| 151 |
If P(A) = 0.5, P(B) = 0.4 and P(A ∪ B) = 0.8, then P(A′|B) equals |
Mathematics/Applied Mathematics
Conditional probability |
Hard |
| 152 |
A and B are independent events with P(A) = 0.3 and P(B) = 0.5. Then P(A ∩ B) is |
Mathematics/Applied Mathematics
Multiplication theorem and independent events |
Easy |
| 153 |
A bag has 4 red and 6 black balls. Two balls are drawn one after the other without replacement. The probabili… |
Mathematics/Applied Mathematics
Multiplication theorem and independent events |
Easy |
| 154 |
A and B are independent with P(A) = 0.4 and P(B) = 0.5. Then P(A ∪ B) equals |
Mathematics/Applied Mathematics
Multiplication theorem and independent events |
Medium |
| 155 |
A and B are mutually exclusive events with P(A) > 0 and P(B) > 0. Which statement is true? |
Mathematics/Applied Mathematics
Multiplication theorem and independent events |
Medium |
| 156 |
Three students independently try a problem with probabilities 1/2, 1/3 and 1/4 of solving it. The probability… |
Mathematics/Applied Mathematics
Multiplication theorem and independent events |
Hard |
| 157 |
One of two bags is chosen at random. Bag I has 2 red and 3 white balls; bag II has 4 red and 1 white ball. On… |
Mathematics/Applied Mathematics
Total probability and Bayes’ theorem |
Easy |
| 158 |
Bayes' theorem is mainly used to find |
Mathematics/Applied Mathematics
Total probability and Bayes’ theorem |
Easy |
| 159 |
Bag A has 3 red and 1 blue ball; bag B has 1 red and 3 blue balls. A bag is picked at random and a red ball i… |
Mathematics/Applied Mathematics
Total probability and Bayes’ theorem |
Medium |
| 160 |
Machines X and Y make 70% and 30% of a factory's bulbs, with 2% and 5% of their output defective. A bulb is c… |
Mathematics/Applied Mathematics
Total probability and Bayes’ theorem |
Medium |
| 161 |
Machines P and Q make 60% and 40% of the items in a factory, with 1% and 4% defective respectively. An item p… |
Mathematics/Applied Mathematics
Total probability and Bayes’ theorem |
Hard |
| 162 |
The value of 47 mod 5 is |
Mathematics/Applied Mathematics
Modulo arithmetic and congruence |
Easy |
| 163 |
Which of these congruences modulo 7 is correct? |
Mathematics/Applied Mathematics
Modulo arithmetic and congruence |
Easy |
| 164 |
The value of (17 × 23) mod 5 is |
Mathematics/Applied Mathematics
Modulo arithmetic and congruence |
Medium |
| 165 |
Today is a Wednesday. Which day of the week will it be 100 days from today? |
Mathematics/Applied Mathematics
Modulo arithmetic and congruence |
Medium |
| 166 |
The remainder when 2⁵⁰ is divided by 7 is |
Mathematics/Applied Mathematics
Modulo arithmetic and congruence |
Hard |
| 167 |
Rice costing ₹40 per kg and rice costing ₹60 per kg are mixed in the ratio 1 : 1. The mean price of the mixtu… |
Mathematics/Applied Mathematics
Alligation and mixtures |
Easy |
| 168 |
By the rule of alligation, with cheaper price c, dearer price d and mean price m, the ratio quantity of cheap… |
Mathematics/Applied Mathematics
Alligation and mixtures |
Easy |
| 169 |
In what ratio must tea at ₹120 per kg be mixed with tea at ₹180 per kg so that the mixture is worth ₹140 per … |
Mathematics/Applied Mathematics
Alligation and mixtures |
Medium |
| 170 |
A grocer mixes 3 kg of sugar at ₹50 per kg with 2 kg at ₹75 per kg. The cost price of the mixture per kg is |
Mathematics/Applied Mathematics
Alligation and mixtures |
Medium |
| 171 |
A vessel holds 40 litres of milk. Four litres are taken out and replaced with water, and this is done once mo… |
Mathematics/Applied Mathematics
Alligation and mixtures |
Hard |
| 172 |
A boat goes at 10 km/h in still water and the stream flows at 2 km/h. Its downstream speed is |
Mathematics/Applied Mathematics
Boats and streams |
Easy |
| 173 |
A boat's downstream speed is 15 km/h and its upstream speed is 9 km/h. Its speed in still water is |
Mathematics/Applied Mathematics
Boats and streams |
Easy |
| 174 |
A boat with a speed of 8 km/h in still water travels 30 km upstream in a stream flowing at 2 km/h. How long d… |
Mathematics/Applied Mathematics
Boats and streams |
Medium |
| 175 |
A man rows 24 km downstream in 2 hours and 12 km upstream in 2 hours. The speed of the stream is |
Mathematics/Applied Mathematics
Boats and streams |
Medium |
| 176 |
A boat goes 24 km downstream and returns in a total of 5 hours. The stream flows at 2 km/h. The speed of the … |
Mathematics/Applied Mathematics
Boats and streams |
Hard |
| 177 |
A pipe can fill a tank in 6 hours. What part of the tank does it fill in one hour? |
Mathematics/Applied Mathematics
Pipes and cisterns |
Easy |
| 178 |
Pipe A fills a tank in 10 hours and pipe B fills it in 15 hours. Working together, they fill it in |
Mathematics/Applied Mathematics
Pipes and cisterns |
Easy |
| 179 |
A pipe fills a tank in 4 hours, but an outlet empties the full tank in 6 hours. If both are open, the tank fi… |
Mathematics/Applied Mathematics
Pipes and cisterns |
Medium |
| 180 |
Three pipes can fill a tank in 12, 18 and 36 hours respectively. All three together fill it in |
Mathematics/Applied Mathematics
Pipes and cisterns |
Medium |
| 181 |
Pipes A and B can fill a tank in 20 minutes and 30 minutes. Both are opened together, and B is closed after 6… |
Mathematics/Applied Mathematics
Pipes and cisterns |
Hard |
| 182 |
In a 100 m race, A beats B by 10 m. This means that when A finishes, B has run |
Mathematics/Applied Mathematics
Races and games |
Easy |
| 183 |
A runs 100 m in 20 seconds and B runs 100 m in 25 seconds. By how many seconds does A beat B in a 100 m race? |
Mathematics/Applied Mathematics
Races and games |
Easy |
| 184 |
A runs 100 m in 20 seconds and B runs 100 m in 25 seconds. By how many metres does A beat B in a 100 m race? |
Mathematics/Applied Mathematics
Races and games |
Medium |
| 185 |
In a 1 km race A beats B by 100 m, and in a 1 km race B beats C by 100 m. By how much does A beat C in a 1 km… |
Mathematics/Applied Mathematics
Races and games |
Medium |
| 186 |
In a 200 m race, A gives B a start of 20 m and still beats B by 10 m. The ratio of the speeds of A and B is |
Mathematics/Applied Mathematics
Races and games |
Hard |
| 187 |
The statement "a person must be at least 18 years old to vote", with age x in years, is written as |
Mathematics/Applied Mathematics
Numerical inequalities |
Easy |
| 188 |
The solution of 3x − 5 < 7 is |
Mathematics/Applied Mathematics
Numerical inequalities |
Easy |
| 189 |
A student scored 70 and 75 in two tests. What must she score in the third test so that her average over the t… |
Mathematics/Applied Mathematics
Numerical inequalities |
Medium |
| 190 |
The solution of the inequality −2x ≥ 6 is |
Mathematics/Applied Mathematics
Numerical inequalities |
Medium |
| 191 |
The set of real numbers x satisfying |x − 3| < 2 is |
Mathematics/Applied Mathematics
Numerical inequalities |
Hard |
| 192 |
If y = x³ − 4x, the value of d²y/dx² at x = 2 is: |
Mathematics/Applied Mathematics
Derivatives in applications |
Easy |
| 193 |
If x = 2t + 1 and y = t³, the value of dy/dx at t = 2 is: |
Mathematics/Applied Mathematics
Derivatives in applications |
Easy |
| 194 |
The slope of the tangent to the curve xy = 12 at the point (3, 4) is: |
Mathematics/Applied Mathematics
Derivatives in applications |
Medium |
| 195 |
The radius of a spherical balloon increases at 2 cm/s. How fast is its volume increasing when the radius is 5… |
Mathematics/Applied Mathematics
Derivatives in applications |
Medium |
| 196 |
If x = a cos t and y = a sin t, then d²y/dx² equals: |
Mathematics/Applied Mathematics
Derivatives in applications |
Hard |
| 197 |
Marginal cost is best described as: |
Mathematics/Applied Mathematics
Marginal cost and marginal revenue |
Easy |
| 198 |
If the total revenue from selling x units is R(x) = 3x² + 36x + 5, the marginal revenue when x = 5 is: |
Mathematics/Applied Mathematics
Marginal cost and marginal revenue |
Easy |
| 199 |
The total cost of producing x units is C(x) = 0.005x³ − 0.02x² + 30x + 5000. The marginal cost when 3 units a… |
Mathematics/Applied Mathematics
Marginal cost and marginal revenue |
Medium |
| 200 |
The demand function for a product is p = 50 − 2x. For what output x is the marginal revenue zero? |
Mathematics/Applied Mathematics
Marginal cost and marginal revenue |
Medium |