1. If x=3x = 3x=3 and y=4y = 4y=4, what is the value of x2+y2x^2 + y^2×2+y2?

A) 5
B) 7
C) 25
D) 25

Answer: D
Explanation:
The formula is x2+y2x^2 + y^2×2+y2. Substituting the values:

x2+y2=32+42=9+16=25x^2 + y^2 = 3^2 + 4^2 = 9 + 16 = 25×2+y2=32+42=9+16=25

2. Simplify: (2x+3)−(x−5)(2x + 3) – (x – 5)(2x+3)−(x−5)

A) x+8x + 8x+8
B) x−8x – 8x−8
C) x+2x + 2x+2
D) x−2x – 2x−2

Answer: A
Explanation:
Distribute and combine like terms:

(2x+3)−(x−5)=2x+3−x+5=x+8(2x + 3) – (x – 5) = 2x + 3 – x + 5 = x + 8(2x+3)−(x−5)=2x+3−x+5=x+8

3. What is the least common multiple (LCM) of 12 and 18?

A) 36
B) 54
C) 72
D) 18

Answer: A
Explanation:
Prime factorization:
12 = 22×32^2 times 322×3, 18 = 2×322 times 3^22×32.
LCM = 22×32=362^2 times 3^2 = 3622×32=36.

4. A rectangle has a length of 8 cm and width of 6 cm. Find its area.

A) 24 cm²
B) 28 cm²
C) 48 cm²
D) 64 cm²

Answer: C
Explanation:
Area = length × width = 8×6=48 cm28 times 6 = 48 , text{cm}^28×6=48cm2.

5. Solve: 3(x+4)=183(x + 4) = 183(x+4)=18

A) x=6x = 6x=6
B) x=2x = 2x=2
C) x=4x = 4x=4
D) x=0x = 0x=0

Answer: B
Explanation:
Distribute 333:

3x+12=18then subtract 12:3x=6so x=2.3x + 12 = 18 quad text{then subtract } 12: quad 3x = 6 quad text{so } x = 2.3x+12=18then subtract 12:3x=6so x=2.

6. If a number is increased by 20% and then decreased by 20%, what is the net change?

A) No change
B) 4% decrease
C) 4% increase
D) 20% increase

Answer: B
Explanation:
Let the number be 100. Increasing by 20% gives 120120120.
Decreasing 120120120 by 20% gives 120−(0.2×120)=96120 – (0.2 times 120) = 96120−(0.2×120)=96.
Net change: 100−96=4% decrease100 – 96 = 4% , text{decrease}100−96=4%decrease.

7. What is the slope of the line y=2x+5y = 2x + 5y=2x+5?

A) 2
B) 5
C) -2
D) -5

Answer: A
Explanation:
The slope-intercept form y=mx+cy = mx + cy=mx+c identifies the slope m=2m = 2m=2.

8. Convert 34frac{3}{4}43​ into percentage.

A) 0.75%
B) 7.5%
C) 75%
D) 750%

Answer: C
Explanation:

34=0.75and 0.75×100=75%.frac{3}{4} = 0.75 quad text{and } 0.75 times 100 = 75%.43​=0.75and 0.75×100=75%.

9. Simplify 49+5sqrt{49} + 549​+5:

A) 12
B) 9
C) 10
D) 11

Answer: D
Explanation:

49=7and 7+5=11.sqrt{49} = 7 quad text{and } 7 + 5 = 11.49​=7and 7+5=11.

10. Solve for xxx: 2x−7=132x – 7 = 132x−7=13

A) 5
B) 10
C) 7
D) 3

Answer: B
Explanation:

2x−7=13Add 7:2x=20then divide by 2:x=10.2x – 7 = 13 quad text{Add } 7: quad 2x = 20 quad text{then divide by } 2: quad x = 10.2x−7=13Add 7:2x=20then divide by 2:x=10.

11. If x2−25=0x^2 – 25 = 0x2−25=0, find $x$.

A) 5
B) -5
C) $\pm 5$
D) 25

Answer: C
Explanation:
Factorize:

x2−25=(x−5)(x+5)=0⇒x=±5.x^2 – 25 = (x – 5)(x + 5) = 0 \quad \Rightarrow \quad x = \pm 5.x2−25=(x−5)(x+5)=0⇒x=±5.

12. A car travels 60 km in 2 hours. What is its average speed?

A) 15 km/h
B) 30 km/h
C) 45 km/h
D) 60 km/h

Answer: B
Explanation:

Speed=DistanceTime=602=30 km/h.\text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{60}{2} = 30 \, \text{km/h}.Speed=TimeDistance​=260​=30km/h.

13. What is the next term in the sequence 2, 4, 8, 16, …?

A) 20
B) 32
C) 24
D) 18

Answer: B
Explanation:
The sequence doubles each term:

$$16\times 2=32.$$

14. Solve for $x$: x3=6\frac{x}{3} = 63x​=6.

A) 12
B) 18
C) 9
D) 24

Answer: B
Explanation:
Multiply both sides by 3:

$$x=6\times 3=18.$$

15. A circle has a radius of 7 cm. Find its circumference.

A) $14\text{cm}$
B) $21\text{cm}$
C) $44\text{cm}$
D) $28\text{cm}$

Answer: C
Explanation:

$$\text{Circumference}=2\pi r=2\times 3.14\times 7=44\text{cm}.$$

16. What is $25\%$ of 200?

A) 25
B) 50
C) 75
D) 100

Answer: B
Explanation:

25% of 200=25100×200=50.25\% \text{ of } 200 = \frac{25}{100} \times 200 = 50.25% of 200=10025​×200=50.

17. Solve: $15-[3\times (2+4)]$

A) 9
B) 3
C) -3
D) 7

Answer: C
Explanation:
Simplify inside the parentheses first:

$$15-[3\times 6]=15-18=-3.$$

18. If a bag contains 3 red balls and 2 blue balls, what is the probability of selecting a red ball?

A) 15\frac{1}{5}51​
B) 35\frac{3}{5}53​
C) 25\frac{2}{5}52​
D) 12\frac{1}{2}21​

Answer: B
Explanation:
Total balls = 3 + 2 = 5. Probability of red = Red BallsTotal Balls=35\frac{\text{Red Balls}}{\text{Total Balls}} = \frac{3}{5}Total BallsRed Balls​=53​.

19. Solve for $x$: $5x+10=0$.

A) $-2$
B) 2
C) 0
D) $-5$

Answer: A
Explanation:

$$5x+10=0\Rightarrow 5x=-10\Rightarrow x=-2.$$

20. If $a:b=2:3$, find the value of $3a+2b$ when $b=12$.

A) 60
B) 48
C) 50
D) 54

Answer: D
Explanation:
If $b=12$, then a=23×12=8a = \frac{2}{3} \times 12 = 8a=32​×12=8.

$$3a+2b=3(8)+2(12)=24+30=54.$$

21. Simplify: 45÷23\frac{4}{5} \div \frac{2}{3}54​÷32​.

A) 815\frac{8}{15}158​
B) 107\frac{10}{7}710​
C) 620\frac{6}{20}206​
D) 58\frac{5}{8}85​

Answer: A
Explanation:
Dividing fractions:

45÷23=45×32=1210=815.\frac{4}{5} \div \frac{2}{3} = \frac{4}{5} \times \frac{3}{2} = \frac{12}{10} = \frac{8}{15}.54​÷32​=54​×23​=1012​=158​.

22. A train travels at 60 km/h for 2.5 hours. What distance does it cover?

A) 150 km
B) 120 km
C) 180 km
D) 90 km

Answer: C
Explanation:

$$\text{Distance}=\text{Speed}\times \text{Time}=60\times 2.5=150\text{km}.$$

23. Find the square root of 81.

A) 7
B) 8
C) 9
D) 10

Answer: C
Explanation:

81=9.\sqrt{81} = 9.81​=9.

24. If $2x=10$ and $y=x+4$, what is $y$?

A) 6
B) 8
C) 10
D) 12

Answer: B
Explanation:
Solve $x$:

$$2x=10\Rightarrow x=5.$$

Then $y=x+4=5+4=8$.

25. A triangle has sides 3 cm, 4 cm, and 5 cm. What type of triangle is this?

A) Equilateral
B) Right-angled
C) Isosceles
D) Scalene

Answer: B
Explanation:
Use the Pythagorean theorem:

32+42=9+16=25=52.3^2 + 4^2 = 9 + 16 = 25 = 5^2. 32+42=9+16=25=52.

This satisfies the condition for a right-angled triangle.

26. Solve for $x$: x2−16=0x^2 – 16 = 0x2−16=0.

A) 4
B) $\pm 4$
C) 16
D) $\pm 8$

Answer: B
Explanation:
Factorize:

x2−16=(x−4)(x+4)=0⇒x=±4.x^2 – 16 = (x – 4)(x + 4) = 0 \quad \Rightarrow \quad x = \pm 4.x2−16=(x−4)(x+4)=0⇒x=±4.

27. Convert 0.05 into a fraction.

A) 5100\frac{5}{100}1005​
B) 120\frac{1}{20}201​
C) 12\frac{1}{2}21​
D) 510\frac{5}{10}105​

Answer: B
Explanation:

0.05=5100=120.0.05 = \frac{5}{100} = \frac{1}{20}.0.05=1005​=201​.

28. A shopkeeper sells an item for Rs. 500 after a discount of 20%. What was the original price?

A) Rs. 600
B) Rs. 625
C) Rs. 700
D) Rs. 750

Answer: A
Explanation:
Let the original price be $x$:

$$x-0.2x=500\Rightarrow 0.8x=500\Rightarrow x=625.$$

29. If a = 5 and b = 3, find the value of (a+b)2−4ab(a + b)^2 – 4ab(a+b)2−4ab.

A) 49
B) 25
C) 36
D) 16

Answer: A
Explanation:
Expand (a+b)2−4ab(a + b)^2 – 4ab(a+b)2−4ab:

(a+b)2−4ab=a2+b2+2ab−4ab=a2+b2−2ab.(a + b)^2 – 4ab = a^2 + b^2 + 2ab – 4ab = a^2 + b^2 – 2ab. (a+b)2−4ab=a2+b2+2ab−4ab=a2+b2−2ab.

Substitute:

52+32−2(5)(3)=25+9−30=49.5^2 + 3^2 – 2(5)(3) = 25 + 9 – 30 = 49.52+32−2(5)(3)=25+9−30=49.

30. If a man completes 1/3 of a task in 2 hours, how long will it take him to complete the entire task?

A) 4 hours
B) 6 hours
C) 8 hours
D) 10 hours

Answer: B
Explanation:
Time for full task = $3\times 2=6\text{hours}.$