Mathematics | Mechanical Engineering | TANCET Anna University Online Objective Test

TANCET Anna University Mechanical Engineering # Mathematics Continuity and Differentiability Prepare / Learn

Q1. limx→01−cosxx2 is equal to

A. 1/2

B. -1

C. 0

D. 1

Answer : Option A
Explaination / Solution:

lim_{x \to 0} \frac{1 - \cos x}{x^{2}} = lim_{x \to 0} \frac{\sin x}{2 x} = \frac{1}{2}

(UsingL’hospital Rule ).

TANCET Anna University Mechanical Engineering # Mathematics Principle of Mathematical Induction Prepare / Learn

Q2.

(x^{n} - y^{n})

is divisible by ( x - y ) for

A. all n ∈ N

B. n > 2

C. n > 1

D. none of these.

Answer : Option A
Explaination / Solution:

Replacing n by 1,2,3... we get the expression with the factor ( x - y ).Hence it is divisible by ( x - y ).

TANCET Anna University Mechanical Engineering # Mathematics Conic Sections Prepare / Learn

Q3. Circumcentre of the triangle, whose vertices are (0, 0), (6, 0) and (0, 4) is

A. ( 3, 2)

B. (2, 0)

C. (0, 3)

D. (3, 0)

Answer : Option A
Explaination / Solution:

circumcentre of a right angled triangle ABC right angled at A is $\frac{b + c}{2}$ as circumcentre of right angled triangle lies on the mid pont of the hypotenuse.

so mid point of BC=( $\frac{6 + 0}{2}$ , $\frac{0 + 4}{2}$ ) i.e.(3,2)

TANCET Anna University Mechanical Engineering # Mathematics Permutations and Combinations Prepare / Learn

Q4. The number of arrangements of n different things taken r at a time which include a particular thing is

A. n P(n-1,r)

B. P(n-1, r-1 )

C. None of these

D. r P (n-1,r-1)

Answer : Option D
Explaination / Solution:

The number of arrangements of n different things taken r at a time which include a particular thing is r n-1Pr-1 = rP(n-1,r-1)

TANCET Anna University Mechanical Engineering # Mathematics Differential Equations Prepare / Learn

Q5. The degree of the equation

(\frac{d y}{d x})^{2} + \frac{d y}{d x} - s i n^{2} y = 0

A. 1

B. 2

C. 0

D. 3

Answer : Option B
Explaination / Solution:

the power of the highest order derivative i.e .

(\frac{d y}{d x})^{2}

is 2.hence the degree 2

TANCET Anna University Mechanical Engineering # Mathematics Three Dimensional Geometry Prepare / Learn

Q6. Skew lines are lines in different planes which are

A. parallel

B. neither parallel nor intersecting

C. parallel and intersecting

D. intersecting

Answer : Option B
Explaination / Solution:

By definition : The Skew lines are lines in different planes which are neither parallel nor intersecting .

TANCET Anna University Mechanical Engineering # Mathematics Trigonometric Functions Prepare / Learn

Q7. The perimeter of a triangle ABC is 6 times the arithmetic mean of the sines of its angles. If the side b is 2, then the angle B is

A. 120∘

B. 90∘

C. 30∘

D. 60∘

Answer : Option B
Explaination / Solution:

$G i v e n a + b + c = \frac{6 (s i n A + s i n B + s i n C)}{3} \Rightarrow a + b + c = 2 (s i n A + s i n B + s i n C) N o w u s i n g s i n e r u l e a = k \sin A, b = k \sin B, c = k \sin C \Rightarrow k (s i n A + s i n B + s i n C) = 2 (s i n A + s i n B + s i n C) \Rightarrow k = 2$

Now when

TANCET Anna University Mechanical Engineering # Mathematics Application of Integrals Prepare / Learn

Q8. The area lying in the first quadrant and bounded by the curve y =

x^{3}

, the x – axis and the ordinates at x = - 2 and x = 1 is

A. 3

B. 6

C. 2

D. 15/4

Answer : Option D
Explaination / Solution:

Required area :

= \int_{- 2}^{1} x^{3} d x = {[\frac{x^{4}}{4}]}_{- 2}^{1} = \frac{15}{4}

TANCET Anna University Mechanical Engineering # Mathematics Introduction to Three Dimensional Geometry Prepare / Learn

Q9. the numbers 3, 4 , 5 can be

A. coordinates of a point on the line y = 4 , z = 0

B. direction cosines of a line in space

C. direction numbers of a line in space

D. coordinates of a point in the plane x + y – z = 0

Answer : Option C
Explaination / Solution:

the numbers 3, 4 , 5 can be direction ratio of any line these not satisfying any other option

TANCET Anna University Mechanical Engineering # Mathematics Matrices Prepare / Learn

Q10. If

[\begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 1 & 0 \end{matrix}]

then A is

A. a nilpotent matrix

B. an invertible matrix

C. an idempotent matrix

D. none of these

Answer : Option A
Explaination / Solution:

A square matrix A for which $A^{n} = 0$ , where n is a positive integer, is called a Nilpotent matrix.

The determinant and trace of the matrix is always Zero for a Nilpotent Matrix.

For the given matrix "A", determinant (A)=0 and trace(A)=0.

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