| 4401 |
The feasible region of an LPP is unbounded, and M is the largest value of Z = ax + by at its corners. If the … |
Mathematics/Applied Mathematics
Feasible and optimal solutions |
Medium |
| 4402 |
The minimum value of Z = 2x + 3y subject to x + y ≥ 4, x ≥ 0 and y ≥ 0 is |
Mathematics/Applied Mathematics
Feasible and optimal solutions |
Medium |
| 4403 |
For the LPP "maximise Z = x + 2y subject to x + y ≥ 2, x ≥ 0, y ≥ 0", which statement is correct? |
Mathematics/Applied Mathematics
Feasible and optimal solutions |
Hard |
| 4404 |
If P(B) = 0.5 and P(A ∩ B) = 0.2, then P(A|B) equals |
Mathematics/Applied Mathematics
Conditional probability |
Easy |
| 4405 |
A fair die is thrown and the number shown is known to be even. What is the probability that it is 6? |
Mathematics/Applied Mathematics
Conditional probability |
Easy |
| 4406 |
Two fair coins are tossed. Given that at least one shows a head, what is the probability that both show heads? |
Mathematics/Applied Mathematics
Conditional probability |
Medium |
| 4407 |
Two fair dice are thrown and the sum is 8. What is the probability that one of the dice shows 3? |
Mathematics/Applied Mathematics
Conditional probability |
Medium |
| 4408 |
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 |
| 4409 |
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 |
| 4410 |
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 |
| 4411 |
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 |
| 4412 |
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 |
| 4413 |
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 |
| 4414 |
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 |
| 4415 |
Bayes' theorem is mainly used to find |
Mathematics/Applied Mathematics
Total probability and Bayes’ theorem |
Easy |
| 4416 |
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 |
| 4417 |
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 |
| 4418 |
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 |
| 4419 |
The value of 47 mod 5 is |
Mathematics/Applied Mathematics
Modulo arithmetic and congruence |
Easy |
| 4420 |
Which of these congruences modulo 7 is correct? |
Mathematics/Applied Mathematics
Modulo arithmetic and congruence |
Easy |
| 4421 |
The value of (17 × 23) mod 5 is |
Mathematics/Applied Mathematics
Modulo arithmetic and congruence |
Medium |
| 4422 |
Today is a Wednesday. Which day of the week will it be 100 days from today? |
Mathematics/Applied Mathematics
Modulo arithmetic and congruence |
Medium |
| 4423 |
The remainder when 2⁵⁰ is divided by 7 is |
Mathematics/Applied Mathematics
Modulo arithmetic and congruence |
Hard |
| 4424 |
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 |
| 4425 |
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 |
| 4426 |
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 |
| 4427 |
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 |
| 4428 |
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 |
| 4429 |
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 |
| 4430 |
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 |
| 4431 |
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 |
| 4432 |
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 |
| 4433 |
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 |
| 4434 |
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 |
| 4435 |
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 |
| 4436 |
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 |
| 4437 |
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 |
| 4438 |
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 |
| 4439 |
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 |
| 4440 |
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 |
| 4441 |
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 |
| 4442 |
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 |
| 4443 |
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 |
| 4444 |
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 |
| 4445 |
The solution of 3x − 5 < 7 is |
Mathematics/Applied Mathematics
Numerical inequalities |
Easy |
| 4446 |
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 |
| 4447 |
The solution of the inequality −2x ≥ 6 is |
Mathematics/Applied Mathematics
Numerical inequalities |
Medium |
| 4448 |
The set of real numbers x satisfying |x − 3| < 2 is |
Mathematics/Applied Mathematics
Numerical inequalities |
Hard |
| 4449 |
If y = x³ − 4x, the value of d²y/dx² at x = 2 is: |
Mathematics/Applied Mathematics
Derivatives in applications |
Easy |
| 4450 |
If x = 2t + 1 and y = t³, the value of dy/dx at t = 2 is: |
Mathematics/Applied Mathematics
Derivatives in applications |
Easy |