Q. What is the 101st term of the sequence: 1, 4 7, 10, …. ?
Answer: 301 Solution This is an arithmetic sequence with common difference of 3. The first element is 1, and total elements are 101. So, a1 = 1, d = 3 and n = 101. So, by using the formula of nth term of an arithmetic sequence, we have
Q. What is the sum of the sequence: 10, 20, 30, 40, …. , 1000 ?
Answer: 50,500 This is an arithmetic sequence with common difference of 10. The first element is 10, and total elements are 100 (Total elements in the sequence 10, 20, 30, … , 1000 are 100). And, the last element is 1000. So, a1 = 10, an = 1000, d = 10 and n = 100. So, by using the formula for the sum of n elements of an arithmetic sequence, we have
Q. What is the solution of the equation
Answer: Solution
Q. If , then what is the value of the function
Answer: 12 Solution
Q. What comes next in the sequence: 2, 3, 7, 23, __?
Answer: 87 Solution Multiply the element with 4 and then subtract 5 to obtain the next term
Q. What is the value of in the equation
Answer: 3 Solution
Q. How many feet there are in 4.5 meters? If 1 meter = 3.281 feet.
Answer:(C) 14.76 Solution
3.281 ⇒ three digits after decimal 4.5 ⇒ one digit after decimal. Hence, 14.7645 ⇒ (3+1=4 digits after decimal)
Q. If person-A can complete a particular work in 10 days and person-B can completes that same work in 12 days. How much time it will take if they work together?
Answer: 5 days and 11 hours Solution
Q. A student obtained the marks: 60, 50, 70, 65 and 85 in Physics, Chemistry, Statistics, English and Biology respectively, and 0 marks in Mathematics. What the average marks he obtained?
Answer: 55 Solution Average is calculated as, sum of elements divided by number of elements, that is
Q. What are values of and in the following pair of equations
Answer: and Solution
Q. What is the geometric mean of the numbers: 2, 4 and 8?
Answer: 4 Solution By applying formula for calculating geometric mean, we have
Q. What is the 71st term of the sequence: 4, 7, 10, 13, …. ? (A) 214 (B) 216 (C) 218 (D) 220
Answer: 214 Solution This is an arithmetic sequence with common difference 3, and the first term is 4. By applying, formula for finding the nth term of an arithmetic sequence we have
Q. What is the sum of the sequence: 5, 10, 15, …., 5000 ? (A) 250,2200 (B) 250,2300 (C) 250,2400 (D) 250,2500
Answer: 250,2500 Solution This is an arithmetic sequence with common difference 5, the first term is 5, and the last term is 5000. By applying, formula for finding the sum of the n terms of an arithmetic sequence, we have
NOTE: There are 1000 terms from 5 to 5000, so n = 1000.
Question: If x is an odd number, which of the following is definitely even? A. x² B. x(x + 1) C. x + 2
Time to test-drive each option:
A: An odd number squared is still odd (3² = 9). Nope.
B: Odd × Even (x + 1 is even) = Even. Ding ding ding!
C: Odd + 2 = Still odd (5 + 2 = 7). Not it.
Answer:B
Question: Solve for x: x² – 5x + 6 = 0
Let’s not overthink it. This is a classic “factor me!” problem.
Try to break it into two brackets:
(x – 2)(x – 3) = 0
Set each part to zero:
x = 2 or x = 3
Answer:x = 2 or 3
Question: What’s the area of a circle with a radius of 7?
Use this formula: Area = π × r² = π × 7² = π × 49 = 49π
No need to punch numbers into a calculator unless they ask for a decimal.
Answer:49π
Question: A phone goes from $80 to $100. What’s the percent increase?
Let’s break it down:
The change = 100 – 80 = $20
Now compare: 20 is what percent of 80?
20 ÷ 80 = 0.25 → That’s 25%
Answer:25% increase
Tip: formula: (New – Old) ÷ Old × 100
Question: You’ve got 5 liters of a 50% alcohol solution. How much of a 20% solution should you add to get a 30% blend?
Think it through:
You already have 5 liters with 50% alcohol = 2.5 liters of pure alcohol
You’re adding x liters of 20% alcohol = 0.2x
Total solution becomes (5 + x) liters
Total alcohol: 2.5 + 0.2x
Set up the equation:
(2.5 + 0.2x) / (5 + x) = 0.3
Solving that gives you: x = 10
Answer:Add 10 liters of the 20% solution
Question: If 3 < 2x + 1 < 9, what values can x take?
Split it up:
3 < 2x + 1 → Subtract 1 → 2x > 2 → x > 1
2x + 1 < 9 → Subtract 1 → 2x < 8 → x < 4
So x has to be between 1 and 4
Answer:1 < x < 4
Question: A bag has 3 red and 2 blue balls. You pick one at random. What’s the chance it’s red?
So simple it hurts:
Total balls = 3 + 2 = 5
Red balls = 3
So, chance of red = 3 out of 5 = 3/5
Answer:3/5
Question: What’s the slope of a line through points (1, 2) and (4, 6)?
Use the slope formula: Change in y ÷ Change in x = (6 – 2) ÷ (4 – 1) = 4 ÷ 3
Answer:4/3
Q. If the base of a triangle is 8 cm and the height is 4 cm, what would be the area of the triangle? Answer: 16 cm² Explanation: Area of Triangle = ½ × Base × Height = ½ × 8 × 4 = 16 cm²
Q. If a total of 15 kg of solid material is placed into a 100-liter container, what would be the density of the solid material? Answer: 0.15 kg/liter Explanation: Density = Mass ÷ Volume = 15 ÷ 100 = 0.15 kg/liter
Q. A student obtained 16, 50, 70, 65 and 85 marks in five subjects. What would be the average marks? Answer: 57.2 Explanation: Total Marks = 16 + 50 + 70 + 65 + 85 = 286 Average = 286 ÷ 5 = 57.2
Q. If 20/x + 16/x = 12, then the value of x is? Answer: 3 Explanation: 20/x + 16/x = 12 36/x = 12 x = 36 ÷ 12 x = 3
Q. What is the geometric mean of 2, 4 and 8? Answer: 4 Explanation: Geometric Mean = ∛(2 × 4 × 8) = ∛64 = 4
Q. What is 75% of 200? Answer: 150 Explanation: 75% of 200 = (75/100) × 200 = 150
Q. What is the value of 4 + 4 − 4 × 4 ÷ 4? Answer: 4 Explanation: According to DMAS rule: 4 ÷ 4 = 1 4 × 1 = 4 Now, 4 + 4 − 4 = 8 − 4 = 4
Q. The ages of Sohail, Afzal and Bilal are 17, 16 and 12 years respectively. If the age of Aslam is also included, the average age increases by 5 years. What is the age of Aslam? Answer: 35 years Explanation: Initial Average = (17 + 16 + 12) ÷ 3 = 45 ÷ 3 = 15 years
New Average = 15 + 5 = 20 years
Total age of 4 persons = 20 × 4 = 80 years
Age of Aslam = 80 − 45 = 35 years
Q. If 6 men can complete a work in 15 hours, how many hours will 10 men take to complete the same work at the same speed? Answer: 9 hours Explanation: Men₁ × Hours₁ = Men₂ × Hours₂
6 × 15 = 10 × Hours
90 = 10 × Hours
Hours = 90 ÷ 10 = 9 hours
Q. If the total distance is 540 km and the total time is 3 hours 20 minutes + 2 hours 40 minutes, what would be the average speed? Answer: 90 km/h Explanation: Total Time = 3 hours 20 minutes + 2 hours 40 minutes = 6 hours
Average Speed = Total Distance ÷ Total Time = 540 ÷ 6 = 90 km/h
Q. An angle measuring less than 90° is called? Answer: Acute Angle Explanation: An angle less than 90° is called an acute angle.
Q. The sum of three consecutive integers is 72. What is the smallest integer? Answer: 23 Explanation: Let the integers be x, x+1 and x+2. x + (x+1) + (x+2) = 72 3x + 3 = 72 3x = 69 x = 23
Q. Which of the following is not a sublimable solid material? (Glucose, Sodium Chloride, Iodine, Camphor) Answer: Glucose and Sodium Chloride Explanation: Iodine and Camphor sublime, while Glucose and Sodium Chloride do not.
Q. What is the sum of the interior angles of a triangle? Answer: 180° Explanation: The sum of all interior angles of a triangle is always 180°.
Q. The volume of a cylinder is calculated by V = πr²L. If r = 3 cm and L = 10 cm, find the volume. Answer: 90π cm³ Explanation: V = π × 3² × 10 = π × 9 × 10 = 90π cm³
Q. If the numerator is greater than or equal to the denominator, the fraction is called? Answer: Improper Fraction Explanation: In an improper fraction, numerator ≥ denominator.
Q. What is the 101st term of the sequence 1, 4, 7, 10, …? Answer: 301 Explanation: a = 1, d = 3 a₁₀₁ = 1 + (101 − 1) × 3 = 301
Q. A total of Rs.129,000 is divided among 5 sons, 4 daughters and 3 nephews. Each son gets 5 times and each daughter gets 4 times the amount received by each nephew. What is the amount each nephew gets? Answer: Rs. 2931.82 (approximately) Explanation: Let nephew’s share = x 5(5x) + 4(4x) + 3(x) = 129000 25x + 16x + 3x = 129000 44x = 129000 x = 2931.82
Q. If 1/8 of a pencil is black, 1/4 is white and the remaining 5.25 cm is grey, what is the total length of the pencil? Answer: 8.4 cm Explanation: Remaining fraction = 1 − (1/8 + 1/4) = 5/8 5/8 × L = 5.25 L = 8.4 cm
Q. A circle has radius 4 m. If an object travels 14 m along its circumference, find the displacement. Answer: 8 m Explanation: Maximum displacement across the circle is its diameter. Diameter = 2 × 4 = 8 m
Q. A car travels 300 km in 3 hours 20 minutes and another 280 km in 2 hours 80 minutes. Find the average speed. Answer: 87.1 km/h Explanation: Total Distance = 580 km Total Time = 6 hours 40 minutes = 6.67 hours Average Speed = 580 ÷ 6.67 = 87.1 km/h
Q. If sin(60° + X) = cos(30°), then X = ? Answer: 0° Explanation: cos(30°) = sin(60°) Therefore, X = 0°
Q. If x + y = 6 and xy = 5, then x² + y² = ? Answer: 26 Explanation: (x + y)² = x² + y² + 2xy 36 = x² + y² + 10 x² + y² = 26
Q. Which of the following is an arithmetic sequence? Answer: 31, 32, 33, 34 Explanation: The common difference is 1.
Q. Which of the following is irrational? Answer: √11 Explanation: √11 cannot be expressed as a rational number.
Q. Which of the following is not a valid type of root in a quadratic equation? Answer: Cubic Explanation: Cubic refers to third-degree equations, not root types.
Q. What is the value of 180° in radians? Answer: π radians Explanation: 180° = π radians.
Q. What type of roots does the equation x² + 4 = 0 have? Answer: Imaginary Roots Explanation: x² = −4 x = ±2i
Q. If abc = a² and ac = 2, then the value of b is? Answer: a²/2 Explanation: b(ac) = a² b(2) = a² b = a²/2
Q. If 2ᵃ × 2ᵇ = 3ᶜ, what is the value of a + b? Answer: Cannot be determined Explanation: No unique value can be found without additional information.
Q. In how many ways can 5 children be arranged in a line? Answer: 120 Explanation: 5! = 5 × 4 × 3 × 2 × 1 = 120
Q. If 4 members are to be seated from a group of 6, how many arrangements are possible? Answer: 360 Explanation: ⁶P₄ = 6! / 2! = 360
Q. If a coin is flipped 3 times, what is the probability of getting 3 heads? Answer: 1/8 = 0.125 Explanation: (1/2)³ = 1/8
Q. Which is the solution set of |-x| = 0? Answer: {0} Explanation: Absolute value becomes zero only when x = 0.
Q. Solve: 2x + 3 = 3x − 2 Answer: x = 5 Explanation: 2x + 3 = 3x − 2 3 + 2 = x x = 5
Q. Find the range of the data: 85, 87, 90, 92, 95. Answer: 10 Explanation: Range = 95 − 85 = 10
Q. If the cost of 5 pens is Rs.125, find the cost of one pen. Answer: Rs.25 Explanation: 125 ÷ 5 = 25
Q. Plane geometry has how many dimensions? Answer: 2 Explanation: Plane geometry deals with length and width only.
Q. A rectangular box has dimensions 10 cm, 15 cm and 20 cm. Find its volume. Answer: 3000 cm³ Explanation: Volume = 10 × 15 × 20 = 3000 cm³
Q. Four pizzas are shared equally among 6 persons. Each pizza has 8 slices. How many slices will each person get? Answer: 5.33 slices Explanation: Total slices = 4 × 8 = 32 32 ÷ 6 = 5.33
Q. A man sells 48 toys in four days. How many toys are sold per day? Answer: 12 Explanation: 48 ÷ 4 = 12
Q. Vinay’s mother is three times his age. After 5 years, the sum of their ages will be 70 years. Find their present ages. Answer: Vinay = 15 years, Mother = 45 years Explanation: x + 5 + 3x + 5 = 70 4x = 60 x = 15
Q. A student scores 78, 85, 90 and 92 in four tests. What marks are required in the fifth test to maintain an average of 85? Answer: 80 Explanation: Required total = 85 × 5 = 425 Current total = 345 Required marks = 425 − 345 = 80
Q. Two numbers are in the ratio 6:7 and their sum is 52. Find the numbers. Answer: 24 and 28 Explanation: 6x + 7x = 52 13x = 52 x = 4 Numbers = 24 and 28
Q. A monkey climbs 30 ft every hour and slips 20 ft before the next climb. A flag is at 120 ft. At what time will it first touch the flag if it starts at 8 AM? Answer: 5 PM Explanation: Net gain per hour = 10 ft. After 9 hours it reaches 90 ft. At 5 PM, it climbs 30 ft more and reaches 120 ft.
Q. Solve: 3x + 7 < 22 Answer: x < 5 Explanation: 3x < 15 x < 5
Q. The price of a product is reduced by 30%. If the original price is Rs.120, what is the new price? Answer: Rs.84 Explanation: 30% of 120 = 36 120 − 36 = 84
Q. In a school of 600 students, if 45% are girls, how many girls are there? Answer: 270 Explanation: 45% of 600 = 270
Q. If base of triangle is 8 cm and height is 4 cm, what would be the area of triangle? Answer: 16 cm² وضاحت: مثلث کا رقبہ = ½ × Base × Height ½ × 8 × 4 = 16 cm²
Q. If a total of 15 kg of solid material is placed into a 100 liter container, what would be the density of solid material? Answer: 0.15 kg/liter وضاحت: Density = Mass ÷ Volume 15 ÷ 100 = 0.15 kg/liter
Q. A student obtained the marks 16, 50, 70, 65 and 85 in five subjects. What would be the average marks? Answer: 57.2 وضاحت: کل نمبر = 16 + 50 + 70 + 65 + 85 = 286 Average = 286 ÷ 5 = 57.2
Q. If 20/x + 16/x = 12, then the value of x is? Answer: 3 وضاحت: 36/x = 12 x = 36 ÷ 12 = 3
Q. What is the geometric mean of 2, 4 and 8? Answer: 4 وضاحت: 2 × 4 × 8 = 64 ∛64 = 4
Q. What is 75% of 200? Answer: 150 وضاحت: (75/100) × 200 = 150
Q. The ages of Sohail, Afzal and Bilal are 17, 16 and 12 respectively. If Aslam is included and average age increases by 5 years, what is the age of Aslam? Answer: 35 years وضاحت: پہلے اوسط = (17+16+12) ÷ 3 = 15 نئی اوسط = 20 کل عمر = 20 × 4 = 80 Aslam = 80 − 45 = 35
Q. If 6 men can complete a work in 15 hours, then how many hours will 10 men take? Answer: 9 hours وضاحت: 6 × 15 = 10 × x x = 90 ÷ 10 = 9
Q. If total distance is 540 km and total time is 6 hours, what would be average speed? Answer: 90 km/h وضاحت: Speed = Distance ÷ Time 540 ÷ 6 = 90 km/h
Q. An angle measuring less than 90° is called? Answer: Acute Angle وضاحت: 90° سے کم زاویہ Acute Angle کہلاتا ہے۔
Q. The sum of three consecutive integers is 72. What is the smallest integer? Answer: 23 وضاحت: x + (x+1) + (x+2) = 72 3x + 3 = 72 x = 23
Q. What is the sum of the interior angles of a triangle? Answer: 180° وضاحت: ہر مثلث کے اندرونی زاویوں کا مجموعہ 180° ہوتا ہے۔
Q. The volume of a cylinder is calculated by V = πr²L. If r = 3 cm and L = 10 cm, what is the volume? Answer: 90π cm³ وضاحت: π × 3² × 10 = 90π cm³
Q. If numerator is greater than or equal to denominator, the fraction is called? Answer: Improper Fraction وضاحت: جس کسر میں شمار مخرج سے بڑا یا برابر ہو اسے Improper Fraction کہتے ہیں۔
Q. What is the 101st term of the sequence 1, 4, 7, 10, …? Answer: 301 وضاحت: aₙ = a + (n−1)d 1 + (100 × 3) = 301
Q. If 1/8 pencil is black, 1/4 is white and remaining 5.25 cm is grey, what is total length of pencil? Answer: 8.4 cm وضاحت: باقی حصہ = 5/8 5/8 × Length = 5.25 Length = 8.4 cm
Q. If sin(60° + X) = cos(30°), then value of X is? Answer: 0° وضاحت: cos30° = sin60° لہٰذا X = 0°
Q. If x + y = 6 and xy = 5, then x² + y² = ? Answer: 26 وضاحت: (x+y)² = x²+y²+2xy 36 = x²+y²+10 x²+y² = 26
Q. Which of the following is an arithmetic sequence? Answer: 31, 32, 33, 34 وضاحت: ہر عدد میں فرق 1 ہے۔
Q. Which of the following is irrational? Answer: √11 وضاحت: √11 کو مکمل عدد یا سادہ کسر میں ظاہر نہیں کیا جا سکتا۔
Q. What is the value of 180 degrees in radians? Answer: π وضاحت: 180° = π radians
Q. What type of roots does the equation x² + 4 = 0 have? Answer: Imaginary Roots وضاحت: x = ±2i
Q. In how many ways can 5 children be arranged in a line? Answer: 120 وضاحت: 5! = 120
Q. If you flip a coin 3 times, what is the probability of getting 3 heads? Answer: 1/8 (0.125) وضاحت: (1/2)³ = 1/8
Q. Which one is the solution set of |-x| = 0? Answer: {0} وضاحت: Absolute value صرف صفر پر صفر ہوتی ہے۔
Q. Solve the equation 2x + 3 = 3x. Answer: x = 3 وضاحت: 3 = x
Q. Find the range from data 85, 87, 90, 92, 95. Answer: 10 وضاحت: 95 − 85 = 10
Q. If the cost of 5 pens is 125 rupees, find the cost of one pen. Answer: 25 rupees وضاحت: 125 ÷ 5 = 25
Q. Plane geometry has how many dimensions? Answer: 2 وضاحت: Plane Geometry لمبائی اور چوڑائی پر مشتمل ہوتی ہے۔
Q. A rectangular box has dimensions 10 cm, 15 cm, and 20 cm. Find its volume. Answer: 3000 cm³ وضاحت: 10 × 15 × 20 = 3000 cm³
Q. A man sells 48 toys in four days. How many toys are sold per day? Answer: 12 وضاحت: 48 ÷ 4 = 12
Q. A student has marks 78, 85, 90 and 92. What marks are required in the fifth exam to maintain an average of 85? Answer: 80 وضاحت: مطلوبہ کل نمبر = 425 حاصل شدہ = 345 فرق = 80
Q. Solve the equation: 2x + 5 = 13. Answer: x = 4 وضاحت: 2x = 8 x = 4
Q. The sum of two consecutive even integers is 46. Find the integers. Answer: 22 and 24 وضاحت: x + (x+2) = 46 x = 22
Q. Find the value of y in the equation 3x − 2y = 9, where x = 5. Answer: y = 3 وضاحت: 15 − 2y = 9 y = 3
Q. A farmer used 27 fence poles on each side of a square plot. How many poles were needed altogether? Answer: 104 وضاحت: 4 × 27 − 4 = 104
Q. Solve √(x + 3) = 2. Answer: x = 1 وضاحت: x + 3 = 4 x = 1
Q. Solve for x: 4x + 5 = 2x − 3. Answer: x = −4 وضاحت: 2x = −8 x = −4
Q. Sara has 5 red, 3 green and 2 blue marbles. What fraction are green? Answer: 3/10 وضاحت: کل ماربل = 10 سبز = 3
Q. A pizza is divided into 10 equal slices. If 4 slices are eaten, what fraction remains? Answer: 3/5 وضاحت: 6/10 = 3/5
Q. In a parallelogram, one angle measures 120°. What is the adjacent angle? Answer: 60° وضاحت: Adjacent angles کا مجموعہ 180° ہوتا ہے۔
Q. What is the value of x in 3x + 7 = 22? Answer: 5 وضاحت: 3x = 15 x = 5
Q. What is the sum of prime numbers between 20 and 30? Answer: 52 وضاحت: 23 + 29 = 52
Q. If radius of a circle is 5 m, find its diameter. Answer: 10 meters وضاحت: Diameter = 2 × Radius = 10 m
One Comment
Alhamdulilah ya to sari ho gi ma’am Allah apko hamesha kush rakhna
, then what is the value of the function
in the equation
Alhamdulilah ya to sari ho gi ma’am Allah apko hamesha kush rakhna