If the roots of ax² + bx + c = 0 are α and β, then α + β = ?
A -b/a B b/a C c/a D -c/a
By Vieta's formulas, sum of roots = -b/a
A person walks 3 km north, then 4 km east. What is the shortest distance from the starting point?
A 5 km B 6 km C 7 km D 8 km
Using Pythagoras theorem: distance = √(3² + 4²) = √(9 + 16) = √25 = 5 km
If 2x + 3y = 13 and 3x + 2y = 12, find x + y.
A 5 B 4 C 3 D 6
Adding both equations: 5x + 5y = 25, so x + y = 5
What is the area of a circle with radius 7 cm? (Use π = 7 22
A 154 cm² B 176 cm² C 198 cm² D 220 cm²
Area = πr² = (7 22
If tan θ = 12 5
A 13 5 B 13 12 C 12 5 D 5 12
tan θ = 12 5 13 5
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If ∫(2x + 3)dx = ?
A x² + 3x + C B 2x² + 3x + C C x² + 3 + C D 2x + 3x + C
∫(2x + 3)dx = x² + 3x + C
A triangle has sides 5, 12, and 13 cm. What type of triangle is it?
A Acute B Right-angled C Obtuse D Isosceles
5² + 12² = 25 + 144 = 169 = 13². Satisfies Pythagoras theorem, so it's right-angled
Find the value of (x³ - 8)/(x - 2) when x ≠ 2.
A x² + 2x + 4 B x² - 2x + 4 C x² + 2x - 4 D x² - 2x - 4
x³ - 8 = (x-2)(x² + 2x + 4), so (x³ - 8)/(x - 2) = x² + 2x + 4
If the ratio of two numbers is 3:5 and their sum is 64, find the larger number.
A 24 B 32 C 40 D 48
Let numbers be 3x and 5x. 3x + 5x = 64 → 8x = 64 → x = 8. Larger number = 5 × 8 = 40.
If a quadratic equation has roots α and β, and α + β = 7, αβ = 10, what is the equation?
A x² - 7x + 10 = 0 B x² + 7x + 10 = 0 C x² - 7x - 10 = 0 D x² + 7x - 10 = 0
Quadratic equation is x² - (sum of roots)x + (product of roots) = 0, which gives x² - 7x + 10 = 0.
The volume of a cone with radius 5 cm and height 12 cm is: (use π = 7 22
A 314.29 cm³ B 628.57 cm³ C 471.43 cm³ D 314.86 cm³
Volume of cone = (3 1 3 1 7 22 3 1 7 22
In a triangle, if one angle is 90° and the other two angles are in ratio 1:2, the angles are:
A 30°, 60°, 90° B 45°, 45°, 90° C 20°, 70°, 90° D 40°, 50°, 90°
One angle = 90°. Other two in ratio 1:2. Let them be x and 2x. x + 2x + 90 = 180 → 3x = 90 → x = 30°. Angles are 30°, 60°, 90°.
If cos θ = 25 7
A 24 7 B 7 24 C 24 25 D 25 24
cos θ = 25 7 7 24
The average of five numbers is 35. If one number is replaced by 50, the new average becomes 38. What was the original number?
A 30 B 35 C 40 D 45
Sum of 5 numbers = 35 × 5 = 175. New sum = 38 × 5 = 190. Difference = 190 - 175 = 15. Original number = 50 - 15 = 35.
If log₁₀ 2 = 0.301, find log₁₀ 200.
A 2.301 B 2.602 C 1.301 D 3.301
log₁₀ 200 = log₁₀(2 × 100) = log₁₀ 2 + log₁₀ 100 = 0.301 + 2 = 2.301.
If ABCD is a rhombus with diagonals 6 cm and 8 cm, find its area.
A 24 cm² B 48 cm² C 28 cm² D 56 cm²
Area of rhombus = (2 1 2 1
What is the compound interest on Rs. 8000 at 10% per annum for 2 years?
A Rs. 1680 B Rs. 1600 C Rs. 1800 D Rs. 1500
A = P(1 + r/100)ⁿ = 8000(1.1)² = 8000 × 1.21 = 9680. CI = 9680 - 8000 = 1680.
In an AP, if first term a = 5, common difference d = 3, find the 10th term.
A 30 B 32 C 35 D 38
nth term = a + (n-1)d = 5 + (10-1) × 3 = 5 + 27 = 32.
If |x - 3| = 5, what are the possible values of x?
A 2 and 8 B 2 and -8 C -2 and 8 D 3 and 5
|x - 3| = 5 means x - 3 = 5 or x - 3 = -5. So x = 8 or x = -2.
A ladder of length 13 m leans against a wall. If the foot of the ladder is 5 m away from the wall, find the height reached on the wall.
A 8 m B 10 m C 12 m D 15 m
Using Pythagoras: h² + 5² = 13² → h² + 25 = 169 → h² = 144 → h = 12 m.
