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Topics in Vikas Gupta Maths Pdf
The topics in the Vikas Gupta Maths book for JEE are given below-
- Continuity, Differentiability, and Differentiation
- Application of Derivatives
- Indefinite and Definite Integration
- Area Under Curves
- Differential Equations
- Quadratic Equations
- Sequence and Series
- Complex Numbers
- Permutations and Combinations
- Binomial Theorem
3. Co-ordinate Geometry
- Straight Lines
- 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
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)?
Ans. B) 1
What is the first derivative of the natural logarithm function, ln(x)?
Ans. A) 1/x
If f(x) = x^3 – 4x^2 + 6x – 2, what is the local minimum value of the function?
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
The Fundamental Theorem of Calculus relates differentiation and integration. Which of the following statements is true?
A) The first derivative of an integral is the original function.
B) The second derivative of an integral is always zero.
C) Integrals and derivatives are unrelated concepts.
D) Integration is the reverse process of differentiation.
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?
Ans. C) 6
Questions of Calculus for JEE
If a function is continuous on a closed interval [a, b] and differentiable on the open interval (a, b), which theorem guarantees the existence of at least one c in (a, b) such that f'(c) = (f(b) – f(a))/(b – a)?
A) Mean Value Theorem
B) Intermediate Value Theorem
C) L’Hôpital’s Rule
D) Rolle’s Theorem
Ans. A) Mean Value Theorem
What is the slope of the tangent line to the curve y = x^2 at the point (2, 4)?
Ans. C) 1
If the derivative of a function f(x) is f'(x) = 2x + 1, what is the original function f(x)?
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)?
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?
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?
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 Size||74 MB & 53 MB|
|Total Pages||387 & 378|
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