Mathematics (Test 4)

Tancet Anna University : Mechanical Engineering

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Mathematics

Mathematics
| Engineering Mathematics | | Maths Sets | | Relations and Functions | | Trigonometric Functions | | Principle of Mathematical Induction | | Complex Numbers and Quadratic Equations | | Linear Inequalities | | Permutations and Combinations | | Binomial Theorem | | Sequences and Series | | Straight Lines | | Conic Sections | | Introduction to Three Dimensional Geometry | | Limits and Derivatives | | Mathematical Reasoning | | Statistics | | Probability | | Inverse Trigonometric Functions | | Matrices | | Determinants | | Continuity and Differentiability | | Application of Derivatives | | Integrals | | Application of Integrals | | Differential Equations | | Vector Algebra | | Three Dimensional Geometry | | Linear Programming | | Chapter 1: Sets, Relations and Functions | | Chapter 2: Basic Algebra | | Chapter 3: Trigonometry | | Chapter 4: Combinatorics and Mathematical Induction | | Chapter 5: Binomial Theorem, Sequences And Series | | Chapter 6: Two Dimensional Analytical Geometry | | Chapter 1: Applications of Matrices and Determinants | | Chapter 2: Complex Numbers | | Chapter 3: Theory of Equations | | Chapter 4: Inverse Trigonometric Functions | | Chapter 5: Two Dimensional Analytical Geometry II | | Chapter 6: Applications of Vector Algebra |
Q.1
If  are three unit vectors such that  is perpendicular to  , and is parallel to  then  x ( x  ) is equal to
A.
B.
C.
D.
Answer : Option B
Explaination / Solution:
No Explaination.


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Q.2
If  then a vector perpendicular to  and lies in the plane containing  and  is
A. -17iˆ + 21 ˆj - 97kˆ
B. 17iˆ + 21 ˆj -123kˆ
C. -17iˆ - 21 ˆj + 97kˆ
D. -17iˆ - 21 ˆj - 97kˆ
Answer : Option D
Explaination / Solution:
No Explaination.


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Q.3
If the planes .(2 ˆi - λ ˆj + ˆk ) = 3 and .(4 ˆi + ˆj - μ ˆk ) = 5 are parallel, then the value of λ and μ are
A. 1/2 , -2
B. –1/2 ,2
C. – 1/2 , -2
D. 1/2 ,2
Answer : Option C
Explaination / Solution:
No Explaination.


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Q.4
The radius of the circle passing through the point (6, 2) two of whose diameter are x + y = 6 and x + 2 y = 4 is
A. 10
B. 2√5
C. 6
D. 4
Answer : Option B
Explaination / Solution:


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Q.5
An ellipse has OB as semi minor axes, F and F ′ its foci and the angle FBF ′ is a right angle. Then the eccentricity of the ellipse is
A. 1/√2
B. 1/2
C. 1/4
D. 1/√3
Answer : Option A
Explaination / Solution:


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Q.6
If sin1 x = 2 sin1 α has a solution, then
A. |α| ≤ (1/√2)
B. |α| ≥ (1/√2)
C. |α| < (1/√2)
D. |α| > (1/√2)
Answer : Option A
Explaination / Solution:


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Q.7
sin1 (2 cos2 x 1) + cos1 (1 2 sin2 x) =
A. π/2
B. π/3
C. π/4
D. π/6
Answer : Option A
Explaination / Solution:


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Q.8
If α , β , and  γ  are the zeros of  x+ px+ qx + r , then  is
A. -q/r
B. -p/r
C. q/r
D. -q/p
Answer : Option B
Explaination / Solution:


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Q.9
The conjugate of a complex number is 1/i-2 Then, the complex number is
A. 1/[i+2]
B. -1/[i+2]
C. -1/[i-2]
D. 1/[i-2]
Answer : Option B
Explaination / Solution:


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Q.10
If (z-1) / (z+1), is purely imaginary, then | z | is
A. 1/2
B. 1
C. 2
D. 3
Answer : Option B
Explaination / Solution:


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Mechanical Engineering