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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
- Function
- Limit
- Continuity, Differentiability, and Differentiation
- Application of Derivatives
- Indefinite and Definite Integration
- Area Under Curves
- Differential Equations
2. Algebra
- Quadratic Equations
- Sequence and Series
- Determinants
- Complex Numbers
- Matrices
- Permutations and Combinations
- Binomial Theorem
- Probability
- Logarithms
3. Co-ordinate Geometry
- Straight Lines
- Circle
- Parabola
- Ellipse
- Hyperbola
4. Trigonometry
- Compound Angles
- Trigonometric Equations
- Solution of Triangles
- Inverse Trigonometric Functions
5. Vector & 3-Dimensional Geometry
- 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
Details of Book of Vikas Gupta Maths Pdf
Book Name | Advanced Problems in Mathematics For JEE Main & Advanced |
Author Name | Vikas Gupta & Pankaj Joshi |
Pdf Language | English |
Pdf Size | 74 MB & 53 MB |
Total Pages | 387 & 378 |
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