Question 1 |

The value of the definite integral \int_{-3}^{3} \int_{-2}^{2} \int_{-1}^{1} (4x^2y-z^3)dzdydx is _____. (Rounded off to the nearest integer)

0 | |

1 | |

2 | |

3 |

Question 1 Explanation:

Question 2 |

Let f(x)=x^3+15x^2-33x-36 be a real-valued function.

Which of the following statements is/are TRUE?

Which of the following statements is/are TRUE?

f(x) does not have a local maximum.
| |

f(x) has a local maximum. | |

f(x) does not have a local minimum. | |

f(x) has a local minimum. |

Question 2 Explanation:

Question 3 |

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 3 Explanation:

Question 4 |

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 4 Explanation:

Question 5 |

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 5 Explanation:

There are 5 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

Question no. 33 Gate overflow Solution link wrong , please check and update.

We have updated the link. We have also shifted this question to Numerical Method chapter.