Algebra
11 questions available
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Q1.x+y=16, x-y=3 than x2 -y2 =?
Correct Answer: D
Q2.correct form of given equation 16X2+24x+9is?
Correct Answer: D
16x²+24x+9 = (4x)² + 2(4x)(3) + 3² = (4x+3)².
Q3.Find the value of a^2 + b^2, when a + b = 5 and ab = 6.
Correct Answer: C
a^2+b^2 = (a+b)^2 - 2ab = 25 - 12 = 13.
Q4.When the equation y = x^2 + 8x - 5 is written in the form (x + a)^2 + b, then a is:
Correct Answer: C
Completing the square: x^2+8x-5 = (x+4)^2 - 21, so a = 4.
Q5.Given; x^2 - 11x + 10 = 0, then x is:
Correct Answer: D
Correct answer is D: None of these
Q6.Find the value of a^3 + b^3, when a+b=5 and ab=6.
Correct Answer: D
Correct answer is D: None of these
Q7.When the equation, y = x^2 + 8x - 5 is written in the form = (x + a)^2 + b, then a is:
Correct Answer: C
Correct answer is C: 4
Q8.If x+y=16 and x-y=3, then x^2 - y^2 =?
Correct Answer: B
Using algebraic identity: x^2 - y^2 = (x+y)(x-y). Here, x^2 - y^2 = 16 * 3 = 48.
Q9.If a² - b² = 9 and (a - b)² = 3, then what is the value of ab?
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.
Q10.If T³ - 3T + 1 = 0, find the value of T³ + 1/T³?
Correct Answer: D
Dividing T³ - 3T + 1 = 0 by T gives T² - 3 + 1/T = 0, so T + 1/T = 3. Using the algebraic identity (T + 1/T)³ = T³ + 1/T³ + 3(T + 1/T), we substitute 3: 3³ = T³ + 1/T³ + 3(3) => 27 = T³ + 1/T³ + 9 => T³ + 1/T³ = 18.
Q11.What is (a² - b²) equal to?
Correct Answer: C
The difference of squares formula states: a² - b² = (a+b)(a-b).