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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

8. Quadratic Equations
9. Sequence and Series
10. Determinants
11. Complex Numbers
12. Matrices
13. Permutations and Combinations
14. Binomial Theorem
15. Probability
16. Logarithms

3. Co-ordinate Geometry

17. Straight Lines
18. Circle
19. Parabola
20. Ellipse
21. Hyperbola

4. Trigonometry

22. Compound Angles
23. Trigonometric Equations
24. Solution of Triangles
25. Inverse Trigonometric Functions

5. Vector & 3-Dimensional Geometry

26. 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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