List of practice Questions

Let $R$ be a relation on $R$, given by $R=\{(a, b): 3 a-3 b+\sqrt{7}$ is an irrational number $\}$Then $R$ is

Form the differential equation of $y=a{e}^{3x}\cos (x+b)$ Where $y^{\prime }=\frac{dy}{dx}$ and $y^n=\frac{d^{2}y}{d{x}^2}$?

Find the centre and radius of $x^2+y^2+6y=0$.

If $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ are non-coplanar vectors and $\lambda$ is a real number, then$[\lambda (\overrightarrow{a}+\overrightarrow{b}){\lambda }^2\overrightarrow{b}\lambda \overrightarrow{c}]=[\overrightarrow{a}\overrightarrow{b}+\overrightarrow{c}\overrightarrow{b}]$ for

The angle $\theta$ between the vectors $\overrightarrow{a}=5\hat{i}-\hat{j}+\hat{k}$ and $\overrightarrow{b}=\hat{i}+\hat{j}-\hat{k}$ is:

If 4x² + py² = 45 and x² - 4y² = 5 cut orthogonally, then the value of p is:

At 16°C, two open-end organ pipes, when sounded together produce 34 beats in 2 seconds. How many beats per second will be produced if the temperature rises to 51°C? Neglect the increase in the length of the pipes.

If the orthocentre of the triangle, whose vertices are $(1,2),(2,3)$ and $(3,1)$ is $(\alpha, \beta)$, then the quadratic equation whose roots are $\alpha+4 \beta$ and $4 \alpha+\beta$, is

A rectangular plot of land measures 55 meters by 25 meters. A path of uniform width surrounds the plot. If the area of the path is equal to the area of the plot, what is the width of the path in meters?

Bala bought 100 kg of flour and 100 kg of sugar. The flour was 25% cheaper than the sugar per kg. He mixed the entire quantity and sold the mixture at ₹275.50 per kg, making an overall profit of 50%. What is the cost price of flour per kg?

All the vertices of a rhombus lie on a circle of radius R. If the length of one diagonal of the rhombus is D, then the area of the rhombus is:

Old Mr. Baker was known for his impeccable calculations. He had a small bakery, and every day, he meticulously recorded the number of loaves he baked. One week, he found the average number of loaves baked per day was thirteen. Determined to maintain his bakery's reputation for consistency, he decided to include the next day's loaf count in his average. However, he wanted to ensure the average for the six days remained a whole number. What was the smallest number of loaves he could bake on the sixth day to achieve this?

A chemist has two solutions, A and B. Solution A is 30% acid and the rest water, while solution B is 60% acid and the rest water. If equal amounts of solutions A and B are mixed to form a new solution C, what is the percentage of acid in solution C?

A tailor had a piece of cloth. He initially reduced its length by 80%. After this, he further shortened it by 90% of its new length. What was the percentage decrease in the cloth's length from the first to the second cut?

A fruit basket contains 80 apples, 70 oranges, and 60 bananas. Some fruits might be rotten and discarded. What is the difference between the maximum and minimum possible number of fruits that are both apples and oranges?

A triangular garden has its corners at points A(2, 3), B(5, 7), and C(1, 6) on a coordinate plane. If a fourth point D is added to form a parallelogram ABCD, what are the coordinates of point D?

Raj invested a certain sum of money in two schemes. The first scheme offers a simple interest of 10% per annum, and the second scheme offers a simple interest of 12% per annum. If the total interest earned from both schemes after 3 years is Rs. 1980, and the ratio of the amounts invested in the two schemes is 5:4, what is the amount invested in the second scheme?

A group of friends decided to share the cost of a gift equally. If each person contributed Rs. 50, the amount would have been short by Rs. 20. However, if each person contributed Rs. 60, they would have Rs. 30 more than the required amount. What is the price of the gift?

At what exact time between 3:00 PM and 4:00 PM do the hour and minute hands of a standard clock coincide?

A factory produces a certain number of toys in a week using a team of 40 workers who work for 8 hours daily. Due to an increase in demand, the factory needs to double the production while maintaining the same work schedule. How many additional workers should be hired?

Vrushali invested Rs. (X + 3000) on compound interest of r% p.a. compounded annually for 2 years and Tarushi invested Rs. (X - 2000) on simple interest of (r - 2)% p.a. for 3 years. The total interest received by both of them is together Rs. 12360. If Anant invested Rs. (X + 8000) on simple interest for 3 years on 15% and received an interest of Rs. 13500, find the value of ‘r’.

If a, b and c are integers such that a² + b² + c² = 228, a + b + c = 26 and b = c, then what is the value of a ?

If \((4x^2+\frac{1}{4x^2})=2\), then what is the value of \((8x^3+\frac{1}{8x^3})\) ?
A) +2
B) -2
C) +4
D) -4

Consider the following reaction scheme and choose the correct option(s) for the major products Q, R and S.