Algebra

161 questions available

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All Algebraic Expressions 69 Linear Equations 69 Simultaneous Equations 6 Algebraic Identities 11 Factorization 4 Basic Inequalities 2
Showing 101–120 of 161

Q101.If 2b - 5 = 6, what is the value of b?

Medium
A 6
B 7
C 5.5
D 4
Algebraic Expressions PPSC

Correct Answer: C

2b = 11 => b = 11 / 2 = 5.5.

Q102.A number's fifth part increased by 4 equals its fourth part reduced by 10. Find the number.

Medium
A 200
B 240
C 280
D none
Algebraic Expressions PPSC

Correct Answer: C

Equation: x/5 + 4 = x/4 - 10 => x/4 - x/5 = 14 => (5x - 4x)/20 = 14 => x/20 = 14 => x = 280.

Q103.What is the value of x in the equation 3x - 15 - 6 = 0?

Medium
A -7
B 9
C -9
D 7
Algebraic Expressions PPSC

Correct Answer: D

3x - 15 - 6 = 0 → 3x - 21 = 0 → 3x = 21 → x = 7.

Q104.ABC corporation sold 30% of stock to S. Company T owns 12,000 shares. Company R owns remaining. If R has 15% more shares than S, how many shares does Company S own?

Medium
A 10,140 shares
B 11,160 shares
C 94,860 shares
D 7,230 shares
Algebraic Expressions PPSC

Correct Answer: A

Let total shares = T. S = 0.30T. R = T - (0.3T + 12000) = 0.70T - 12000. R is 15% more than S: R = 1.15 × S → 0.7T - 12000 = 1.15 × 0.3T = 0.345T → 0.355T = 12000 → T ≈ 33,802.82. S = 0.30 × 33,802.82 ≈ 10,140 shares.

Q105.If a² - b² = 9 and (a - b)² = 3, then what is the value of ab?

Medium
A 2
B 3
C 4
D 6
Algebraic Identities PPSC

Correct Answer: D

We can write: a² − b² = (a + b)(a − b) = 9. (a − b)² = 3 → a − b = √3. Hence (a + b)(√3) = 9 → a + b = 3√3. Solve for a and b: a = 2√3, b = √3. ab = a × b = 2√3 × √3 = 6.

Q106.If x = 5 and y = 2, what is the value of 2x + 3y?

Medium
A 09
B 22
C 16
D 31
Algebraic Expressions PPSC

Correct Answer: C

Given: x = 5, y = 2. Expression: 2x + 3y = 2(5) + 3(2) = 10 + 6 = 16.

Q107.The average of a non-zero number and its square is 5 times the number. What is the number?

Medium
A 9
B 17
C 29
D 295
Algebraic Expressions PPSC

Correct Answer: A

(x + x²) / 2 = 5x → x + x² = 10x → x² - 9x = 0. Since x is non-zero, x = 9.

Q108.The two lines x + y = 3 and 4x + 4y = 12 intersect?

Medium
A At one point
B At two points
C At all points
D Don’t intersect
Linear Equations PPSC

Correct Answer: C

The second equation 4x + 4y = 12 can be divided by 4 on both sides to yield x + y = 3. Since both represent the same line, they intersect at all points on the line.

Q109.If x=10, what is the value of 3x +5?

Medium
A 25
B 30
C 35
D 40
Algebraic Expressions PPSC

Correct Answer: C

Substituting x = 10 into the expression: 3(10) + 5 = 30 + 5 = 35.

Q110.What is the value of x in the equation x/5 - 3x/2 = 7 + x/2?

Medium
A -35/9
B 35/9
C -18/70
D 5
Linear Equations PPSC

Correct Answer: A

Multiply the entire equation by 10 to clear denominators: 2x - 15x = 70 + 5x => -13x = 70 + 5x => -18x = 70 => x = -70/18 = -35/9.

Q111.Which number can replace both the question marks in 2/? = ?/50?

Medium
A 5
B 10
C 25
D 100
Algebraic Expressions PPSC

Correct Answer: B

Let the number be y. 2/y = y/50 => y^2 = 100 => y = 10.

Q112.A and B do a business together. Their incomes are in the ratio 3 : 2, and their expenses are in the ratio 5 : 3. If each saves Rs. 1000, what are their incomes?

Medium
A Rs. 3000 and Rs. 2000
B Rs. 4500 and Rs. 3000
C Rs. 6000 and Rs. 4000
D Rs. 7500 and Rs. 5000
Algebraic Expressions PPSC

Correct Answer: C

Let incomes be 3x, 2x and expenses 5y, 3y. 3x - 5y = 1000 and 2x - 3y = 1000. Solving these: x = 2000, y = 1000. Incomes: 3(2000) = Rs. 6000 and 2(2000) = Rs. 4000.

Q113.Solve: (25*10)/(5(6-4)2)

Medium
A 200
B 25/2
C 50
D 25
Algebraic Expressions PPSC

Correct Answer: B

Numerator: 25 * 10 = 250. Denominator: 5 * (2) * 2 = 20. Fraction = 250 / 20 = 25/2.

Q114.If 1.02 × ? = 0.5, what is the approximate value of the missing term?

Medium
A 0.49
B 0.52
C 1.5
D 2.0
Algebraic Expressions PPSC

Correct Answer: A

? = 0.5 / 1.02 ≈ 0.49.

Q115.Expression: (x + 1/x)(x − 1/x) = ?

Medium
A x² − 1/x²
B x² + 1/x²
C x − 1/x
D x² − 1/x
Algebraic Expressions PPSC

Correct Answer: A

Difference of squares formula: (a+b)(a-b) = a^2 - b^2. Here, a=x, b=1/x => x^2 - 1/x^2.

Q116.Find the value of 100² − 99²?

Medium
A 1
B 199
C 100
D 198
Algebraic Expressions PPSC

Correct Answer: B

100^2 - 99^2 = (100 - 99)(100 + 99) = 1 * 199 = 199.

Q117.If P * Q = P + Q + P / Q, then 8 * 2 is?

Medium
A 6
B 10
C 14
D 16
Algebraic Expressions PPSC

Correct Answer: C

Using the operator: 8 * 2 = 8 + 2 + 8/2 = 10 + 4 = 14.

Q118.If -2x - 5 = 48, what is the value of 2x + 57?

Medium
A -48
B 48
C 26
D 4
Algebraic Expressions PPSC

Correct Answer: D

From -2x - 5 = 48, we get -2x = 53, which means 2x = -53. Substituting this into the target expression: 2x + 57 = -53 + 57 = 4.

Q119.In 1999, Danish read 10 English books and 7 Urdu books. In 2000, he read twice as many Urdu books as English books. If 60% of the books that he read during the two years were Urdu, how many books did he read in 2000?

Medium
A 26
B 32
C 39
D 48
Simultaneous Equations PPSC

Correct Answer: D

Let English books in 2000 = x, so Urdu books in 2000 = 2x. Total Urdu over two years = 7 + 2x. Total books over two years = (10 + 7) + (x + 2x) = 17 + 3x. Given (7 + 2x) / (17 + 3x) = 0.60. Solving: 7 + 2x = 10.2 + 1.8x => 0.2x = 3.2 => x = 16. In 2000, total books read = 3x = 3(16) = 48.

Q120.If 2a – 3b = 10, what is the value of (2a – 3b)³ ?

Medium
A 100
B 1000
C 1500
D 2000
Algebraic Expressions PPSC

Correct Answer: B

Since (2a - 3b) is equal to 10, then (2a - 3b)³ = 10³ = 10 × 10 × 10 = 1000.