Mathematics – Class 11 Practice Test 4

1. 7²ⁿ + 2^{2n – 2} . 3^{n – 1} is divisible by 50 by principle of mathematical induction.

2. By principle of mathematical induction, 2^4n-1 is divisible by which of the following?

3. Find the principal solutions of the equation cos x = 1/2.

4. i⁷ =______________

5. Solve x²+1 = 0.

6. \(\sqrt{x^2+y^2}\) distance of point representing complex number x+y i from origin.

7. State whether the following series is true or not.
1 + 2 + 3 +…..+ n = \(\frac{n(n + 1)}{2}\)

8. Find the principal solutions of the equation sec x = -2.

9. If z₁ = 2+3i and z₂ = 5+2i, then find z₁-z₂.

10. The expression involving integer ‘n’ which gives all solutions of a trigonometric equation is called the principal solution.