Mathematics-I - January 2024 Exam

If for the vectors a and b, |a|=1, |b|=2 and a · b = √3, then angle between the vectors a and b is

If one root of the equation x² - 6x + m = 0 be double the other, then the value of m is

The value of 2log₂5 + 9log₃√3 is

The value of the expression ω²(1+i)(iω - 1) is

The value of k · (i j) is

If z = 2 + i√3, then z z is

The coefficient of x³ in the expansion of (1 + 3x + 3x² + x³)¹⁰ is

If the vectors 2i - 3j + k and m i - j + m k are perpendicular to each other, then the value of m is

If cos(sin⁻¹ (1/5) + cos⁻¹ x) = 0, then the value of x is

If cos 3x = sin 2x, then x is

If f(x - 2) = 2x² + 3x - 5, then f(-1) =

Mathematics-I - January 2024 Exam

Time Allowed: 2.5 hours
Full Marks: 60
Instructions: Answer question 1 of Group A, and 5 questions from Group B. Question 1 MCQ's each carry 2 marks. Correct explanations are necessary to score marks.

Group A - Multiple Choice Questions

Q1-i: If |𝒂| = 1, |𝒃| = 2, 𝒂⋅𝒃 = √3, then the angle between 𝒂 and 𝒃 is 45°.
Q1-ii: If one root of x² – 6x + m = 0 is double the other, then m = 8.
Q1-iii: The value of 2log₂5 + 9log₁₀√3 ≈ 9.
Q1-iv: The value of w² (1+i) (iω - 1) = -1.
Q1-v: The value of k(i j) = 0.
Q1-vi: If z = 2+i√3, then zz = 7.
Q1-vii: The coefficient of x³ in the expansion of (1 + 3x + 3x² + x³)¹⁰ is 10C3 = 120.
Q1-viii: If the vectors 2i – 3j + k and mi – j + mk are perpendicular, then m = -2.
Q1-ix: If cos (sin x + cos x) = 0, then x = 5π/4.
Q1-x: If cos 3x = sin 2x, then x = 15°.
Q1-xi: If f(x – 2) = 2x² + 3x – 5, then f(-1) = 0.
Q1-xii: The domain of the function √((x-2)(3-x)) is 2 ≤ x ≤ 3.
Q1-xiii: lim (cot x)/(x-π/2) as x → π/2 = -1.
Q1-xiv: If f(x) = logₑx + eˣ, then f'(x) = eˣ + 1/x.
Q1-xv: The function (3-x) (x-1)² is maximum for x = 2.

Group B - Extended Answer Questions

Instructions: Answer any five questions.

(Note: Detailed solutions and explanations to Group B questions are not provided in these concise notes)

Prepare for your Mathematics-I January 2024 exam with this comprehensive quiz. Covering multiple choice questions from key topics, this quiz ensures you revise effectively and understand the concepts thoroughly. Dive in and test your knowledge before the exam!