## Vikas Gupta Maths Pdf

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## Topics in Vikas Gupta Maths Pdf

The topics in the Vikas Gupta Maths book for JEE are given below-

1. Calculus

1. Function
2. Limit
3. Continuity, Differentiability, and Differentiation
4. Application of Derivatives
5. Indefinite and Definite Integration
6. Area Under Curves
7. Differential Equations

2. Algebra

2. Sequence and Series
3. Determinants
4. Complex Numbers
5. Matrices
6. Permutations and Combinations
7. Binomial Theorem
8. Probability
9. Logarithms

3. Co-ordinate Geometry

1. Straight Lines
2. Circle
3. Parabola
4. Ellipse
5. Hyperbola

4. Trigonometry

1. Compound Angles
2. Trigonometric Equations
3. Solution of Triangles
4. Inverse Trigonometric Functions

5. Vector & 3-Dimensional Geometry

1. Vector & 3-Dimensional Geometry

## Important Questions of Calculus for JEE

What is the derivative of the function f(x) = 3x^2 – 2x + 1 with respect to x?
A) 6x – 2
B) 3x^2 – 2x
C) 6x – 2x + 1
D) 3

Ans. A) 6x – 2

What is the integral of the function ∫(2x + 3) dx?
A) x^2 + 3x + C
B) x^2 + 3x
C) x + 3
D) 2x^2 + 3x

Ans. A) x^2 + 3x + C (where C is the constant of integration)

What is the limit of the function lim (x -> 0) (sin(x)/x)?
A) 0
B) 1
C) ∞
D) Undefined

Ans. B) 1

What is the first derivative of the natural logarithm function, ln(x)?
A) 1/x
B) e^x
C) 0
D) x

Ans. A) 1/x

If f(x) = x^3 – 4x^2 + 6x – 2, what is the local minimum value of the function?
A) -2
B) -1
C) 0
D) 1

Ans. A) -2

What is the second derivative of the function f(x) = 4x^3 – 6x^2 + 2x – 5?
A) 24x^2 – 12x + 2
B) 12x^2 – 12x + 2
C) 8x^2 – 6x + 2
D) 4x^2 – 6x + 2

Ans. A) 24x^2 – 12x + 2

Ans. A) The first derivative of an integral is the original function.

What is the area under the curve y = 2x between x = 1 and x = 3?
A) 2
B) 4
C) 6
D) 8

Ans. C) 6

## Questions of Calculus for JEE

What is the slope of the tangent line to the curve y = x^2 at the point (2, 4)?
A) 2
B) 4
C) 1
D) 0

Ans. C) 1

If the derivative of a function f(x) is f'(x) = 2x + 1, what is the original function f(x)?
A) x^2
B) x^2 + 1
C) x^2 + x
D) x^2 + 2

Ans. B) x^2 + 1

What is the limit of the function lim (x -> ∞) (1/x)?
A) 0
B) 1
C) ∞
D) Undefined

Ans. A) 0

Which of the following functions is not continuous at x = 2?
A) f(x) = 2x + 3
B) g(x) = |x – 2|
C) h(x) = 1/x
D) j(x) = x^2 – 4

Ans. C) h(x) = 1/x

What is the derivative of the constant function f(x) = 7?
A) 0
B) 1
C) 7
D) Undefined

Ans. A) 0

If the velocity of an object is given by v(t) = 3t^2 – 6t + 2, what is the object’s acceleration at time t?
A) 6t – 6
B) 6t – 6t^2
C) 6t – 6t^2 + 2
D) 3t^2 – 6t

Ans. A) 6t – 6

What is the area enclosed by the curve y = sin(x) and the x-axis between x = 0 and x = π?
A) 2
B) π
C) 1
D) 0

Ans. B) π

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