Quantitative Aptitude

Algebra

3,715 Questions
All Polynomial Roots and Coefficients 2451 Zero-Product Root Finding 667 Linear System Manipulation 162 Polynomial Theorems and Reduction 85 Algebraic Identity Simplification 82 Surds and Indices 70 Modulus and Absolute Value 54 Algebraic Expression Substitution 46 Algebraic Fraction Simplification 33 Logarithmic Equations 25 Repeated Series Sum 12 Linear Equation Word Problems 9

Algebra Questions

Multiple choice

Directions: In the given question, two equations (I) and (II) are given. You have to solve both the equations and select answer from the given options. I. 2x2 - 15x + 28 = 0 II. 4y2 - 16y + 15 = 0

  1. If x < y

  2. If x ≥ y

  3. If x > y

  4. If x ≤ y

  5. x = y, or the relationship cannot be established.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

I: 2x^2 - 15x + 28 = 0. (2x-7)(x-4) = 0. x = 3.5 or 4. II: 4y^2 - 16y + 15 = 0. (2y-3)(2y-5) = 0. y = 1.5 or 2.5. Comparing values, x > y in all cases.

Multiple choice

If tanA and tanB are the roots of the quadratic equation, 3x2−10x−25=0, then the value of 3 sin2(A+B) −10 sin(A+B)⋅cos(A+B)−25 cos2(A+B) is :

  1. -10

  2. 10

  3. -25

  4. 25
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Given tanA and tanB are roots of 3x^2 - 10x - 25 = 0. tanA + tanB = 10/3 and tanA*tanB = -25/3. tan(A+B) = (tanA + tanB) / (1 - tanA*tanB) = (10/3) / (1 + 25/3) = (10/3) / (28/3) = 10/28 = 5/14. The expression is cos^2(A+B) * [3*tan^2(A+B) - 10*tan(A+B) - 25]. Since tanA, tanB are roots, 3*tan^2(A+B) - 10*tan(A+B) - 25 = 0 is not directly applicable, but the expression simplifies to -25.

Multiple choice

In each of these questions, two equations (I) and (II) are given. You have to solve both the equations and give answer I. 15x²- 11x-12=0 II. 20y²- 49y+30=0

  1. if x < y

  2. if x ≤ y

  3. if x = y or no relation can be established

  4. if x > y

  5. if x ≥ y
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

I: 15x^2 - 11x - 12 = 0. Roots: x = (11 +/- sqrt(121 + 720))/30 = (11 +/- 29)/30. x = 40/30 = 4/3 or x = -18/30 = -3/5. II: 20y^2 - 49y + 30 = 0. Roots: y = (49 +/- sqrt(2401 - 2400))/40 = (49 +/- 1)/40. y = 50/40 = 5/4 or y = 48/40 = 6/5. Comparing: 4/3 (1.33) vs 5/4 (1.25) and 6/5 (1.2). No consistent relation.

Multiple choice

In each of these questions, two equations (I) and (II) are given. You have to solve both the equations and give answer I. 2x²+28=15x II. -17y+36=-2y²

  1. if x < y

  2. if x ≤ y

  3. if x = y or no relation can established

  4. if x > y be

  5. if x ≥ y
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

I: 2x^2 - 15x + 28 = 0. Roots: (2x-7)(x-4) = 0, so x = 3.5, 4. II: 2y^2 - 17y + 36 = 0. Roots: (2y-9)(y-4) = 0, so y = 4.5, 4. Comparing: x=3.5 < y=4.5, x=3.5 < y=4, x=4 <= y=4.5, x=4 = y=4. Thus x <= y.

Multiple choice

In each of these questions, two equations (I) and (II) are given. You have to solve both the equations and give answer I. 12x²-17x+6=0 II. y²-16y+63=0

  1. if x < y

  2. if x ≤ y

  3. if x = y or no relation can be established

  4. if x > y

  5. if x ≥ y
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For 12x^2 - 17x + 6 = 0, the roots are x = 2/3 and x = 3/4. For y^2 - 16y + 63 = 0, the roots are y = 7 and y = 9. Since both roots of x are smaller than both roots of y, x < y.

Multiple choice

In each of these questions, two equations (I) and (II) are given. You have to solve both the equations and give answer I. 2x²-21x+54=0 II. y²-14y+49=0

  1. if x < y

  2. if x ≤ y

  3. if x = y or no relation can be established

  4. if x > y

  5. if x ≥ y
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

I: 2x^2 - 21x + 54 = 0. Roots are (21 +/- sqrt(441 - 432))/4 = (21 +/- 3)/4. Roots are 6 and 4.5. II: y^2 - 14y + 49 = 0. (y-7)^2 = 0. Root is 7. Comparing: 6 < 7 and 4.5 < 7, so x < y.

Multiple choice

Rocky and Anthony are solving a quadratic equation. While solving, Rocky commits a mistake in the constant term and finds the roots to be 8 and 2. Anthony commits a mistake in the coefficient of X and finds the roots to be -9 and -1. Find the correct roots.

  1. -9 and 1

  2. 9 and -1

  3. 9 and 1

  4. 8 and 1

  5. 8 and - 1
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Rocky: roots 8, 2 => sum=10, product=16. Constant term is wrong, so sum (coefficient of x) is correct: -b/a = 10. Anthony: roots -9, -1 => sum=-10, product=9. Coefficient of x is wrong, so product (constant term) is correct: c/a = 9. Equation is x^2 - 10x + 9 = 0. Roots are (x-9)(x-1) = 0, so 9 and 1.

Multiple choice

If a, b, c > 0, then both the roots of the equation ax2 + bx + c = 0

  1. are real and negative

  2. have negative real part

  3. are rational

  4. are always imaginary
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For ax^2 + bx + c = 0 with a, b, c > 0, the roots are given by (-b +/- sqrt(b^2 - 4ac)) / 2a. The real part is -b/2a, which is negative. If the discriminant is negative, the roots are complex with a negative real part; if positive, the roots are negative real numbers.