Solution

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,

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

$=\sqrt{16}$

$=4$

Solution

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.

Solution

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.

Solution

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.

Solution

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:

$15\times 2=30$

Solution

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:

$x+10=50+10=60$

Solution

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,

$C=160-36-24$

$C=100$

Solution

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,

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

Solution

Solution

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.

Solution

In each figure, the four symbols are moving one position in the clockwise direction.

From first figure to second figure:

Top-left symbol moves to top-right.
Top-right symbol moves to bottom-right.
Bottom-right symbol moves to bottom-left.
Bottom-left symbol moves to top-left.

The same clockwise shifting continues in the next figure also.

So, after the third figure, the required fourth figure will have the same clockwise shift.

This matches with option $1$.

Solution

Observe the pattern:

$28=2\ 8=2\ 2^3$

$327=3\ 27=3\ 3^3$

$464=4\ 64=4\ 4^3$

$5125=5\ 125=5\ 5^3$

So, the next term will be:

$6\ 6^3$

$6^3=216$

Therefore, the next term is:

$6216$

Solution

India is coded as $JLGEF$.

Check the pattern:

$I\to J$ means $+1$

$N\to L$ means $-2$

$D\to G$ means $+3$

$I\to E$ means $-4$

$A\to F$ means $+5$

So, the pattern is:

$+1,-2,+3,-4,+5$

Now apply this to $ROME$:

$R+1=S$

$O-2=M$

$M+3=P$

$E-4=A$

Therefore,

$ROME=SMPA$

Solution

Excel Spreadsheets are:

$S,T,U$

Read-only files are:

$Q,R,T,U$

Files stored only on Local Disk are:

$R,T,U$

Now, files which are Excel Spreadsheets, Read-only, and stored only on Local Disk are:

$T,U$

Solution

Observe the last row:

$9,\ 6,\ 5,\ 5$

Using the row-wise relation,

$\text{Required number}=(\text{first number}\times \text{third number})-(\text{second number}+\text{fourth number})$

So,

$?=(9\times 5)-(6+5)$

$?=45-11$

$?=34$

Solution

Initially, Vikram is facing West.

From West, left turn means South.
Then from South, right turn means West.
Then from West, right turn means North.
Then from North, left turn means West.
Finally, from West, right turn means North.

So, at the end, he is facing North.

Solution

Using the given conditions, Devika is fixed as the Operations analyst.

Bhavesh must sit between Devika and the Strategy analyst.

Also, Arjun cannot be Finance or HR, and the Strategy analyst is not Farah.

Farah sits second to the right of the Analytics analyst.

After arranging all persons and domains according to these conditions, the Finance analyst comes third to the left of Arjun.

The person at that position is Farah.

Therefore, Farah is the Finance analyst.