A wall clock was set correctly at 8:00 a.m. It gains 10 minutes in 24 hours. The next day, when it shows 1:00 p.m., what is the correct time?
See answer
Correct answer: (C) 12:48 p.m.
1 marks · 2023 · Set A
Question 103
The mean and mode of a frequency distribution are 28 and 16, respectively. Find the median.
See answer
Correct answer: (A) 24
1 marks · 2023 · Set A
Question 104
Under compound interest, an amount becomes ₹9,680 after 2 years and ₹10,648 after 3 years. Find the principal.
See answer
Correct answer: (A) ₹8,000
1 marks · 2023 · Set A
Question 105
Two different dice are rolled together. What is the probability that the sum of the numbers is 5?
See answer
Correct answer: (A) 1/9
1 marks · 2023 · Set A
Question 106
When x³¹ + 31 is divided by x + 1, the remainder is
See answer
Correct answer: (C) 30
1 marks · 2023 · Set A
Question 107
A ticket is drawn at random from tickets numbered 1 to 40. What is the probability that its number is a multiple of 7?
See answer
Correct answer: (B) 1/8
1 marks · 2023 · Set A
Question 108
A person bought a horse and a car for ₹20,000. The horse was sold at 20% profit and the car at 10% loss, giving an overall profit of 2%. What was the horse’s purchase cost?
See answer
Correct answer: (C) ₹8,000
1 marks · 2023 · Set A
Question 109
A lottery has 6 prizes and 24 blanks. What is the probability of not winning a prize?
See answer
Correct answer: (C) 4/5
1 marks · 2023 · Set A
Question 110
The quadratic equation ax² + bx + c = 0 (a ≠ 0) has two distinct real roots if
See answer
Correct answer: (A) the discriminant > 0
1 marks · 2023 · Set A
Question 111
a and b are positive integers whose least prime factors are 2 and 5, respectively. What is the least prime factor of a + b?
See answer
Correct answer: (E) None of the above
1 marks · 2023 · Set A
Question 112
XY is parallel to AC in ΔABC and divides the triangle into two equal-area parts. Find AX/AB.
See answer
Correct answer: (B) (2 − √2)/2
1 marks · 2023 · Set A
Question 113
Which term of the AP 72, 63, 54, … is 0?
See answer
Correct answer: (B) 9th
1 marks · 2023 · Set A
Question 114
For the polynomial x⁴ + x³ − 9x² − 3x + 8, two zeros are −√3 and √3. The remaining zeros are
See answer
Correct answer: (E) None of the above
1 marks · 2023 · Set A
Question 115
If (cos θ − sin θ)/(cos θ + sin θ) = (1 − √3)/(1 + √3) and 0° < θ < 90°, find θ.
See answer
Correct answer: (B) 60°
1 marks · 2023 · Set A
Question 116
If tan² θ = 1 + 2 tan² α, then sin² θ equals
See answer
Correct answer: (A) ½(1 + sin² α)
1 marks · 2023 · Set A
Question 117
Taxi charges include a fixed charge and a per-kilometre charge. A 60 km trip costs ₹960 and an 80 km trip costs ₹1,260. Find the fixed charge and rate per kilometre.
See answer
Correct answer: (A) ₹60 and ₹15/km
1 marks · 2023 · Set A
Question 118
A vertical tower is surmounted by a vertical flagstaff of height h. From a point on the horizontal plane, the angles of elevation of the flagstaff’s bottom and top are α and β, respectively. Find the tower’s height.
See answer
Correct answer: (C) h tan α/(tan β − tan α)
1 marks · 2023 · Set A
Question 119
A girl 90 cm tall walks away from a lamppost at 1.2 m/s. The lamp is 3.6 m above the ground. What is the length of her shadow after 4 seconds?
See answer
Correct answer: (A) 1.6 m
1 marks · 2023 · Set A
Question 120
(sin θ − cos θ + 1)/(sin θ + cos θ − 1) is equal to