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

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

Q1. Determine order and degree (if defined) of

\frac{d^{2} y}{d x^{2}} = c o s 3 x + s i n 3 x

A. 3,1

B. 2,1

C. 1,2

D. 1,1

Answer : Option B
Explaination / Solution:

Order = 2 , degree = 1 .Since the highest derivative term is

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

and its power is 1

Under Graduate Entrance Exams IIT JEE IEEE Entrance Exam # Mathematics Permutations and Combinations Prepare / Learn

Q2. The sum of all the numbers which can be formed by using the digits 1 , 3 , 5 , 7 ,9 all at a time and which have no digit repeated is

A. 666660

B. 33333000

C. 600

D. 266664

Answer : Option A
Explaination / Solution:

First we will fix any one digit in a fixed position .Then we have the remaining 4 digits can be arranged in 4! different ways.

Which means each of the five digits can appear in each of the five places in 4! times.

Hence the sum of the digits in each position is $4! (1 + 3 + 5 + 7 + 9) = 25 \times 4!$

Now to find the sum of these numbers formed we have to consider the place values for these digits

So the sum of all the numbers which can be formed by using the digits 1 , 3 , 5 , 7 ,9= $25 \times 4! \times (1 + 10 + 100 + 1000 + 10000) = 25 \times 4! \times 11111 = 666660$

Under Graduate Entrance Exams IIT JEE IEEE Entrance Exam # Mathematics Three Dimensional Geometry Prepare / Learn

Q3. Vector equation of a line that passes through two points whose position vectors are

Answer : Option D
Explaination / Solution:

Vector equation of a line that passes through two points whose position vectors are

is given by:

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

Q4.

$b c \cos^{2} \frac{A}{2} + c a \cos^{2} \frac{B}{2} + a b \cos^{2} \frac{C}{2} i s$ $b c \cos^{2} \frac{A}{2} + c a \cos^{2} \frac{B}{2} + a b \cos^{2} \frac{C}{2} i s$ equal to

A. (s−c)2

B. (s−b)2

C. (s−a)2

D. s²

Answer : Option D
Explaination / Solution:

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

Q5. The area bounded by the curve

| x | + y = 1

and the x –axis is

A. 4

B. 1

C. 2

D. 1/2

Answer : Option B
Explaination / Solution:

The given curve consists of two straight lines x + y = 1 ( x ≥ 0 )and -x + y = 1 ( x < 0 )
Required area :
=

2 \int_{0}^{1} y d x

2 \int_{0}^{1} (1 - | x |) d x

2 \int_{0}^{1} (1 - x) d x

2 {[x - \frac{x^{2}}{2}]}_{0}^{1}

= 1sq.unit

Under Graduate Entrance Exams IIT JEE IEEE Entrance Exam # Mathematics Introduction to Three Dimensional Geometry Prepare / Learn

Q6.

The graph of the equation

x^{2} + y^{2} = 0

in the three dimensional space is

A. Y - axis

B. Z - axis

C. XY – plane

D. X - axis

Answer : Option B
Explaination / Solution:
No Explaination.

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

Q7. If

[\begin{matrix} a & b \\ c & - a \end{matrix}]

is a square root of the

2 \times 2

identity matrix, then a, b, c satisfy the relation

A. 1+a2+bc=0

B. a2+bc=1

C. 1+a2−bc=0

D. 1−a2+bc=0

Answer : Option B
Explaination / Solution:

⎡⎣⎢⎢⎢acb−a⎤⎦⎥⎥⎥⎡⎣⎢⎢⎢acb−a⎤⎦⎥⎥⎥=⎡⎣⎢⎢⎢1001⎤⎦⎥⎥⎥⇒a2+bc=1

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

Q8.

At (0, 0) the curve

y^{2} = x^{3} + x^{2}

y^{2} = x^{3} + x^{2}

A. makes an angle of

60^{o}

with OX

B. none of these.

C. touches X – axis

D. bisects the angle between the axes

Answer : Option D
Explaination / Solution:

{(\frac{d y}{d x})}_{(0, 0)} = 1

and hence the tangent to the curve at ( 0 , 0 ) makes an angle of

\frac{π}{4}

with +ve X-axis.

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

Q9. Distance of the representative of the number 1 +i from the origin ( in Argand’s diagram ) is

A. 2

B. √2

C. 1

D. None of these

Answer : Option B
Explaination / Solution:

Let P(x,y) represent the complex number Z=x+iy in the complex plane(Argand plane) and let O(0,0) be the origin

Then we have OP= $\sqrt{x^{2} + y^{2}}$

Here Z=1+i so that P(x,y)=P(1,1)

Hence OP= $\sqrt{1 + 1} = \sqrt{2}$

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

Q10. Which of the following is a null set ?

A. { x :

x^{2}

=4 or x = 3 }

B. {x∈R}{x : x² + 1 = 0,x∈R}

C. {0}

D. { x : x > 0 or x < 0 }

Answer : Option B
Explaination / Solution:

$\begin{aligned} x^{2} + 1 = 0 \\ \Rightarrow x^{2} = - 1 \\ \Rightarrow x^{2} = \sqrt{- 1} \\ \Rightarrow x = i \in C \end{aligned}$

[i=imaginory root of unity which is a complex no.]

since the solution of x doesnot belongs to real no hence the set is null set

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