Mathematics | Civil Engineering | TANCET Anna University Online Objective Test

TANCET Anna University Civil Engineering # Mathematics Limits and Derivatives Prepare / Learn

Q1.

\underset{x \to \infty}{L t} x (a^{1 / x} - 1)

, where a > 0, is equal to

A. logae

B. 1

C. e

D. logea

Answer : Option D
Explaination / Solution:

letx=1t;⇒Ltt→0at−1t=lna

TANCET Anna University Civil Engineering # Mathematics Linear Programming Prepare / Learn

Q2. If two corner points of the feasible region are both optimal solutions of the same type, i.e., both produce the same maximum or minimum.

A. then no point on the line segment joining these two points is an optimal solution of thesame type

B. then any point on the line segment joining these two points is also an optimal solution of the opposite type

C. then no point on the line segment joining these two points is an optimal solution of the opposite type

D. then any point on the line segment joining these two points is also an optimal solution of the same type

Answer : Option D
Explaination / Solution:

If two corner points of the feasible region are both optimal solutions of the same type, i.e., both produce the same maximum or minimum , then any point on the line segment joining these two points is also an optimal solution of the same type .

TANCET Anna University Civil Engineering # Mathematics Sequences and Series Prepare / Learn

Q3. If x, y, z are in A.P., then (x + 2y – z) (x + z – y) (z + 2y – x) is equal to

A. None of these

B. 4 x y z

C. 2 x yz

D. x y z

Answer : Option B
Explaination / Solution:

TANCET Anna University Civil Engineering # Mathematics Statistics Prepare / Learn

Q4. The coefficient of correlation r satisfies

A. − 1 < r < 0

B. I r I > 1

C. 0 < r < 1

D. I r I ≤ 1

Answer : Option D
Explaination / Solution:

r can't be numerically more than 1

TANCET Anna University Civil Engineering # Mathematics Relations and Functions Prepare / Learn

Q5. Let A = {1, 2, 3, 4, 5, 6}. Which of the following partitions of A correspond to an equivalence relation on A?

A. {1, 2, 3}, {3, 4, 5, 6}.

B. {1, 3}, {2, 4, 5}, {6}

C. {1, 2, }, {4, 5, 6}

D. {1, 2, }, {3, 4}, {2, 3, 5, 6}

Answer : Option B
Explaination / Solution:

Conditions for the partition sub-sets to be an equivalence relation:

(i) The partition sub-sets must be disjoint i.e.their is no common elements between them

(ii) Their union must be equal to the main set (super-set)

Here the set A={1,2,3,4,5,6},the partition sub-sets {1,3},{2,4,5},{6} are pairwise disjoint and their union i.e. {1,3} U {2,4,5} U {6} = {1,2,3,4,5,6} = A,which is the condition for the partition sub-sets to be an equivalence relation of the set A.

TANCET Anna University Civil Engineering # Mathematics Determinants Prepare / Learn

Q6. The value of the determinant