Mathematical Tools DPP 03 focuses on essential concepts and problem-solving techniques for JEE 2025 aspirants. This document includes various mathematical problems and solutions that are crucial for mastering the subject. It covers topics such as acceleration due to gravity, slope calculations, and graph interpretations. Ideal for students preparing for competitive exams, this resource enhances understanding and application of mathematical principles. Each question is designed to challenge and improve critical thinking skills necessary for success in JEE.

Key Points

  • Includes practice problems on acceleration due to gravity and its variations.
  • Covers slope calculations for linear equations and their graphical representations.
  • Features multiple-choice questions with detailed solutions for JEE preparation.
  • Explains the application of the binomial theorem in gravitational contexts.
Bhumika Rajput
3 pages
Language:English
Type:Answer Key
Exams
Bhumika Rajput
3 pages
Language:English
Type:Answer Key
Exams
226
/ 3
JEE
Arjuna
JEE
(2025)
Q
1
Calculate
.
(
A
) 10.00
(
B
) 10.0034
(
C
) 10.003333
(
D
) 10.003
Q
2
The
equation
has
(
A
)
No
root
(
B
)
One
root
(
C
)
Two
root
(
D
)
Four
roots
Q
3
If
acceleration
due
to
gravity
at
height
where
is
radius
of
earth
then
using
binomial
theorem
which
is
correct
(
A
)
(
B
)
(
C
)
(
D
)
Q
4
Find
the
slope
of
a
line
whose
coordinates
are
and
(
A
)
(
B
)
(
C
)
(
D
)
Q
5
Which
of
the
following
statement
is
not
correct
for
following
straight
line
graph
(
A
)
Line has
negative
intercept
(
B
)
Line
has
positive
intercept
(
C
)
Line
has
positive
slope
(
D
)
Line
has
negative
slope
Q
6
Which
graph
is
the
best
representation
for
the
given
equation
,
(
A
)
(
B
)
(
C
)
(
D
)
|
|
Physics
Mathematical
Tools
DPP
: 3
(1001
)
1/3
+ 8
x
+ 12 = 0
x
2
g
h
≪
R
R
=
g
n
g
0
(
1 +
)
h
R
−2
=
g
n
g
0
=
(
1 −
)
g
n
g
0
2
h
R
=
(
1 +
)
g
n
g
0
2
h
R
=
(
1 −
)
g
n
g
0
h
2
R
(1, 1) (3, 2)
1
3
1
4
2
1
2
(2)
y
(1)
y
(2)
(1)
y
= 2
x
− 1
Android
App iOS
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JEE
Q
7
The
slope
of
graph
in
figure
at
point
and
is
,
and
respectively
,
then
:
(
A
)
(
B
)
(
C
)
(
D
)
Q
8
At
point
,
the
value
of
slope
is
(
A
)
Zero
(
B
)
Positive
(
C
)
Negative
(
D
)
Infinite
Q
9
At
,
value
of
slope
is
:
(
A
) (
B
)
(
C
) (
D
)
Infinite
Q
10
Distance
between
points
and
is
(
A
)
(
B
)
(
C
)
(
D
)
Q
11
Correct
graph
of
is
:
(
A
)
(
B
)
(
C
)
(
D
)
|
|
A
,
B
C
m
A
m
B
m
C
> >
m
A
m
B
m
C
< <
m
A
m
B
m
C
= =
m
A
m
B
m
C
= <
m
A
m
B
m
C
P
x
= 0
0 1
−1
(2, 3, −7)
(−2, 0, 5)
5
13
145
−−−
√
119
−−−
√
3
x
+ 3
y
+ 1 = 0
Android
App iOS
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JEE
AnswerKey
Q
1 (
C
)
Q
2 (
C
)
Q
3 (
B
)
Q
4 (
D
)
Q
5 (
D
)
Q
6 (
A
)
Q
7 (
A
)
Q
8 (
A
)
Q
9 (
D
)
Q
10 (
B
)
Q
11 (
D
)
|
|
Android
App iOS
App PW
Website
/ 3
End of Document
226

Figures

Android App
Mathematical Tools DPP 03 - Arjuna JEE 2025 — Arjuna JEE (2025)
Mathematical Tools DPP 03 - Arjuna JEE 2025 — Arjuna JEE (2025)
Mathematical Tools DPP 03 - Arjuna JEE 2025 — Arjuna JEE (2025)
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Mathematical Tools DPP 03 - Arjuna JEE 2025 — Android App
A) Zero
D) Infinite
Mathematical Tools DPP 03 - Arjuna JEE 2025 — Android App
Mathematical Tools DPP 03 - Arjuna JEE 2025 — Android App
Mathematical Tools DPP 03 - Arjuna JEE 2025 — Android App
Mathematical Tools DPP 03 - Arjuna JEE 2025 — Android App

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FAQs

What is the correct answer for the equation x^2 + 8x + 12 = 0?
The correct answer for the equation x^2 + 8x + 12 = 0 is option (C), which indicates that the equation has two roots. This is derived from the standard form of a quadratic equation and can be solved using factoring or the quadratic formula.

How does the acceleration due to gravity change with height?
According to the document, the acceleration due to gravity at a height h above the Earth's surface can be expressed using the binomial theorem. The formula provided is gn = g0(1 - 2h/R), where g0 is the acceleration due to gravity at the Earth's surface and R is the radius of the Earth. This illustrates how gravity decreases with increasing height.

What is the slope of the line connecting the points (1, 1) and (3, 2)?
To find the slope of the line connecting the points (1, 1) and (3, 2), we use the slope formula, which is (y2 - y1) / (x2 - x1). Substituting the coordinates, we get (2 - 1) / (3 - 1) = 1/2. Therefore, the slope of the line is 1/2.

Which graph correctly represents the equation 3x + 3y + 1 = 0?
The correct graph representing the equation 3x + 3y + 1 = 0 is option (D). This equation can be rearranged to express y in terms of x, providing a linear relationship that can be visualized graphically.

What is the distance between the points (2, 3, -7) and (-2, 0, 5)?
The distance between the points (2, 3, -7) and (-2, 0, 5) can be calculated using the distance formula in three-dimensional space. The formula is √((x2 - x1)² + (y2 - y1)² + (z2 - z1)²). Substituting the given coordinates, the distance is found to be √(5² + 3² + 12²), which results in option (B) as the correct answer.

What is the significance of the slope at point P in the graph?
At point P in the graph, the value of the slope is indicated as zero. This means that the graph is flat at this point, suggesting that there is no change in the y-value as the x-value changes, which is a critical concept in understanding the behavior of functions at specific points.