Select the correct word from the following list and fill in the blanks.
float, water, crop, nutrients, preparation
(a) The same kind of plants grown and cultivated on a large scale at a
place is called _____________.
(b) The first step before growing crops is _____________ of the soil.
(c) Damaged seeds would _____________ on top of water.
(d) For growing a crop, sufficient sunlight and _____________ and
_____________ from the soil are essential.
Define an arithmetic progression. If the first term of an arithmetic progression is 7 and the common difference is 3, find the 15th term of the sequence.
Define the modulus of a complex number. Find the modulus of the complex number 3 plus 4i.
Prove by induction that the sum of the first n natural numbers is equal to n times n plus 1 over 2.
Prove that the sum of the angles in a triangle is equal to 180 degrees. Use trigonometric identities to show that sine of x plus cosine of x is equal to 1.
Define the union and intersection of two sets. Given set A equal to 1, 2, 3 and set B equal to 2, 3, 4, find A union B and A intersection B.
Define the equation of a plane in 3D space. How do you find the distance of a point from a plane?
Define the scalar product of two vectors. If vector A is equal to i plus 2j and vector B is equal to 3i minus j, find the scalar product of A and B.
Explain the concept of feasible region in linear programming. Formulate a linear programming problem to maximize profit given constraints on resources.
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