Part – 1 English
Was she sewing the curtains? (Passive Voice)
Answer: Were the curtains being sewed by her?
He told me that he———– do this work.
Answer: could
Even Children in the elementary schools ________ assigned homework.
Answer: are
Choose the correct verb: It is necessary for the government to ____ their people’s life better.
Answer: make
We were listening to the radio all evening. Which tense is this?
Answer: Past Continuous Tense
He ______ from the East Indies and was ___________ in the Thames. (Past Indefinite)
Answer: came, drowned
—————–raining outside?
Answer: it’s
Graham Bell invented Telephone in the year?
Answer: 1876
Objectives limiting the meaning of a noun showing either possession, demonstration, or number are called.
Answer: Limiting
He has been waiting ________ 3 hours.
Answer: For
He knew Jinnah. (Passive Voice)
Answer: Jinnah was known to him
Why do you object to _____ asset to the company?
Answer: him being taken on
This book contains maps. (Passive Voice)
Answer: Maps are contained in this book
She knows me. (Passive Voice)
Answer: I am known to her
He took me to hospital and the doctors operated me. (Passive Voice)
Answer: I was taken to hospital by him and operated on by the doctors
Cut the tree. (Passive Voice)
Answer: You are ordered to cut the tree
I have _________ my book.
Answer: Lost
I never miss a football match. I ____ fond of it since my childhood.
Answer: Have been
He said, “I have passed the examination.” (Indirect Speech)
Answer: He said that he had passed the examination
“The fool shot himself in the foot” is a ______ pronoun.
Answer: Reflexive Pronoun
Photo of his headmaster __________ in the newspaper.
Answer: resist adding
I hope you excuse my ______ early.
Answer: leaving
My brother fell asleep while he ____________
Answer: was reading the book
You will praise her very much. (Passive Voice)
Answer: She will be praised very much by you
They _________ a movie next weekend.
Answer: will watch
Abdullah __________ his leg when he played cricket last month.
Answer: broke
Who knows you? (Passive Voice)
Answer: To whom are you known?
_____ is a Relative Pronoun?
Answer: Who
______ are used in Present Perfect Continuous tense to show time of action?
Answer: Since & For
Who taught Political Science to you? (Passive Voice)
Answer: By whom was Political Science taught to you?
Who has deceived you? (Passive Voice)
Answer: By whom have you been deceived?
The king _________ by the rebel.
Answer: was killed
He ___________ flying a kite since morning.
Answer: has been
Part-I: Teaching Methodology
Which decision-making rule tries to equally satisfy both parties?
Answer: Compromise
Which branch of philosophy deals with knowledge, its structure, method and validity?
Answer: Epistemology
The teaching method recommended for elementary school science in Pakistan is _____?
Answer: Activity method
Frustration and anxiety produce ______ in an individual.
Answer: Tension
Who raised the slogan “Back to Nature”?
Answer: Naturalism (Rousseau)
Which does not fit into the scheme of educational goals of the Idealists?
Answer: Care of body
Which question have increasing good objectivity of marking?
Answer: Multiple type questions
Position power of the principal is limited to ______?
Answer: Both (Teachers and Students)
Interviews may be conducted to ______ adaptive behaviour of candidates.
Answer: Assess
The school headmaster operates the following administrative functions except?
Answer: Recruiting
Measurement answers the question?
Answer: How much
According to Einstein, education should be a fun rather than _____?
Answer: Pushed
Religious education is strongly advocated by _______?
Answer: Idealists
An outline of the topic of the subject to be covered in specific time is called ______?
Answer: Syllabus
The growth of organizational needs to be meshed with the ______ growth.
Answer: Individual
The effectiveness of the curriculum depends on the interest of the ______?
Answer: Teachers
______ evaluates how people perform and how activities have been done.
Answer: Appraisal
What is meant by the term “interference”?
Answer: Nepotism
A sound curriculum must be based on the needs and aspiration of _____?
Answer: Society
Two students A and B achieved 25 and 75 marks. What is percentile for A?
Answer: 50
Which one of the following terms is most inclusive?
Answer: Assessment
_____ involves a sequence of work.
Answer: Life style concept
Curriculum could not be built without which things?
Answer: All of these
Students are directly involved as experiential learning in _____?
Answer: Simulation
A choice made between two or more alternatives is called ______?
Answer: Decision
Part – II Mathematics
Q: Find the Fourier sine transformation for the function
f(x) = x e⁻ˣ
A: Formula:
Fₛ(s) = √(2/π) ∫₀^∞ x e⁻ˣ sin(sx) dx
Standard result استعمال کریں:
∫₀^∞ x e⁻ˣ sin(sx) dx = 2s / (1 + s²)²
Final Answer:
Fₛ(s) = √(2/π) × (2s / (1 + s²)²)
Q: Find the Laplace transform of
f(t) = e⁻⁴ᵗ sin 3t
A: L{sin 3t} = 3 / (s² + 9)
Shift property:
L{e⁻⁴ᵗ sin 3t} = 3 / ((s + 4)² + 9)
Look at this series: V, VIII, XI, XIV, _____ XX. What number should fill the blank?
Answer: XVII
Steps: V=5, VIII=8, XI=11, XIV=14. Series increases by 3 each time. 14+3=17 → XVII.
An Urdu class has 12 boys and 18 girls. Boys are what fraction of the class?
Answer: 2/5
Steps: Total students = 12+18=30. Fraction of boys = 12/30=2/5.
A figure whose all four sides are equal is called ____?
Answer: Square
Steps: All four sides equal → the shape is a square.
The Zoo had some lions and some parrots. The supervisor counted 15 heads and 50 legs. How many lions are there?
Answer: 10
Steps: If all were parrots, legs = 15×2=30. Actual legs=50 → extra legs = 50−30=20. Each lion contributes 2 extra legs → 20/2=10 lions.
The age of Ashraf is 15 years, 10 months and the age of Akmal is 17 years, 5 months. Find the ratio between their ages?
Answer: 10:11
Steps: Ashraf = 15×12+10=190 months, Akmal =17×12+5=209 months. Ratio=190:209=10:11.
3/4 + 5/8 – 1/2 =?
Answer: 0.875
Steps: Convert to same denominator 8: 3/4=6/8, 5/8=5/8, 1/2=4/8 → 6+5−4=7/8=0.875.
12 men can do a piece of work in 10 days. How many men would be required to do the same work in 8 days?
Answer: 15
Steps: 12×10 = M×8 → M=120/8=15 men.
Convert 2/5 into percentage?
Answer: 40%
Steps: 2/5 ×100=40%.
Complete the series: 0, 1, 3, 6, 10, ______?
Answer: 15
Steps: Add +1,+2,+3,+4,+5 → next=10+5=15.
Q360. Complete the series: 0, 1, 3, 6, 10, ______?
Answer: 15
Steps: Same as Q359.
A, B and C together earn Rs. 150 per day while A and C together earn Rs. 94 and B and C together earn Rs. 76. They daily earning of C is _____?
Answer: Rs. 20
Steps: (A+C)+(B+C)=94+76=170 → C=170−150=20.
1 square foot is equal to ______?
Answer: 144 square inches
Steps: 1 foot =12 inches → area =12×12=144 sq in.
Which number should come next in the pattern: 37, 34, 31, 28, _____?
Answer: 25
Steps: Series subtracts 3 each time → 28−3=25.
Which of the following is divisible by 12?
Answer: 4404
Steps: 4404 ÷12=367 → divisible.
If 100 Kg of meat is divided into packages of 4/7 kg each, the total number of packages will be ____?
Answer: 175
Steps: 100 ÷(4/7)=100×7/4=175.
There are 56 boys in a class of 140 students. What is the percentage of boys?
Answer: 40%
Steps: 56 ÷140 ×100=40%.
9 is 1/3% of what number?
Answer: 2700
Steps: 1/3% × X=9 → X=9×3×100=2700.
A is thrice as good as B in work. A is able to finish a job in 60 days less than B. They can finish the work in ______ days if they work together.
Answer: 22.5 days
Steps: B=90 days, A=30 days → Together = (30×90)/(30+90)=2700/120=22.5 days.
What is 25% of 200?
Answer: 50
Steps: 25/100 ×200=50.
Complete the series: 2, 4, 6, 8, ______?
Answer: 10
Steps: Series +2 → 8+2=10.
Complete the series: 1, 4, 9, 16, _____?
Answer: 25
Steps: Series of squares: 1²,2²,3²,4²,5²=25.
18 is 75 percent of what number?
Answer: 24
Steps: 18 ÷0.75=24.
30 % of 100 is equal to 3% of ____?
Answer: 1000
Steps: 30 ÷0.03=1000.
If 2^x =32, What is x^2 ?
Answer: 25
Steps: 2^5=32 → x=5 → x²=25.
120 men can do a work in 90 days, how many more men required to complete the same work in 40 days?
Answer: 150 more men
Steps: 120×90 = M×40 → M=270 → extra=270−120=150.
The population of a town increased from 1,75,000 to 2,62,500 in a decade. The average percent increase of population per year is _____?
Answer: 5%
Steps: Increase=2,62,500−1,75,000=87,500 → % increase=87,500/1,75,000×100=50% in 10 years → 50/10=5% per year.
Saeed receives a commission of Rs. 25 for every Rs. 250 worth of merchandise he sells; therefore, the percentage (%) of his commission is?
Answer: 10%
Steps: 25 ÷250 ×100=10%.
Ali ran around a 1/4 kilometer jogging track 17 times. How many kilometers did he run?
Answer: 4.25 km
Steps: 17×1/4=17/4=4.25 km.
One mile is equal to ______?
Answer: 1.6 km
Steps: 1 mile ≈1.6 km.
3/1000 written as a decimal is?
Answer: 0.003
Steps: 3 ÷1000=0.003.
Complete the series: 21, 20, 18, 15, 11, ______?
Answer: 6
Steps: Differences: −1,−2,−3,−4 → next −5 →11−5=6.
Who was the founder of the basic laws of Geometry?
Answer: Pythagoras
Steps: Pythagoras gave the basic rules of geometry.
Which is the most common measure of central tendency?
Answer: Mean
Steps: Mean (average) is used most often.
What percent of 120 are 90?
Answer: 75%
Steps: 90 ÷120 ×100=75%.
5448 rounded off to the nearest 1000 is _______?
Answer: 5000
Steps: 448<500 → round to 5000.
Izza gave 20% of her candies to Urooj and 15% to Mehwish. If she still had 520 candies, how many did she have originally?
Answer: 800
Steps: 100%−35%=65% left → 520 ÷0.65=800.
Which number can replace both the questions marks in 2/? = ?/50
Answer: 10
Steps: x² = 2×50=100 → x=10.
Complete the series: 3, 4, 6, 9, 13, ______?
Answer: 18
Steps: Differences +1,+2,+3,+4,+5 → 13+5=18.
Ramees buys goods worth Rs. 6650. He gets a rebate of 6% on it. After getting the rebate, he pays sales tax @ 10%. Find the amount he will have to pay for the goods.
Answer: Rs. 6876.10
Steps: 6650−6%=6251 → 6251+10%=6251+625.1=6876.1
If 15 men can do a piece of work in 20 days. In how many days can 25 men finish the same work?
Answer: 12
Steps: 15×20 = 25×D → D=300/25=12 days.
If 25 students took the exam and 4 of them fails. What percent of them passed?
Answer: 84%
Steps: Passed=25−4=21 → 21/25×100=84%.
What is the average of all prime numbers between 30 to 50?
Answer: 39.8
Steps: Primes=31,37,41,43,47 → sum=199 → average=199/5=39.8
A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets Rs. 1000 more than D. What is B’s share?
Answer: 2000
Steps: C−D=1 share=1000 → B=2 shares → 2×1000=2000
What is the value of the product? 5/5 x 5/10 x 5/15 x 5/20 x 5/25 = ?
Answer: 1/120
Steps: Multiply fractions: 1×1/2×1/3×1/4×1/5=1/120
If a square is rotated by 90 degrees, what shape does it become?
Answer: Square
Steps: Square stays square even after rotation.
Q396. The square of 35 is ____?
Answer: 1225
Steps: 35×35=1225
Which letter is midway between the 8th letter from A and 7th letter from Z?
Answer: N
Steps: 8th from A=H, 7th from Z=T → midway=(H+T)/2=N
40 is subtracted from 60% of a number, the result is 50. Find the number?
Answer: 150
Steps: 0.6x−40=50 → 0.6x=90 → x=150
The mean proportional of 4 and 16 is ______?
Answer: 8
Steps: √(4×16)=√64=8
A cyclist covers a distance of 750 meters in 2 minutes and 30 seconds. What is his speed in km/hr?
Answer: 18 km/hr
Steps: Time=2.5min=150s → speed=750/150=5 m/s → 5×18/5=18 km/hr
Find the average of 5/6, 4/3, 3/4?
Answer: 35/36
Steps: Sum=5/6+4/3+3/4=35/12 → Average=35/12÷3=35/36
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