Practice Questions

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If the roots of the equation x² + px + q = 0 differ by 1, then
If the roots of the equation x² – 2ax + (a² + a – 3) = 0 are real and less than 3, where ‘a’ is some constant, then:
For real numbers a, b, c we have c(a+b+c) < 0, then which of the following is true about the roots of the quadratic equation ax² + bx + c = 0?
Minimum value of (b+c)/a + (a+c)/b + (a+b)/c, for real positive numbers ‘a’, ‘b’, ‘c’, is

Each of six persons, Anil, Karthik, Jayanta, Lakshman, Pankaj and Raju, are standing in a queue, one behind the other, all facing the same direction. Each person has with him a different number of chocolates among 10, 14, 18, 19, 23 and 29.

It is also known that:
(I) For any pair of persons adjacent to each other, the difference between the number of chocolates with the two of them is greater than four.
(II) Karthik, who is standing behind Anil, has four chocolates more than the number of chocolates with the person standing at the end of the queue.
(III) Not more than four persons are standing in front of the person with the least number of chocolates.
(IV) Jayanta is standing immediately behind Lakshman.
(V) Pankaj, who has five chocolates more than Lakshman, is standing three places away from Anil.

Who has the highest number of chocolates?
How many chocolates does the person standing at the beginning of the queue have?
What is the total number of chocolates with the last three persons in the queue?
For how many persons is the number of chocolates with them greater than that with any person standing adjacent to them?

Suppose C1, C2, C3, C4, C5 are five companies. The profits made by C1, C2, C3 are in the ratio 9 : 10 : 8, while the profits made by C2, C4, C5 are in the ratio 18 : 19 : 20. If C5 has made a profit of Rs. 19 crore more than C1, then the total profit made by all five companies is
If Fatima sells 60 identical toys at a 40% discount on the printed price, then she makes 20% profit. Ten of these toys are destroyed in fire. While selling the rest, how much discount should be given on the printed price so that she can make the same amount of profit?
Arun drove from home to his hostel at 60 miles per hour. While returning home he drove halfway along the same route at a speed of 25 miles per hour and then took a bypass road which increased his driving distance by 5 miles, but allowed him to drive at 50 miles per hour. If his return journey took 30 minutes more than the onwards journey, then the total distance travelled by him is
The average height of 22 toddlers increases by 2 inches when two of them leave the group. If the average height of these two toddlers is one-third the average height of all the 22 toddlers, then the average height of the remaining 20 toddlers is

The average income of n members in a family is Rs.16000 per month. If the salary of each of the 25% of the members’ is doubled and the salary of each of the remaining members become 3 times their original values, by what percentage could the current average exceed the original average?
Directions for the next two questions: A and B start from P and Q at 20 km/hr and 15 km/hr, at the same time respectively and meet every day at X on the way.

One day B starts ‘t’ minutes late. So he meets A 5 km ahead of X at Y. Find ‘t’.
If B had increased his speed by 20% at Q and left at the normal time, he would have met A at Z. If XZ = 5 km, find the distance QX.
A can do a work in 30 days, B can do it in 40 days and C can destroy the work in 50 days. If A and B work together, alternating with C, (i.e. A & B together on day 1 and C alone on day 2 and so on), how long will it take to complete the work?

The annual salaries (in lakhs) of six employees – Aman, Bibek, Jai, Kumar, Pritam and Tanmay of a mineral water plant – are 4, 7, 8, 9, 10 and 12, in no particular order. Each of them saves a different percentage of his/her annual salary among 5%, 10%, 15%, 20%, 25% and 30%, and invests his/her entire savings in a different investment option among Real Estate, Gold, PMVVY, POSS, NPS and Direct Equities, in no particular order. It is also known that:

(I) The employee who earns the highest, saves 2.4 lakhs and invests it in POSS. Jai saves 15% of her annual salary.
(II) The annual salary of Pritam is the least among the six. He saves one-twelfth of the amount saved by the employee who invests in PMVVY.
(III) The average of the annual salaries of Aman, Bibek and Kumar is 8 lakhs.
(IV) Bibek invests in NPS. The employee who saves 25% does not invest in Gold.
(V) The sum of the annual salaries of the employee who invests in Real Estate and the employee who saves 10% is equal to the sum of the annual salaries of Aman and another employee who saves 30%.

What is the absolute difference (in lakhs) between the savings of Pritam and Jai?
Who among the following invests his/her savings in Real Estate?
What is the annual salary (in lakhs) of Tanmay?
Which of the following employees have the same annual savings?

In the figure, CX bisects ∠ACB. Which of the following is then true?

In the figure, AD = AC and ∠BCA = 2∠E. The distance between parallel lines AB and CD is ‘h’. If the area of parallelogram ABCD is written as ‘X’ and the area of ∆ADE is written as ‘Y’, then what can be the relation between X and Y?

The figure shows an isosceles triangle ABC with AB = BC. The line DE cuts the line AC extended at point F. If AD = 5, CE = 3 and EF = 8, find DE
Find the area of a triangle having sides as √13, √61, √80