If $\sum\limits^{n}_{r=0} \frac{r+2}{r+1} \,^{n}C_{r} = \frac{2^{8}-1}{6} $, then $n =$
- 8
- 4
- 6
- 5
The Correct Option is D
Solution and Explanation
Top Questions on Limits
- The limit of \( \lim_{x \to 0} \frac{\sin x}{x} \) is:
- Evaluate the following limit:
\[ \lim_{x \to 0} \frac{\ln(1+x)}{2 \sin(x)} \quad \text{(rounded off to two decimal places).} \] - A function \( f(x) \) is given by:
\[ f(x) = \begin{cases} \frac{1}{e^x - 1}, & \text{if } x \neq 0 \\ \frac{1}{e^x + 1}, & \text{if } x = 0 \end{cases} \] Then, which of the following is true? - The value of \[ \lim_{x \to 1} \frac{x^4 - \sqrt{x}}{\sqrt{x} - 1} \] is:
- Given below are two statements: Statement I: $\lim_{x \to 0} \left( \frac{\tan^{-1} x + \log_e \sqrt{\frac{1+x}{1-x}} - 2x}{x^5} \right) = \frac{2}{5}$ Statement II: $\lim_{x \to 1} \left( \frac{2}{x^{1-x}} \right) = \frac{1}{e^2}$ In the light of the above statements, choose the correct answer from the options given below
Questions Asked in BITSAT exam
- Inside a solenoid of radius \( 0.5 \) m, the magnetic field is changing at a rate of \( 50 \times 10^{-6} \) T/s. The acceleration of an electron placed at a distance of \( 0.3 \) m from the axis of the solenoid will be:
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- thermal properties of matter
In the given cycle ABCDA, the heat required for an ideal monoatomic gas will be:
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- specific heat capacity
- If \( a, c, b \) are in GP, then the area of the triangle formed by the lines \( ax + by + c = 0 \) with the coordinate axes is equal to:
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- Vectors
- A spherical ball of mass \( 20 \) kg is stationary at the top of a hill of height \( 100 \) m. It rolls down a smooth surface to the ground, then climbs up another hill of height \( 30 \) m and finally rolls down to a horizontal base at a height of \( 20 \) m above the ground. The velocity attained by the ball is:
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- Reflection Of Light By Spherical Mirrors
Evaluate the following limit: $ \lim_{n \to \infty} \prod_{r=3}^n \frac{r^3 - 8}{r^3 + 8} $.
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- limits and derivatives
Concepts Used:
Limits
A function's limit is a number that a function reaches when its independent variable comes to a certain value. The value (say a) to which the function f(x) approaches casually as the independent variable x approaches casually a given value "A" denoted as f(x) = A.
If limx→a- f(x) is the expected value of f when x = a, given the values of ‘f’ near x to the left of ‘a’. This value is also called the left-hand limit of ‘f’ at a.
If limx→a+ f(x) is the expected value of f when x = a, given the values of ‘f’ near x to the right of ‘a’. This value is also called the right-hand limit of f(x) at a.
If the right-hand and left-hand limits concur, then it is referred to as a common value as the limit of f(x) at x = a and denote it by lim x→a f(x).