Podcast
Questions and Answers
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 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
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 2log₂5 + 9log₃√3 is
The value of the expression ω²(1 + i)(iω -1) is
The value of the expression ω²(1 + i)(iω -1) is
Signup and view all the answers
If z=2+i√3, then z.z* is
If z=2+i√3, then z.z* is
Signup and view all the answers
The coefficient of x³ in the expansion of (1 + 3x + 3x² + x³)¹⁰ is
The coefficient of x³ in the expansion of (1 + 3x + 3x² + x³)¹⁰ is
Signup and view all the answers
If the vectors 2i-3j+k and mi-j+mk are perpendicular to each other, then the value of m is
If the vectors 2i-3j+k and mi-j+mk are perpendicular to each other, then the value of m is
Signup and view all the answers
If cos(sin⁻¹(1/5) + cos⁻¹(x)) = 0, then the value of x is
If cos(sin⁻¹(1/5) + cos⁻¹(x)) = 0, then the value of x is
Signup and view all the answers
If cos 3x = sin 2x, then x is
If cos 3x = sin 2x, then x is
Signup and view all the answers
If f(x-2)=2x²+3x-5, then f(-1) is
If f(x-2)=2x²+3x-5, then f(-1) is
Signup and view all the answers
The domain of the function 1/√(x-2)(3-x) is
The domain of the function 1/√(x-2)(3-x) is
Signup and view all the answers
Lim_(x→(π/2)) (cot x) / (π/2 -x) is
Lim_(x→(π/2)) (cot x) / (π/2 -x) is
Signup and view all the answers
If f(x) = logeˣ + e^lox , then f'(x) is
If f(x) = logeˣ + e^lox , then f'(x) is
Signup and view all the answers
The function (3-x)(x-1) is maximum for x =
The function (3-x)(x-1) is maximum for x =
Signup and view all the answers
If α and β be the roots of the equation x² - 3x + 2 = 0, find the equation whose roots are 1/α and 1/β.
If α and β be the roots of the equation x² - 3x + 2 = 0, find the equation whose roots are 1/α and 1/β.
Signup and view all the answers
The fifth term in the expansion of (x² - 1/x)ⁿ is independent of x. Find n.
The fifth term in the expansion of (x² - 1/x)ⁿ is independent of x. Find n.
Signup and view all the answers
Prove that √i + √-i = √2 where i = √-1.
Prove that √i + √-i = √2 where i = √-1.
Signup and view all the answers
If a = 2i+j-k, b=i-2j-2k and c=3i-4j+2k, find the projection of a + c in the direction of b.
If a = 2i+j-k, b=i-2j-2k and c=3i-4j+2k, find the projection of a + c in the direction of b.
Signup and view all the answers
Prove that 2log(a+b) = 2loga+log(1 + b²/a²).
Prove that 2log(a+b) = 2loga+log(1 + b²/a²).
Signup and view all the answers
If ω³ = 1 and 1 + ω + ω² = 0, find the value of ω²⁰²² + ω²⁰²³ +ω²⁰²⁴
If ω³ = 1 and 1 + ω + ω² = 0, find the value of ω²⁰²² + ω²⁰²³ +ω²⁰²⁴
Signup and view all the answers
If tan⁻¹(1/2)+ 4 tan⁻¹(1/3) = θ/2, find the value of sin θ.
If tan⁻¹(1/2)+ 4 tan⁻¹(1/3) = θ/2, find the value of sin θ.
Signup and view all the answers
If log₃(x) = 1/9, find the value of x.
If log₃(x) = 1/9, find the value of x.
Signup and view all the answers
Find the number of terms in the expansion of (x + y)⁷ (x - y)⁷.
Find the number of terms in the expansion of (x + y)⁷ (x - y)⁷.
Signup and view all the answers
Find the modulus of (a-ib)², where i = √-1.
Find the modulus of (a-ib)², where i = √-1.
Signup and view all the answers
Prove that sec²(tan⁻¹√5) + cosec²(cot⁻¹5) = 32.
Prove that sec²(tan⁻¹√5) + cosec²(cot⁻¹5) = 32.
Signup and view all the answers
Find a unit vector perpendicular to both the vectors i -2j+3k and 2i+j+k.
Find a unit vector perpendicular to both the vectors i -2j+3k and 2i+j+k.
Signup and view all the answers
If one root of the equation x² + ax + 8 = 0 is 4 and the roots of the equation x² + ax + b = 0 are equal, find the value of b.
If one root of the equation x² + ax + 8 = 0 is 4 and the roots of the equation x² + ax + b = 0 are equal, find the value of b.
Signup and view all the answers
If tan x tan 5x = 1, prove that tan 3x = 1.
If tan x tan 5x = 1, prove that tan 3x = 1.
Signup and view all the answers
The position vectors of A, B, C, D are given by the vectors i+j+k, 2i+3j, 3i+5j-2k and k-j. Prove that AB and CD are parallel vectors.
The position vectors of A, B, C, D are given by the vectors i+j+k, 2i+3j, 3i+5j-2k and k-j. Prove that AB and CD are parallel vectors.
Signup and view all the answers
If tan(A+B) = 1/2 and tan(A-B) = 1, find the value of tan 2A.
If tan(A+B) = 1/2 and tan(A-B) = 1, find the value of tan 2A.
Signup and view all the answers
Show that sin(x + y) / sin(x - y) = (tan x + tan y) / (tan x - tan y).
Show that sin(x + y) / sin(x - y) = (tan x + tan y) / (tan x - tan y).
Signup and view all the answers
If f(x) = log₂ x and q(x) = x², find f(q(2)).
If f(x) = log₂ x and q(x) = x², find f(q(2)).
Signup and view all the answers
If y = x² e^x and x² d²y / dx² = ay, find the value of a.
If y = x² e^x and x² d²y / dx² = ay, find the value of a.
Signup and view all the answers
Find the derivative of x² with respect to x.
Find the derivative of x² with respect to x.
Signup and view all the answers
If y = logₓ(cot x tan x), prove that dy / dx = 0.
If y = logₓ(cot x tan x), prove that dy / dx = 0.
Signup and view all the answers
Evaluate: lim_(x→0) (3x -1) / (√9 + x - 3)
Evaluate: lim_(x→0) (3x -1) / (√9 + x - 3)
Signup and view all the answers
Prove that sin 3x cosec x - cos 3x sec x = 2.
Prove that sin 3x cosec x - cos 3x sec x = 2.
Signup and view all the answers
Prove that the function log(x + √(x² + 1)) is an odd function.
Prove that the function log(x + √(x² + 1)) is an odd function.
Signup and view all the answers
Find the value of (1/2)sin⁻¹(1/2) - (1/2)cos⁻¹(1/2)
Find the value of (1/2)sin⁻¹(1/2) - (1/2)cos⁻¹(1/2)
Signup and view all the answers
A parachutist falls through a distance x = log(6 - 5e⁻ᵗ) in the tᵗʰ second of its motion. Find dx / dt at t = 0.
A parachutist falls through a distance x = log(6 - 5e⁻ᵗ) in the tᵗʰ second of its motion. Find dx / dt at t = 0.
Signup and view all the answers
If sin⁴ x + sin² x = 1, prove that cot⁴ x + cot² x = 1.
If sin⁴ x + sin² x = 1, prove that cot⁴ x + cot² x = 1.
Signup and view all the answers
If y = e^sin⁻¹x and x = e^cos⁻¹t, prove that dy / dx is constant.
If y = e^sin⁻¹x and x = e^cos⁻¹t, prove that dy / dx is constant.
Signup and view all the answers
Study Notes
Mathematics-I - January 2024 Exam
-
Time Allowed: 2.5 hours
-
Full Marks: 60
-
Group A: Answer Question 1. Answer any 10 parts. Each part is worth 2 marks; one mark for the correct answer, and one mark for the explanation.
-
Group B: Answer any five questions
-
Group A - Question 1: Include relevant questions and answer choices (multiple-choice questions) from the provided text.
-
Vector Angles: Find the angle between two vectors given their magnitudes and dot product.
-
Quadratic Equation Roots: Find the value of m if one quadratic root is double the other; find the relationship between the roots and the equation's coefficients.
-
Logarithms and Square Roots: Evaluate expressions involving logarithms and square roots, including the relationship between radicals/logarithms.
-
Complex Numbers (Magnitude): Given a complex number, find its product of the numbers and its magnitude in multiple parts.
-
Coefficients: Find the coefficient of x3 in a binomial expansion of (1 + 3x + 3x² + x³)² .
-
Vectors and Perpendicularity: Find the value of m where two vectors are perpendicular to each other.
-
Functions (Domain): Determine the domain of a function dependent on a square root expression.
-
Trigonometric Equations: Find an angle (x) when cos(3x) = sin(2x)
-
Function Evaluations: Evaluate a function at a given point (e.g., f(-1)) given the general expression for f(x - 2))
-
-
Detailed Questions for Group B: Complete the questions in Group B from the provided text. These questions are more complex and require a deep understanding of different concepts.
-
Additional Topics: The document presents diverse mathematical problems, and concepts include vector geometry, complex numbers, binomial expansions, trigonometric functions, calculus, and possibly others that could be in the exam.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Related Documents
Description
Prepare for your Mathematics-I January 2024 Exam with this comprehensive quiz designed to test your knowledge across various topics. You will tackle questions on vector angles, quadratic equations, logarithms, complex numbers, and more. Ideal for students aiming for mastery in mathematical concepts and exam readiness.
