unchanged:

$L=12,\ G=7,\ C=3$

Therefore,

$LOGIC=12-17-7-11-3$

The paragraph says that the rules were formulated under the new Code on Social Security and states can notify their own rules by taking cue from the central ones.

This shows that the Code of Social Security rules are connected with the central government.

Option $1$ is incorrect because eligibility is not automatic; workers need to satisfy the required number of working days.

Option $2$ is incorrect because workdays are cumulative across platforms.

Option $3$ is incorrect because the paragraph does not exclude such platforms.

Therefore, the closest conclusion is that the Code of Social Security is given by the central government.