Mathematics | IIT JEE IEEE Entrance Exam | Under Graduate Entrance Exams Online Objective Test

Under Graduate Entrance Exams IIT JEE IEEE Entrance Exam # Mathematics Application of Derivatives Prepare / Learn

Q1.

The function f (x) = $x^{2} e^{- x}$ strictly increases on

A. [0, 2]

B. (0,∞)

C. [ −−∞, 0]∪[2,∞)

D. none of these.

Answer : Option A
Explaination / Solution:

Here ,

f^{'} (x) = \frac{d}{d x} (x^{2} e^{- x})

= x^{2} e^{- x} (- 1) + 2 x e^{- x}

\Rightarrow f^{'} (x) = e^{- x} (2 x - x^{2}) > 0

i f (2 x - x^{2}) > 0

i.e. if x(x – 2 )<0 i.e. if 0 < x < 2. Hence f is strictly increasing on [0,2]

Under Graduate Entrance Exams IIT JEE IEEE Entrance Exam # Mathematics Maths Sets Prepare / Learn

Q2. Two sets A and B are said to be disjoint iff

A. A ∪B = ϕ

B. A – B = A

C. A ∩B ≠ϕ

D. A∩B=∅

Answer : Option D
Explaination / Solution:

Two sets are called disjoint if and only if these two set have no common element i.e A∩B=∅

Under Graduate Entrance Exams IIT JEE IEEE Entrance Exam # Mathematics Complex Numbers and Quadratic Equations Prepare / Learn

Q3. z +

\bar{z} \neq 0

if and only if

A. Re(z) ≠ 0

B. | z | ≠ 0

C. Im ( z ) ≠ 0

D. z ≠ 0

Answer : Option A
Explaination / Solution:

Let Z=x+iy then we have $\bar{Z} = x - i y$

So $Z + \bar{Z} = 2 x$

Now z + $\bar{z} \neq 0$

$\Leftrightarrow 2 x \neq 0 \Leftrightarrow x \neq 0 \Leftrightarrow R e (z) \neq 0$

Under Graduate Entrance Exams IIT JEE IEEE Entrance Exam # Mathematics Determinants Prepare / Learn

Q4.

A. a+b+c

B. 1+a+b+c

C. abc

D. none of these.

Answer : Option B
Explaination / Solution:

Under Graduate Entrance Exams IIT JEE IEEE Entrance Exam # Mathematics Binomial Theorem Prepare / Learn

Q5. If 2nd, 3rd and 4th terms in the expansion of

(x + a)^{n}

are 240, 720 and 1080 respectively, then the value of n is

A. 5

B. 20

C. 10

D. 15

Answer : Option A
Explaination / Solution:

Under Graduate Entrance Exams IIT JEE IEEE Entrance Exam # Mathematics Linear Inequalities Prepare / Learn

Q6. In the first three papers each of 100 marks , Rishi got 95 , 72 , 83 marks . If he wants an average of greater than or equal to 75 marks and less than 80 marks, find the range of marks he should score in the 4th paper .

A. 25 < × < 75

B. 75 < × < 80

C. 73 < × < 100

D. 50 ≤ x < 70

Answer : Option D
Explaination / Solution:

et the marks scored by Rishi in the fourth paper be x.

Then $75 \leq \frac{95 + 72 + 83 + x}{4} < 80 \Rightarrow 75 \leq \frac{250 + x}{4} < 80$

Multipling the inequality throughout by 4 ,we get

Under Graduate Entrance Exams IIT JEE IEEE Entrance Exam # Mathematics Limits and Derivatives Prepare / Learn

Q7.

\underset{x \to 0}{L t} (\frac{\sin x - x}{x}) \cos (\frac{1}{x})

is equal to

A. 1/2

B. -1

C. 1

D. 0

Answer : Option D
Explaination / Solution:

Under Graduate Entrance Exams IIT JEE IEEE Entrance Exam # Mathematics Linear Programming Prepare / Learn

Q8. In Corner point method for solving a linear programming problem the second step after finding the feasible region of the linear programming problem and determining its corner points is

A. Evaluate the objective function Z = ax + by at the mid points

B. None of these

C. Evaluate the objective function Z = ax + by at each corner point.

D. Evaluate the objective function Z = ax + by at the center point

Answer : Option C
Explaination / Solution:

In Corner point method for solving a linear programming problem the second step after finding the feasible region of the linear programming problem and determining its corner points is : To evaluate the objective function Z = ax + by at each corner point.

Under Graduate Entrance Exams IIT JEE IEEE Entrance Exam # Mathematics Sequences and Series Prepare / Learn

Q9.

For what value of b, will the roots of the equation cos x = b, $- 1 \leq b \leq 1$ when arranged in ascending order of their magnitudes, form an A.P?

A. 1√2

B. 12

C. 3√2

D. -1

Answer : Option D
Explaination / Solution:

Under Graduate Entrance Exams IIT JEE IEEE Entrance Exam # Mathematics Statistics Prepare / Learn

Q10. Which one of the following average is most affected of extreme observations ?

A. G.M.

B. Mode

C. Median

D. A. M.

Answer : Option D
Explaination / Solution:

As A/M is calculated as the sum of all the observations divided by number of observations, so it is affected by if there is any change in the outliers

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