Major Competitive Exams
Q. Solve the inequality 7 - x < 2.
A.
x > 5
B.
x < 5
C.
x > 7
D.
x < 7
Show solution
Solution
7 - x < 2 => -x < -5 => x > 5.
Correct Answer: A — x > 5
Learn More →
Q. Solve the inequality 7x + 2 < 3x + 10.
A.
x < 2
B.
x > 2
C.
x ≤ 2
D.
x ≥ 2
Show solution
Solution
7x + 2 < 3x + 10 => 4x < 8 => x < 2.
Correct Answer: B — x > 2
Learn More →
Q. Solve the inequality 7x - 4 < 2x + 11. What is the solution?
A.
x < 3
B.
x > 3
C.
x ≤ 3
D.
x ≥ 3
Show solution
Solution
7x - 4 < 2x + 11 => 5x < 15 => x < 3.
Correct Answer: B — x > 3
Learn More →
Q. Solve the inequality 7x - 5 < 2x + 10. What is the solution?
A.
x < 1
B.
x > 1
C.
x < 2
D.
x > 2
Show solution
Solution
7x - 5 < 2x + 10 => 5x < 15 => x < 3.
Correct Answer: B — x > 1
Learn More →
Q. Solve the inequality 8 - x > 3.
A.
x < 5
B.
x > 5
C.
x < 3
D.
x > 3
Show solution
Solution
8 - x > 3 => -x > -5 => x < 5.
Correct Answer: A — x < 5
Learn More →
Q. Solve the inequality x/3 + 2 > 1. What is the solution?
A.
x > -3
B.
x < -3
C.
x > 3
D.
x < 3
Show solution
Solution
x/3 + 2 > 1 => x/3 > -1 => x > -3.
Correct Answer: C — x > 3
Learn More →
Q. Solve the inequality x/3 - 2 > 1. What is the solution set?
A.
x < 9
B.
x > 9
C.
x < 3
D.
x > 3
Show solution
Solution
x/3 - 2 > 1 => x/3 > 3 => x > 9.
Correct Answer: B — x > 9
Learn More →
Q. Solve the inequality x/3 - 2 ≤ 1. What is the solution?
A.
x ≤ 9
B.
x ≥ 9
C.
x ≤ 3
D.
x ≥ 3
Show solution
Solution
x/3 - 2 ≤ 1 => x/3 ≤ 3 => x ≤ 9.
Correct Answer: A — x ≤ 9
Learn More →
Q. Solve the inequality x/4 - 1 < 0.
A.
x < 4
B.
x > 4
C.
x ≤ 4
D.
x ≥ 4
Show solution
Solution
x/4 - 1 < 0 => x/4 < 1 => x < 4.
Correct Answer: A — x < 4
Learn More →
Q. Solve the inequality: 4x + 1 ≥ 3.
A.
x ≥ 0.5
B.
x ≤ 0.5
C.
x ≥ 1
D.
x ≤ 1
Show solution
Solution
4x + 1 ≥ 3 => 4x ≥ 2 => x ≥ 0.5.
Correct Answer: A — x ≥ 0.5
Learn More →
Q. Solve the inequality: 6 - x ≤ 2.
A.
x ≥ 4
B.
x ≤ 4
C.
x ≥ 6
D.
x ≤ 6
Show solution
Solution
6 - x ≤ 2 => -x ≤ -4 => x ≥ 4.
Correct Answer: B — x ≤ 4
Learn More →
Q. The angle between the lines represented by the equation 2x^2 + 3xy + y^2 = 0 is:
A.
0 degrees
B.
45 degrees
C.
90 degrees
D.
60 degrees
Show solution
Solution
Using the angle formula, we find the angle between the lines is 60 degrees.
Correct Answer: D — 60 degrees
Learn More →
Q. The angle between the lines represented by the equation 3x^2 - 4xy + 2y^2 = 0 is:
A.
30 degrees
B.
45 degrees
C.
60 degrees
D.
90 degrees
Show solution
Solution
Using the formula tan(θ) = |(m1 - m2) / (1 + m1*m2)|, we find that the angle is 60 degrees.
Correct Answer: C — 60 degrees
Learn More →
Q. The area of a rectangle with vertices at (1, 1), (1, 4), (5, 1), and (5, 4) is:
Show solution
Solution
Length = 5 - 1 = 4, Width = 4 - 1 = 3. Area = Length * Width = 4 * 3 = 12.
Correct Answer: B — 16
Learn More →
Q. The area of a triangle with vertices at (0,0), (4,0), and (0,3) is:
Show solution
Solution
Area = 0.5 * base * height = 0.5 * 4 * 3 = 6.
Correct Answer: A — 6
Learn More →
Q. The area of triangle ABC is 24 cm², and the base BC = 8 cm. What is the height from A to BC?
A.
6 cm
B.
8 cm
C.
4 cm
D.
3 cm
Show solution
Solution
Area = 1/2 * base * height => 24 = 1/2 * 8 * height => height = 6 cm.
Correct Answer: A — 6 cm
Learn More →
Q. The area of triangle ABC is 30 square units, and the base BC is 10 units. What is the height from A to BC?
A.
3 units
B.
6 units
C.
5 units
D.
4 units
Show solution
Solution
Area = 1/2 * base * height => 30 = 1/2 * 10 * height => height = 6 units.
Correct Answer: B — 6 units
Learn More →
Q. The argument of the complex number z = -1 - i is?
A.
-3π/4
B.
3π/4
C.
π/4
D.
-π/4
Show solution
Solution
The argument of z = -1 - i is θ = tan^(-1)(-1/-1) = -3π/4.
Correct Answer: A — -3π/4
Learn More →
Q. The Arrhenius equation relates the rate constant to which of the following?
A.
Temperature and concentration
B.
Temperature and activation energy
C.
Concentration and pressure
D.
Temperature and volume
Show solution
Solution
The Arrhenius equation relates the rate constant to temperature and activation energy.
Correct Answer: B — Temperature and activation energy
Learn More →
Q. The average of five numbers is 18. If one number is excluded, the average becomes 16. What is the excluded number?
Show solution
Solution
Total sum = 5 * 18 = 90. New sum = 4 * 16 = 64. Excluded number = 90 - 64 = 26.
Correct Answer: C — 24
Learn More →
Q. The average of five numbers is 18. If one number is removed, the average becomes 16. What was the removed number?
Show solution
Solution
Total of five numbers = 5 * 18 = 90. Total of four numbers = 4 * 16 = 64. Removed number = 90 - 64 = 26.
Correct Answer: C — 24
Learn More →
Q. The concept of an ideal gas is based on which of the following assumptions?
A.
Molecules have no volume
B.
Molecules do not attract or repel each other
C.
Collisions are perfectly elastic
D.
All of the above
Show solution
Solution
The concept of an ideal gas is based on the assumptions that molecules have no volume, do not attract or repel each other, and that collisions are perfectly elastic.
Correct Answer: D — All of the above
Learn More →
Q. The concept of mean free path is associated with which of the following?
A.
Distance traveled by a gas molecule between collisions
B.
Average speed of gas molecules
C.
Pressure of the gas
D.
Volume of the gas
Show solution
Solution
Mean free path is defined as the average distance traveled by a gas molecule between successive collisions.
Correct Answer: A — Distance traveled by a gas molecule between collisions
Learn More →
Q. The condition for the lines represented by ax^2 + 2hxy + by^2 = 0 to be parallel is:
A.
h^2 = ab
B.
h^2 > ab
C.
h^2 < ab
D.
a + b = 0
Show solution
Solution
The lines are parallel if h^2 = ab.
Correct Answer: A — h^2 = ab
Learn More →
Q. The condition for the lines represented by the equation x^2 + y^2 + 2xy = 0 to be coincident is:
A.
Discriminant = 0
B.
Discriminant > 0
C.
Discriminant < 0
D.
None of the above
Show solution
Solution
For the lines to be coincident, the discriminant of the quadratic must be zero.
Correct Answer: A — Discriminant = 0
Learn More →
Q. The condition for the lines represented by the equation x^2 + y^2 - 4x - 6y + 9 = 0 to be coincident is:
A.
Discriminant = 0
B.
Discriminant > 0
C.
Discriminant < 0
D.
None of the above
Show solution
Solution
For the lines to be coincident, the discriminant of the quadratic must equal zero.
Correct Answer: A — Discriminant = 0
Learn More →
Q. The coordinates of the centroid of a triangle with vertices at (0, 0), (6, 0), and (3, 6) are:
A.
(3, 2)
B.
(3, 3)
C.
(2, 3)
D.
(0, 0)
Show solution
Solution
Centroid = ((x1+x2+x3)/3, (y1+y2+y3)/3) = (9/3, 6/3) = (3, 2).
Correct Answer: B — (3, 3)
Learn More →
Q. The coordinates of the centroid of the triangle with vertices (0, 0), (6, 0), and (3, 6) are:
A.
(3, 2)
B.
(2, 3)
C.
(3, 3)
D.
(0, 0)
Show solution
Solution
Centroid = ((0+6+3)/3, (0+0+6)/3) = (3, 2).
Correct Answer: A — (3, 2)
Learn More →
Q. The coordinates of the centroid of the triangle with vertices (2, 3), (4, 5), and (6, 7) are:
A.
(4, 5)
B.
(3, 4)
C.
(5, 6)
D.
(6, 5)
Show solution
Solution
Centroid = ((2+4+6)/3, (3+5+7)/3) = (4, 5).
Correct Answer: B — (3, 4)
Learn More →
Q. The critical points of the function f(x) = x^3 - 6x^2 + 9x + 1 are:
A.
x = 1, 3
B.
x = 0, 2
C.
x = 2, 4
D.
x = 1, 2
Show solution
Solution
Finding f'(x) = 3x^2 - 12x + 9 and solving gives critical points at x = 1 and x = 3.
Correct Answer: A — x = 1, 3
Learn More →
Showing 4561 to 4590 of 9007 (301 Pages)
