Question 1 |

The value of the following limit is _____

\lim_{x \to 0+} \frac{ \sqrt{x}}{1-e^{2 \sqrt{x}}}

\lim_{x \to 0+} \frac{ \sqrt{x}}{1-e^{2 \sqrt{x}}}

-0.5 | |

0.5 | |

0 | |

1 |

Question 1 Explanation:

Question 2 |

For two n-dimensional real vectors P and Q, the operation s(P,Q) is defined as follows:

s(P,Q) = \displaystyle \sum_{i=1}^n (P[i] \cdot Q[i])

Let \mathcal{L} be a set of 10-dimensional non-zero real vectors such that for every pair of distinct vectors P,Q \in \mathcal{L}, s(P,Q)=0. What is the maximum cardinality possible for the set \mathcal{L}?

s(P,Q) = \displaystyle \sum_{i=1}^n (P[i] \cdot Q[i])

Let \mathcal{L} be a set of 10-dimensional non-zero real vectors such that for every pair of distinct vectors P,Q \in \mathcal{L}, s(P,Q)=0. What is the maximum cardinality possible for the set \mathcal{L}?

9 | |

10 | |

11 | |

100 |

Question 2 Explanation:

Question 3 |

Suppose that f: \mathbb{R} \rightarrow \mathbb{R} is a continuous function on the interval [-3,3] and a differentiable function in the interval (-3,3) such that for every x in the interval, f'(x) \leq 2. If f(-3) =7, then f(3) is at most __________

19 | |

32 | |

11 | |

54 |

Question 3 Explanation:

Question 4 |

Consider the following expression.

\lim_{x\rightarrow-3}\frac{\sqrt{2x+22}-4}{x+3}

The value of the above expression (rounded to 2 decimal places) is ___________.

\lim_{x\rightarrow-3}\frac{\sqrt{2x+22}-4}{x+3}

The value of the above expression (rounded to 2 decimal places) is ___________.

0.25 | |

0.45 | |

0.75 | |

0.85 |

Question 4 Explanation:

Question 5 |

Consider the functions

I. e^{-x}

II. x^2-\sin x

III. \sqrt{x^3+1}

Which of the above functions is/are increasing everywhere in [0,1] ?

I. e^{-x}

II. x^2-\sin x

III. \sqrt{x^3+1}

Which of the above functions is/are increasing everywhere in [0,1] ?

III only | |

II only | |

II and III only | |

I and III only |

Question 5 Explanation:

Question 6 |

Compute \lim_{x \to 3}\frac{x^4-81}{2x^2-5x-3}

1 | |

53/12 | |

108/7 | |

Limit does not exist |

Question 6 Explanation:

Question 7 |

The domain of the function \log (\log \sin (x)) is:

0\lt x \lt \pi | |

2 n \pi \lt x \lt (2 n+1) \pi, for n in N | |

Empty set | |

None of the above |

Question 7 Explanation:

Question 8 |

The value of \int_{0}^{\frac{\pi }{4}}x\cos (x^{2})dx correct to three decimal places
(assuming that \pi = 3.14 ) is

0.3 | |

0.2 | |

0.25 | |

0.4 |

Question 8 Explanation:

Question 9 |

Which one of the following is a closed form expression for the generating function of the sequence \left \{ a_{n} \right \}, where a_{n}=2n+3 for all n = 0, 1, 2,...?

\frac{3}{(1-x)^{2}} | |

\frac{3x}{(1-x)^{2}} | |

\frac{2-x}{(1-x)^{2}} | |

\frac{3-x}{(1-x)^{2}} |

Question 9 Explanation:

Question 10 |

If a random variable X has a Poisson distribution with mean 5, then the expectation E[(X+2)^{2}] equals ______________.

49 | |

25 | |

54 | |

64 |

Question 10 Explanation:

There are 10 questions to complete.

Question number 35 of calculas of CS option B is misprinted? Please check!!

Thank You Praful Sambhaji Rane,

We have updated the options.

All questions are quite jumbled up and there are questions from probability, algorithms and numerical methods too when it’s supposed to be only Calculus, please update everything accordingl y