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Sequence and Series – Arithmetic Progression

If the first term of an arithmetic progression is 5 and the common difference is 3, find the tenth term of the progression.

02/11/2024

Mathematics

12th (Science)

Statistics – Mean Calculation

Find the mean of the following data set: 10, 15, 20, 25, 30.

02/11/2024

Mathematics

12th (Science)

Trigonometry – Angle Calculation

Prove that the sine squared of an angle plus cosine squared of the angle equals 1 for any angle.

02/11/2024

Mathematics

12th (Science)

Linear Equations – System of Equations

Solve the system of equations: x plus y equals 5 2x minus y equals 3

02/11/2024

Mathematics

12th (Science)

Sets – Union and Intersection

Given set A equals the set of all even numbers and set B equals the set of all prime numbers, find the union and intersection of sets A and B.

02/11/2024

Mathematics

12th (Science)

Vector Algebra – Dot Product

If vector A is equal to 2i plus 3j and vector B is equal to i minus j, find the dot product of vectors A and B.

02/11/2024

Mathematics

12th (Science)

Probability – Theoretical Probability

A die is rolled. Calculate the probability of getting an even number and the probability of getting a number greater than 4.

02/11/2024

Mathematics

12th (Science)

Integration – Definite Integral

Evaluate the definite integral of the function f of x equal to x cubed from 1 to 3.

02/11/2024

Mathematics

12th (Science)

Differentiation – Application

Differentiate the function f of x equal to x squared plus 3x plus 2 with respect to x and find the equation of the tangent at the point where x equals 1.

02/11/2024

Mathematics

12th (Science)

Environmental Chemistry – Green Chemistry

Explain the principles of green chemistry. Discuss how green chemistry can help in reducing pollution, providing examples of green chemical processes or products.

02/11/2024

Chemistry

12th (Science)