## A Das Gupta Maths Pdf

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## Contents in A Das Gupta Maths Pdf

In this math pdf book, There are a total of 43 chapters. These are the following:

Algebra

1. Progression, Related Inequalities, and Series
2. Determinants and Cramer’s Rule
3. Equations, Inequations, and Expressions
4. Complex Numbers
5. Permutation and Combination
6. Binomial Theorem for Positive Integral Index
7. Principle of Mathematical Induction (PMI)
8. Infinite Series
9. Matrices

Trigonometry

1. Circular Functions, Identities
2. Solution of Equations
3. Inverse Circular Functions
4. Trigonometrical Inequalities and Inequations
5. Logarithm
6. Properties of Triangle
7. Heights and Distances

Coordinate Geometry

1. Coordinates and Straight Lines
2. Pair of Straight Lines and Transformation of Axes
3. Circles
4. Parabola
21 Ellipse and Hyperbola

Calculus

1. Functions
2. Differentiation
3. Limit, Indeterminate Form
4. Continuity, Differentiability, and Graph of Function
5. Application of dy/dx
6. Maxima and Minima
7. Monotonic Function and Lagrange’s Theorem
8. Indefinite Integration of Elementary Functions
9. Indefinite Integration of Rational and Irrational Functions
10. Definite Integration
11. Properties and Application of Definite Integrals
12. Area
13. Differential Equation of the First Order

Vectors

1. Vectors and Addition of Vectors
2. Product of Two Vectors
3. Product of Three or More Vectors
4. Application of Vectors

Probability

1. Elementary Probability
2. Total Conditional Probability and Bayes Theorem

Coordinate Geometry of Three Dimensions

1. Points, Direction cosines, and Direction ratios
2. Equations of a straight line in space
3. Planes

## Important Questions of Maths for IIT JEE

What is a vector quantity?
a) A quantity with magnitude and direction
b) A quantity with magnitude only
c) A quantity with direction only
d) A scalar quantity
Ans. a) A quantity with magnitude and direction

In a 2D Cartesian coordinate system, a vector is often represented by:
a) A single number
b) A point
c) An ordered pair (x, y)
d) A line segment
Ans. c) An ordered pair (x, y)

Which of the following operations is NOT valid for vectors?
b) Vector subtraction
c) Vector multiplication
d) Scalar multiplication
Ans. c) Vector multiplication

The magnitude of a vector represents:
a) Its direction
b) Its length or size
c) Its components
d) Its position
Ans. b) Its length or size

Two vectors are said to be collinear if:
a) They have the same magnitude
b) They have opposite directions
c) They lie on the same straight line
d) They are perpendicular to each other
Ans. c) They lie on the same straight line

The dot product (or scalar product) of two vectors results in a:
a) Vector
b) Scalar
c) Matrix
d) Complex number
Ans. b) Scalar

If two vectors are orthogonal, it means they are:
a) Collinear
b) Parallel
c) Perpendicular
d) Equal in magnitude
Ans. c) Perpendicular

The cross product (or vector product) of two vectors results in a:
a) Scalar
b) Vector
c) Matrix
d) Complex number
Ans. b) Vector

What is the magnitude of the zero vector?
a) 1
b) 0
c) -1
d) Undefined
Ans. b) 0

## Important Questions of Coordinate Geometry for IIT JEE

In the Cartesian coordinate system, which axis is usually represented horizontally?
a) x-axis
b) y-axis
c) z-axis
d) None of the above
Ans. a) x-axis

What are the coordinates of the origin in the Cartesian plane?
a) (0, 1)
b) (1, 0)
c) (0, 0)
d) (1, 1)
Ans. c) (0, 0)

The distance between two points with coordinates (x1, y1) and (x2, y2) is given by:
a) |x1 – x2| + |y1 – y2|
b) √[(x2 – x1)² + (y2 – y1)²]
c) |x1 + x2| + |y1 + y2|
d) √[(x2 + x1)² + (y2 + y1)²]
Ans. b) √[(x2 – x1)² + (y2 – y1)²]

The equation of a vertical line is of the form:
a) y = mx + b
b) x = c
c) y = mx
d) x = my
Ans. b) x = c

What is the slope of a horizontal line?
a) -1
b) 0
c) 1
d) Undefined
Ans. b) 0

The slope-intercept form of a linear equation is given as:
a) y = mx + b
b) x = c
c) y = mx
d) x = my
Ans. a) y = mx + b

The point (3, 4) lies in which quadrant of the Cartesian plane?

What is the equation of a circle with center (h, k) and radius r in the Cartesian plane?
a) (x – h)² + (y – k)² = r²
b) (x + h)² + (y + k)² = r²
c) (x – r)² + (y – r)² = h² + k²
d) (x + r)² + (y + r)² = h² + k²
Ans. a) (x – h)² + (y – k)² = r²

What is the equation of a straight line with slope m passing through the point (x₁, y₁)?
a) y = mx – x₁ + y₁
b) y = mx + x₁ – y₁
c) y = mx + (y₁ – mx₁)
d) y = mx + (x₁ – my₁)
Ans. c) y = mx + (y₁ – mx₁)

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