List of practice Questions

There are two containers of the same volume,first container half-filled with sugar syrup and the second container half-filled with milk.Half the content of the first container is transferred to the second container,and then the half of this mixture is transferred back to the first container.Next, half the content of the first container is transferred back to the second container.Then the ratio of sugar syrup and milk in the second container is

The average of a non-decreasing sequence of N numbers \(a_1,a_2,…,a_N\) is 300.If \(a_1\) is replaced by \(6a_1\), the new average becomes 400.Then,the number of possible values of \(a_1\) is

In an election,there were four candidates and \(80\%\) of the registered voters casted their votes.One of the candidates received \(30\%\) of the casted votes while the other three candidates received the remaining casted votes in the proportion \(1\ratio2\ratio3\).If the winner of the election received 2512 votes more than the candidate with the second highest votes, then the number of registered voters was

The number of integers greater than 2000 that can be formed with the digits 0,1,2,3,4,5 using each digit at most once,is

For some natural number n,assume that \((15,000)!\) is divisible by \((n!)!\) The largest possible value of n is

In an examination,there were 75 questions.3 marks were awarded for each correct answer,1 mark was deducted for each wrong answer and 1 mark was awarded for each unattempted question.Rayan scored a total of 97 marks in the examination.If the number of unattempted questions was higher than the number of attempted questions,then the maximum number of correct answers that Rayan could have given in the examination is

Five students,including Amit,appear for an examination in which possible marks are integers between 0 and 50,both inclusive.The average marks for all the students is 38 and exactly three students got more than 32.If no two students got the same marks and Amit got the least marks among the five students,then the difference between the highest and lowest possible marks of Amit is

The number of integer solutions of the equation \((x^2−10)^{(x2−3x−10)}=1\) is

Mr.Pinto invests one-fifth of his capital at \(6\%\),one-third at \(10\%\) and the remaining at \(1\%\),each rate being simple interest per annum.Then,the minimum number of years required for the cumulative interest income from these investments to equal or exceed his initial capital is

Consider the arithmetic progression 3,7,11,…and let \(A_n\) denote the sum of the first n terms of this progression.Then the value of \(\frac{1}{25}∑^{25}_{n=1}A_n\) is

Let ABCD be a parallelogram such that the coordinates of its three vertices A, B, C are (1, 1), (3, 4), and (−2, 8), respectively. Then, the coordinates of the vertex D are

The number of ways of distributing 20 identical balloons among 4 children such that each child gets some balloons but no child gets an odd number of balloons, is

For natural numbers x,y, and z, if xy+yz=19 and yz+xz=51, then the minimum possible value of xyz is

Trains A and B start traveling at the same time towards each other with constant speeds from stations X and Y, respectively. Train A reaches station Y in 10 minutes while train B takes 9 minutes to reach station X after meeting train A. Then the total time taken, in minutes, by train B to travel from station Y to station X is

The average of three integers is 13. When a natural number n is included, the average of these four integers remains an odd integer. The minimum possible value of n is

Ankita buys 4kg cashews, 14kg peanuts, and 6kg almonds when the cost of 7kg cashews is the same as that of 30kg peanuts or 9kg almonds. She mixes all three nuts and marks a price for the mixture in order to make a profit of ₹1752. She sells 4kg of the mixture at this marked price and the remaining at a 20% discount on the marked price, thus making a total profit of ₹744. Then the amount, in rupees, that she had spent buying almonds is

The largest real value of a for which the equation\( |x+a|+|x−1|=2\) has an infinite number of solutions for x is

A donation box can receive only cheques of ₹100,₹250 and ₹500. On one good day,the donation box was found to contain exactly 100 cheques amounting to a total sum of ₹15250. Then, the maximum possible number of cheques of ₹500 that the donation box may have contained,is

If \(c=\frac{16x}{y}+\frac{49y}{x} \)for some non-zero real numbers x and y,then c cannot take the value

Consider six distinct natural numbers such that the average of the two smallest numbers is 14 and the average of the two largest numbers is 28. Then,the maximum possible value of the average of these six numbers is

Two ships are approaching a port along straight routes at constant speeds. Initially,the two ships and the port formed an equilateral triangle with sides of length 24 km. When the slower ship travelled 8 km,the triangle formed by the new positions of the two ships and the port became right-angled. When the faster ship reaches the port, the distance,in km,between the other ship and the port will be

In an examination,the average marks of students in sections A and B are 32 and 60,respectively. The number of students in section A is 10 less than that in section B. If the average marks of all the students across both the sections combined is an integer,then the difference between the maximum and minimum possible number of students in section A is

If\(\left(\frac{\sqrt{7}}{5}\right)^{3x - y} = \frac{875}{2401}\) and \(\left(\frac{4a}{b}\right)^{6x - y}\)\(=\left(\frac{2a}{b}\right)^{y - 6x}\), for all non-zero real values of a and b,then the value of x+y is

The average of all 3-digit terms in the arithmetic progression 38,55,72,...,is

Pinky is standing in a queue at a ticket counter. Suppose the ratio of the number of persons standing ahead of Pinky to the number of persons standing behind her in the queue is 3:5. If the total number of persons in the queue is less than 300, then the maximum possible number of persons standing ahead of Pinky is