Test: Integrals- 1 - JEE MCQ

# Test: Integrals- 1 - JEE MCQ

Test Description

## 25 Questions MCQ Test Mathematics (Maths) for JEE Main & Advanced - Test: Integrals- 1

Test: Integrals- 1 for JEE 2024 is part of Mathematics (Maths) for JEE Main & Advanced preparation. The Test: Integrals- 1 questions and answers have been prepared according to the JEE exam syllabus.The Test: Integrals- 1 MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Integrals- 1 below.
Solutions of Test: Integrals- 1 questions in English are available as part of our Mathematics (Maths) for JEE Main & Advanced for JEE & Test: Integrals- 1 solutions in Hindi for Mathematics (Maths) for JEE Main & Advanced course. Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free. Attempt Test: Integrals- 1 | 25 questions in 25 minutes | Mock test for JEE preparation | Free important questions MCQ to study Mathematics (Maths) for JEE Main & Advanced for JEE Exam | Download free PDF with solutions
Test: Integrals- 1 - Question 1
Detailed Solution for Test: Integrals- 1 - Question 1

Test: Integrals- 1 - Question 2

### Find the distance travelled by a car moving with acceleration given by a(t)=Sin(t), if it moves from t = 0 sec to t = π/2 sec, and velocity of the car at t=0sec is 10 km/hr.

Detailed Solution for Test: Integrals- 1 - Question 2

Acceleration is the derivative of velocity, so we integrate a(t) to get v(t):

v(t)=∫a(t)dt=∫sin(t)dt=−cos(t)+C

Now, we are given that the velocity at t=0 is 10 km/hr. We can use this information to find the constant C:

v(0)=−cos(0)+C=−1+C=10

Solving for C, we get C=11.

Now, we have the velocity function:

v(t)=−cos(t)+11

Finally, we integrate v(t) to get the displacement function s(t):

s(t)=∫v(t)dt=∫(−cos(t)+11)dt

s(t)=−sin(t)+11t+D

Now, we need to find the constant D. We are given that the car moves from t=0 to t=π/2, and we know that s(0)=0 (starting position). Plugging in these values, we can solve for D:

s(0)=−sin(0)+11(0)+D=0

D=0

So, the displacement function is:

s(t)=−sin(t)+11t

Now, to find the distance traveled, we evaluate s(t) over the given time interval:

Distance=s(π/2​)−s(0)

Distance=(−sin(π/2​)+11(π/2​))−(−sin(0)+11(0))

Distance=−1+11π​/2 = 16.27887 kilometers

Therefore, the distance traveled by the car from t=0 to t=π/2​ is 16.27887 kilometers​.

 1 Crore+ students have signed up on EduRev. Have you?
Test: Integrals- 1 - Question 3
Detailed Solution for Test: Integrals- 1 - Question 3

Using By parts,

2I = x|x|

I=x|x|/2

Test: Integrals- 1 - Question 4

Detailed Solution for Test: Integrals- 1 - Question 4

The greatest integer function ⌊x⌋ returns the largest integer less than or equal to x. For x2, this means that ⌊x2⌋ will be the greatest integer less than or equal to x2.

The integral becomes:

The function ⌊x2⌋ will be 0 on the interval (0,1)(0,1), 1 on the interval [1,√2​], and 4 on the interval [√2,2].

So, the integral is the sum of the areas of these intervals:

Evaluating these integrals:

8 - 1 + √2 - 4√2

7 - 3√2

So, the value of the integral is 7-3√2.

Test: Integrals- 1 - Question 5

Detailed Solution for Test: Integrals- 1 - Question 5

Test: Integrals- 1 - Question 6

Detailed Solution for Test: Integrals- 1 - Question 6

Test: Integrals- 1 - Question 7

Detailed Solution for Test: Integrals- 1 - Question 7

Test: Integrals- 1 - Question 8

Detailed Solution for Test: Integrals- 1 - Question 8

Test: Integrals- 1 - Question 9

Detailed Solution for Test: Integrals- 1 - Question 9

Test: Integrals- 1 - Question 10

Detailed Solution for Test: Integrals- 1 - Question 10

Test: Integrals- 1 - Question 11

Detailed Solution for Test: Integrals- 1 - Question 11

Test: Integrals- 1 - Question 12

Detailed Solution for Test: Integrals- 1 - Question 12

Test: Integrals- 1 - Question 13

Detailed Solution for Test: Integrals- 1 - Question 13

Test: Integrals- 1 - Question 14

Detailed Solution for Test: Integrals- 1 - Question 14

Test: Integrals- 1 - Question 15

Detailed Solution for Test: Integrals- 1 - Question 15

Test: Integrals- 1 - Question 16

Detailed Solution for Test: Integrals- 1 - Question 16

The correct option is d : 26/3

Test: Integrals- 1 - Question 17

Detailed Solution for Test: Integrals- 1 - Question 17

Test: Integrals- 1 - Question 18

Detailed Solution for Test: Integrals- 1 - Question 18

Test: Integrals- 1 - Question 19

dx can be evaluated by the substitution

Detailed Solution for Test: Integrals- 1 - Question 19

Test: Integrals- 1 - Question 20

Detailed Solution for Test: Integrals- 1 - Question 20

Test: Integrals- 1 - Question 21

Detailed Solution for Test: Integrals- 1 - Question 21

Since g(x) and h(x) are integrals of the same function , therefore ; g(x) – h(x) is constant.

Test: Integrals- 1 - Question 22

Detailed Solution for Test: Integrals- 1 - Question 22

Test: Integrals- 1 - Question 23

then the value of the integral

Detailed Solution for Test: Integrals- 1 - Question 23

Test: Integrals- 1 - Question 24

Detailed Solution for Test: Integrals- 1 - Question 24

Test: Integrals- 1 - Question 25

Detailed Solution for Test: Integrals- 1 - Question 25

## Mathematics (Maths) for JEE Main & Advanced

209 videos|443 docs|143 tests
Information about Test: Integrals- 1 Page
In this test you can find the Exam questions for Test: Integrals- 1 solved & explained in the simplest way possible. Besides giving Questions and answers for Test: Integrals- 1, EduRev gives you an ample number of Online tests for practice

## Mathematics (Maths) for JEE Main & Advanced

209 videos|443 docs|143 tests