MCSCCE
If A={1,2,3} and B={3,5,7}, then (A∪B) is -
A)
{3}
B)
{1,2}
C)
{5,7}
D)
{1,2,3,5,7}
The union (A union B) contains all distinct elements present in set A or set B: {1, 2, 3} union {3, 5, 7} = {1, 2, 3, 5, 7} (option d).
MCSCCE
The product of the roots of the equation x² - 3x + 2 = 0 is -
A)
3
B)
-2/3
C)
2
D)
-3/2
For a quadratic equation ax² + bx + c = 0, the product of the roots is c/a. In x² - 3x + 2 = 0, the product is 2/1 = 2.
MCSCCE
The mean of 16 numbers is 8. If 2 is added to every number, what will be the new mean?
A)
10
B)
12
C)
14
D)
16
According to the properties of the arithmetic mean, if a constant value 'k' is added to every observation in a data set, the mean of the new data set increases by that same constant 'k'.
1. Given: Original Mean = 8
2. Constant added to each number (k) = 2
3. New Mean = Original Mean + k = 8 + 2 = 10.
Therefore, option (a) is correct. Options (b), (c), and (d) are incorrect because they do not follow this mathematical property; they represent incorrect calculations or arbitrary additions.
MCSCCE
If θ is the angle (in degrees) of a sector of a circle of radius r, then area of the sector is:
A)
πr²θ/180°
B)
πr²θ/360°
C)
2πrθ/180°
D)
2πrθ/360°
The area of a sector of a circle with radius r and central angle θ (in degrees) is given by the formula (θ / 360°) * πr² = πr²θ/360°.
MCSCCE
A and B together can do a piece of work in 12 days, while B alone can finish it in 30 days. Then the work done by A in 1 day is -
A)
1/20
B)
1/12
C)
1/30
D)
1/60
A's 1-day work = (1/12) - (1/30) = (5 - 2)/60 = 3/60 = 1/20.
MCSCCE
In an AP, if a₁ = 1, aₙ = 20 and Sₙ = 399, then n is:
A)
17
B)
21
C)
42
D)
38
In an Arithmetic Progression, S_n = (n / 2) * (a_1 + a_n). Substituting: 399 = (n / 2) * (1 + 20) => 399 = 21n / 2 => 21n = 798 => n = 38.
MCSCCE
David has invested money in some shares that have a projected accumulated increase of 3.5% a year. In five years’ time, how much money will David have if he invested £450?
A)
£530
B)
£534.46
C)
£528.75
D)
£525.5
Compounded annually over 5 years at 3.5%: Amount = 450 * (1 + 0.035)^5 = 450 * (1.035)^5 ≈ £534.46.
MCSCCE
A bus travelled a distance of 180 m in 12 seconds. The speed of bus is -
A)
15 km/hr
B)
15 m/s
C)
10 km/hr
D)
10 m/s
Speed = Distance / Time. Given Distance = 180 m and Time = 12 seconds. Speed = 180/12 = 15 m/s.
MCSCCE
In ΔABC, right-angled at B, AB = 24cm, BC = 7cm, then AC is equal to:
A)
25cm
B)
26cm
C)
21cm
D)
12cm
By Pythagorean theorem: AC = sqrt(AB^2 + BC^2) = sqrt(24^2 + 7^2) = sqrt(576 + 49) = sqrt(625) = 25 cm (option a).
MCSCCE
Which term of the AP 4, 9, 14, 19, ........... is 124?
A)
20th term
B)
22nd term
C)
23rd term
D)
25th term
For the arithmetic progression 4, 9, 14, 19, ..., first term a = 4 and common difference d = 5. Using the formula a_n = a + (n - 1)d = 124: 4 + 5(n - 1) = 124 => 5(n - 1) = 120 => n - 1 = 24 => n = 25.
MCSCCE
A kite is attached to a string. If the kite is flying at a height of 45 m and the string makes an angle of 30° with the ground, then the length of the string is:
A)
60 m
B)
90 m
C)
120 m
D)
75 m
1. **Correct Option Analysis**: This problem can be modeled as a right-angled triangle where the height of the kite is the opposite side (45 m), the length of the string is the hypotenuse (L), and the angle with the ground is 30°. Using the trigonometric ratio for sine:
sin(θ) = Opposite / Hypotenuse
sin(30°) = 45 / L
Since sin(30°) = 1/2, we have:
1/2 = 45 / L
L = 45 * 2 = 90 m.
Therefore, option (b) is correct.
2. **Incorrect Options Analysis**:
- Option (a) 60 m: This would occur if the angle were approximately 41.8°.
- Option (c) 120 m: This does not correspond to the standard trigonometric ratios for this height and angle.
- Option (d) 75 m: This would occur if the angle were approximately 36.9°.
MCSCCE
The value of 243/363 is -
A)
9/11
B)
81/121
C)
81/9
D)
121/11
Dividing both the numerator and the denominator by their common divisor 3 gives: 243 / 3 = 81 and 363 / 3 = 121, resulting in 81/121.
MCSCCE
The length of the diagonals of a rhombus are 16 cm and 12 cm. Then the length of the side of the rhombus is:
A)
9 cm
B)
8 cm
C)
20 cm
D)
10 cm
The diagonals of a rhombus bisect each other perpendicularly. The half-diagonals are 8 cm and 6 cm. Using the Pythagorean theorem: side = sqrt(8^2 + 6^2) = sqrt(64 + 36) = sqrt(100) = 10 cm.
MCSCCE
Which of the following equations has 2 as a root?
A)
x² – 5x + 5 = 0
B)
x² + 3x – 11 = 0
C)
2x² – 7x + 6 = 0
D)
3x² – 6x – 2 = 0
Substituting x = 2 into 2x² – 7x + 6 gives: 2(2)² – 7(2) + 6 = 2(4) – 14 + 6 = 8 – 14 + 6 = 0. Since the equation evaluates to 0, 2 is a root of this quadratic equation.
MCSCCE
The age of A and B are in the ratio 6:11. Twenty years ago their ages were in the ratio of 2:7. Their present ages are -
A)
30 yrs & 55 yrs
B)
26 yrs & 31 yrs
C)
36 yrs & 41 yrs
D)
26 yrs & 91 yrs
Let present ages be 6x and 11x. Twenty years ago: (6x - 20)/(11x - 20) = 2/7 ⇒ 42x - 140 = 22x - 40 ⇒ 20x = 100 ⇒ x = 5. Present ages are 6(5) = 30 years and 11(5) = 55 years.
MCSCCE
The distance between the points A (6, 5) and B (0, – 3 ) is:
A)
10 units
B)
8 units
C)
14 units
D)
√40 units
Using the distance formula: d = √[(6 - 0)² + (5 - (-3))²] = √[6² + 8²] = √[36 + 64] = √100 = 10 units.
MCSCCE
In a committee, 50 people speak French, 20 speak Spanish and 10 speak both Spanish and French. How many speak at least one of these languages?
A)
10
B)
60
C)
50
D)
80
Using the formula n(A U B) = n(A) + n(B) - n(A ∩ B) = 50 + 20 - 10 = 60.
MCSCCE
The common difference of an AP in which a₁₉ – a₁₅ = 36 is:
A)
4
B)
– 4
C)
– 9
D)
9
a19 - a15 = (a + 18d) - (a + 14d) = 4d = 36 => d = 9 (option d).
MCSCCE
In a throw of a die, the probability of getting a prime number is -
A)
1/2
B)
3/2
C)
1/3
D)
2/3
On a six-sided die, possible outcomes are {1, 2, 3, 4, 5, 6} (total = 6). The prime numbers are {2, 3, 5} (3 outcomes). Probability = 3/6 = 1/2.
MCSCCE
The 9th term from the end of the AP 4, 9, 14, ........... 254 is -
A)
214
B)
209
C)
200
D)
198
For an AP with last term l = 254 and common difference d = 5, the nth term from the end is given by l - (n - 1)d = 254 - (9 - 1) * 5 = 254 - 40 = 214.
MCSCCE
The roots of the equation x² + px + q = 0 are equal if:
A)
p² = 2q
B)
p² = – 4q
C)
p² = – 2q
D)
p² = 4q
For quadratic equation ax^2 + bx + c = 0, roots are equal when Discriminant D = b^2 - 4ac = 0. Here p^2 - 4(1)(q) = 0 => p^2 = 4q (option d).
MCSCCE
The HCF of (x – 3)²( x + 4)² and (x – 1)(x + 4)(x – 3)² is:
A)
(x – 1)(x – 3)(x + 4)
B)
(x – 3)(x + 4)²
C)
(x + 4)(x – 3)²
D)
(x + 4)(x – 3)
The Highest Common Factor (HCF) is obtained by taking the lowest exponent of all common factors. Between (x – 3)²(x + 4)² and (x – 1)(x + 4)(x – 3)², the common factors are (x - 3) with power 2 and (x + 4) with power 1, giving HCF = (x + 4)(x – 3)².
MCSCCE
Solution set of equations x+y=3 and 4x-3y=26 is -
A)
(2, -5)
B)
(-2, 5)
C)
(5, -2)
D)
(-5, 2)
Given equations: (1) x + y = 3 => y = 3 - x. Substituting in (2): 4x - 3(3 - x) = 26 => 4x - 9 + 3x = 26 => 7x = 35 => x = 5. Then y = 3 - 5 = -2. Thus (x, y) = (5, -2).
MCSCCE
A tank which has a leak in its bottom is filled in 20 hours. Had there been no leak in the bottom, it would have been filled in 15 hours. The leak can empty the tank in:
A)
20 hours
B)
60 hours
C)
75 hours
D)
15 hours
Rate with leak = 1/20. Rate without leak = 1/15. Rate of leak = (1/15) - (1/20) = (4-3)/60 = 1/60. The leak empties it in 60 hours.
MCSCCE
The value of (a/b)⁰ is -
A)
-1
B)
1
C)
0
D)
∞
According to the zero exponent law of indices, any non-zero term or fraction raised to the power of 0 is equal to 1: (a/b)⁰ = 1.
