List of practice Questions

A bag contains 3 red, 4 white, and 5 blue balls. Two balls are drawn at random. What is the probability that both are of the same color?
If the roots of the equation \( x^2 - 2px + p^2 - 1 = 0 \) are real and distinct, what is the range of \( p \)?
The area of a rectangle is 63 cm², and its perimeter is 32 cm. What is the length of the rectangle?
In how many ways can 5 different books be arranged on a shelf if two particular books must be together?
A car travels from A to B at 60 km/h and returns at 40 km/h. What is the average speed for the entire journey?
A and B together can complete a work in 12 days, B and C together in 15 days, and C and A together in 20 days. In how many days can A alone complete the work?
If \( a, b, c \) are in geometric progression, and \( a, b, 2c \) are in arithmetic progression, then what is the common ratio of the geometric progression?
A man can row at 5 km/h in still water. If the river flows at 1 km/h and it takes him 1 hour to row to a place and return, what is the distance he rows to the place?
The sum of the first \( n \) terms of an arithmetic progression is \( 3n^2 + 5n \). What is the first term of the series?
A and B run a 1 km race. If A gives B a start of 50 m and still beats him by 15 seconds, and if A gives B a start of 70 m and beats him by 10 seconds, find the time taken by A to run 1 km.
In a class of 50 students, 23 speak English, 15 speak Hindi, and 18 speak Tamil. 8 speak both English and Hindi, 11 speak both Hindi and Tamil, 6 speak both English and Tamil, and 5 speak all three languages. How many students speak exactly two languages?
The cost of a pair of shoes varies directly as the square of its size. If a pair of size 5 costs Rs. 500, what is the cost of a pair of size 7?
If \( \log_3 2, \log_3 (2^x - 5), \log_3 (2^x - 7/2) \) are in arithmetic progression, then what is the value of \( x \)?
A person buys 12 articles for Rs. 12 and sells them at Rs. 12 for 10 articles. What is the profit percentage?
The sum of the ages of a father and his son is 45 years. Five years ago, the product of their ages was 124. What are their current ages?
A shopkeeper sells a product at a 20% profit. If he buys it at 20% less cost and sells it for Rs. 10 less, he earns a 25% profit. What is the original cost price?
In a triangle ABC, the lengths of the sides AB and AC are 17.5 cm and 9 cm respectively. Let D be a point on AB such that AD = 7 cm. What is the length of CD?
A cube of side 4 cm is painted on all its faces. If it is sliced into 1 cm cubes, how many 1 cm cubes will have exactly one face painted?
The average price of 10 books is Rs. 12 while the average price of 8 of these books is Rs. 11.75. Of the remaining two books, if the price of one book is 60% more than the price of the other, what is the price of each of these two books?
Efficiency of drug is checked in modest population in
Potential difference between $A$ and $B$ in the following circuit
In order to make a generic substitution; a pharmacist must do also act as a hydrogen bond acceptor
$A, B, C$ and $D$ are four different physical quantities having different dimensions. None of them is dimensionless. But we know that the equation $AD = C$ ln $(BD)$ holds true. Then which of the combination is not a meaningful quantity ?
A cell organelle containing hydrolytic enzymes is -
A person trying to lose weight by burning at lifts a mass of $10\, kg$ upto a height of $1\, m$ $1000$ times. Assume that the potential energy lost each time he lowers the mass is dissipated. How much fat will he use up considering the work done only when the weight is lifted up ? Fat supplies $3.8 \times 10^7 \, J$ of energy per kg which is converted to mechanical energy with a $20\%$ efficiency rate. Take $g = 9.8 \, ms^{-2}$ :