In the following question, we ask you to prove a statement. List the step in proof, and give the reason for step. If `pge5` is a prime number,show that `p^2+2` is divisible by 3.

If p ge 5 is a prime number, show that p^2 + 2 is a composite number.

Use proof by contradition to prove that if for an integer a, a^2 is divisible by 3, then a is divisible by 3.

Use method of induction, prove that : n^3+3n^2+5n+3 is divisible by 3.

Which of the following substances on treatment with P_2O_5 gives ethanenitrile ?

Combine the following statements using "if and only if' p: if the sum of digit of a number is divisible by3, then the numebr is divisible by 3.

Write the following statements as equation 5 less than thrice the number gives 2.

State whether the following statements are true or false. Justify your answer. : Not all even numbers are divisible by 2.

Direction. In the following questions, a statement of assertion is followed by a statement of reason. While answering a question, you are required to choose the correct are out of the given four responses and mark it as (A). If both assertion and reason are true and reason is the correct explanation of the assertion, (B) if both assertion and reason are true but reason is not correct explanation of the assertion. (C) if assertion is true, but reason if false, (D) if both assertion and reason are false Assertion : A transformers are used only with an a.c. source and not with the d.c. source. Reason : Only a.c. can be stepped up or stepped down by means of transformers.

Direction. In the following questions, a statement of assertion is followed by a statement of reason. While answering a question, you are required to choose the correct are out of the given four responses and mark it as (A). If both assertion and reason are true and reason is the correct explanation of the assertion, (B) if both assertion and reason are true but reason is not correct explanation of the assertion. (C) if assertion is true, but reason if false, (D) if both assertion and reason are false Assertion : We use a thick wire in the secondary of a step down transformer to reduce the production of heat. Reason : When the plane of the armature is parallel to the lines of force of magnetic field, the magnitude of induced e.m.f. is maximum.

Direction. In the follwing questions, a statement of assertion is followed by a statement of reason. While answering a question, you are required to choose the correct are out of the given four responses and mark it as (A). If both assertion and reason are true and reason is the correct explanation of the assertion, (B) if both assertion and reason are true but reason is not correct explanation of the assertion. (C) if assertion is true, but reason if false, (D) if both assertion and reason are false Assertion : A transformer can be used to increase/ decrease both voltage and the current. Reason : In a transformer, e_p I_p = e_sI_s and accordingly, if we gain in voltage, we lose in current and vice-versa.