Q&A: practice questions with answers

Concept: Netiquette (network etiquette) is the set of courteous behaviours expected online – respect for others' time and opinions, honesty and prompt, polite communication.

1. Responding promptly to messages respects the other person's time, a core netiquette rule ("respect other people's time and bandwidth").
2. Ignoring others' opinions (option A) clearly violates netiquette.
3. Sending respectful emails and citing sources are also good online conduct, but the expected answer here is prompt response to messages.

Yaad rakhein: Netiquette = be respectful, be honest, reply in time.

Answer: (D) Responding promptly to messages

Concept: Input devices send data into the computer; output devices present data to the user.

1. Mouse, Optical Character Reader and digitizer (graphics tablet) all feed data in → input devices.
2. A speaker converts electrical signals into sound for the user → output device.

Yaad rakhein: Monitor, printer, speaker, plotter, projector = output.

Answer: (B) Speaker

Concept: MS Word lets you split the document window into two panes to view two parts of the same document.

1. Shortcut: Ctrl + Alt + S (View tab → Split); pressing it again removes the split.
2. Ctrl + Y = Redo; Ctrl + Alt + C = © symbol; Alt + Shift + C = remove split/close pane in some versions.

Yaad rakhein: Ctrl + Alt + S = Split.

Answer: (C) Ctrl + Alt + S

Concept: DAC and MAC are the two classic access-control models in computer security.

1. DAC – Discretionary Access Control: the owner of a resource decides who may access it (e.g. file permissions in Windows/Linux).
2. MAC – Mandatory Access Control: the system enforces access by security labels/clearances (e.g. military systems, SELinux); users cannot change it.
3. "Direct" and "Multiple" are not access-control terms (MAC also means Media Access Control in networking, which is different).

Yaad rakhein: DAC = owner's Discretion; MAC = Mandatory by system.

Answer: (C) Discretionary Access Control and Mandatory Access Control

Concept: HTTP defines request methods that tell the server what action to perform on a resource.

1. GET requests (retrieves) a resource – every time a browser loads a web page it sends a GET.
2. POST sends data to the server (forms), PUT uploads/replaces a resource, DELETE removes one.

Yaad rakhein: GET = get the page; POST = post the form.

Answer: (D) GET

Concept: In an isosceles triangle the angles opposite equal sides are equal; the three angles add to ${180}^{\circ }$.

1. $AC=BC$ ⇒ $\angle A=\angle B=\frac{2}{5}\angle C-9$.
2. Sum: $2(\frac{2}{5}C-9)+C=180$ ⇒ $\frac{9}{5}C=198$ ⇒ $\angle C={110}^{\circ }$.
3. $\angle A=\angle B=44-9={35}^{\circ }$.
4. $\frac{2(110)-3(35)+35}{2}=\frac{220-105+35}{2}=\frac{150}{2}={75}^{\circ }$.

Trick: Since $\angle A=\angle B$, the expression simplifies to $\frac{2C-2A}{2}=C-A=110-35=75$.

Answer: (B) ${75}^{\circ }$

Concept: Simplify the bracket first, take its reciprocal, then divide by a fraction = multiply by its reciprocal.

1. $\frac{5}{6}+\frac{7}{9}=\frac{15+14}{18}=\frac{29}{18}$, so $\frac{1}{29/18}=\frac{18}{29}$.
2. $\frac{18}{29}÷\frac{5}{23}=\frac{18}{29}\times \frac{23}{5}=\frac{414}{145}=2\frac{124}{145}\approx 2.855$.
3. Compare with options: $2\frac{59}{69}\approx 2.855$, $2\frac{5}{6}\approx 2.833$, $2\frac{53}{61}\approx 2.869$, $4\frac{1}{27}\approx 4.04$. The value matches option A.

Trick: When exact fractions in options look odd, convert everything to decimals and pick the closest – it saves time in the exam.

Answer: (A) $2\frac{59}{69}$

Concept: For similar triangles, the ratio of areas equals the square of the ratio of corresponding sides.

1. Side ratio $=6:2$.
2. Area ratio $=6^2:2^2=36:4$ (i.e. $9:1$).
3. Option C gives exactly $36:4$ in the order mentioned.

Trick: Sides → square → areas; areas → square root → sides. For volumes of similar solids, cube the ratio.

Answer: (C) 36 : 4

Concept: Shadow length $=\frac{h}{\tan \theta }$; a higher sun gives a shorter shadow.

1. At ${30}^{\circ }$: shadow $=h\cot {30}^{\circ }=\sqrt{3}h$; at ${45}^{\circ }$: shadow $=h\cot {45}^{\circ }=h$.
2. Difference: $\sqrt{3}h-h=80$ ⇒ $h(\sqrt{3}-1)=80$.
3. $h=\frac{80}{\sqrt{3}-1}=\frac{80(\sqrt{3}+1)}{3-1}=40(\sqrt{3}+1)$ (units as given in the options).

Trick: For ${30}^{\circ }\to {45}^{\circ }$, $h=\frac{\text{decrease}}{\sqrt{3}-1}=\frac{\text{decrease}(\sqrt{3}+1)}{2}$ – rationalise directly.

Answer: (A) $40(\sqrt{3}+1)$

Concept: For $a{x}^2+bx+c=0$, discriminant $D=b^2-4ac$.

1. Here $a=7$, $b=-18$, $c=-11$.
2. $D=(-18{)}^2-4(7)(-11)=324+308=632$.

Trick: When $c$ is negative, $-4ac$ becomes positive – add, don't subtract. $D>0$ ⇒ two real distinct roots.

Answer: (C) 632

Concept: Distance between $(x_1,y_1)$ and $(x_2,y_2)$ is $\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}$.

1. $d=\sqrt{(-3-0{)}^2+(0-3{)}^2}=\sqrt{9+9}$.
2. $=\sqrt{18}=3\sqrt{2}$ units.

Trick: The points are the ends of the legs of a right isosceles triangle with legs 3 and 3, so the hypotenuse is $3\sqrt{2}$.

Answer: (B) $3\sqrt{2}$ units

Concept: When first term $a$ and last term $l$ are known, $S_n=\frac{n}{2}(a+l)$.

1. $574=\frac{n}{2}(36+46)=\frac{n}{2}\times 82=41n$.
2. $n=\frac{574}{41}=14$.

Trick: Number of terms = Sum ÷ (average of first and last term) = $574÷41=14$.

Answer: (B) 14

Concept: For $n$ independent tosses, $P(\text{exactly }r\text{ tails})=\left(\genfrac{}{}{0ex}{}{n}{r}\right){\left(\frac{1}{2}\right)}^n$.

1. $n=8$, $r=5$: $\left(\genfrac{}{}{0ex}{}{8}{5}\right)=\left(\genfrac{}{}{0ex}{}{8}{3}\right)=\frac{8\times 7\times 6}{6}=56$.
2. Total outcomes $=2^8=256$.
3. $P=\frac{56}{256}=0.21875\approx 0.22$.

Trick: $\left(\genfrac{}{}{0ex}{}{8}{5}\right)=\left(\genfrac{}{}{0ex}{}{8}{3}\right)$ – always use the smaller index to compute faster.

Answer: (A) 0.22

Concept: Total surface area of a cone $=\pi r(l+r)$, where slant height $l=\sqrt{r^2+h^2}$.

1. $l=\sqrt{{2.1}^2+{2.8}^2}=\sqrt{4.41+7.84}=\sqrt{12.25}=3.5\text{cm}$.
2. $\text{TSA}=\frac{22}{7}\times 2.1\times (3.5+2.1)=6.6\times 5.6=36.96{\text{cm}}^2$.

Trick: 2.1, 2.8, 3.5 is the 3-4-5 triplet × 0.7 – spot it to get $l$ instantly. Only CSA would be $\pi rl=23.1$.

Answer: (D) 36.96 cm²

Concept: $X\cap Y$ (intersection) contains only the elements common to both sets.

1. $X=\{a,b,c,d\}$, $Y=\{f,b,d,g\}$.
2. Elements present in both: $b$ and $d$ ⇒ $X\cap Y=\{b,d\}$.
3. $\{a,b,c,d,g,f\}$ would be the union $X\cup Y$.

Trick: ∩ looks like a cap – "common" elements only; ∪ looks like a cup – "collect everything" (union).

Answer: (D) { b, d }

Concept: Two dice give $6\times 6=36$ equally likely outcomes; probability = favourable ÷ total.

1. Pairs with sum 8: (2,6), (3,5), (4,4), (5,3), (6,2) – 5 outcomes.
2. $P=\frac{5}{36}$.

Trick: For two dice, number of ways for sum $s$ is $s-1$ for $s\le 7$ and $13-s$ for $s\ge 7$; sum 8 → $13-8=5$.

Answer: (A) $\frac{5}{36}$

Concept: Identify the figure from side lengths and angles of the given vertices.

1. Take the points in order: $A(9,0)$, $B(9,6)$, $C(-9,6)$, $D(-9,0)$.
2. $AB=6$ (vertical), $BC=18$ (horizontal), $CD=6$, $DA=18$.
3. Adjacent sides are horizontal and vertical, so every angle is ${90}^{\circ }$; opposite sides equal but adjacent sides unequal ($6\ne 18$) → a rectangle, not a square.

Trick: Same $x$ for two points → vertical side; same $y$ → horizontal side. All right angles with unequal adjacent sides = rectangle.

Answer: (B) rectangle

Concept: $T_n=a+(n-1)d$; the difference of two terms gives $d$ directly.

1. $T_{12}-T_8=4d=478-82=396\Rightarrow d=99$.
2. $T_{50}=T_{12}+38d=478+38\times 99=478+3762=4240$.
3. (Check: $a=82-7\times 99=-611$; $-611+49\times 99=4240$ ✓)

Trick: $T_m-T_n=(m-n)d$ – no need to find $a$.

Answer: (D) 4240

Concept: Read the value from the graph and convert to a percentage of the maximum marks (50).

1. From the graph, Devi's marks in Punjabi $=45$ (out of 50).
2. Percentage $=\frac{45}{50}\times 100=90\%$.
3. Other points: Math 40 (80%), English 25 (50%), History 35 (70%).

Trick: Out of 50 → simply double the marks to get the percentage.

Answer: (D) 90%

Concept: Division and multiplication are done left to right before subtraction.

1. $9÷6=1.5$.
2. $1.5\times 6=9$.
3. $38-9=29$.

Trick: $÷6\times 6$ cancels out, leaving $38-9$.

Answer: (A) 29