PREVIOUS YEAR SOLVED PAPERS - GATE 2017 Shift 2
- Option : A
- Explanation : X = 4777....(7 29times) It can be written as X = 4.7777... * 1029 X3 = (4.777⋯∗1029)3 = (4.777…)3 ∗ 1087 Now, even if we round up 4.777... to 5, we could represent 53 = 125 in 3 digits. So, can say (4.77...)3also has 3 digits before decimal point. So, X3 requires 3 + 87 = 90 digits.
- Option : B
- Explanation : Here in given question there are three boxes incorrectly labeled: .Box 3 – labeled as Apples and Oranges – Original Content can be Apple or Orange (This box will have only one fruit, so whichever we pick would be the correct label). Let’s say the picked item was Apple, therefore the box labeled Orange will have Apples and Oranges.) .Box 2 – Oranges – This box will definitely not have orange (as its mislabeled) and it can not contain only apple (As it is in box 3) – So this will have Original Content- both oranges and Apples .Box 1 – Apples – This is the leftover box and it can now have Original Content – Orange
- Option : C
- Explanation :
In general thunderstorms are occurred in a region where suddenly air pressure changes (i.e.,) sudden rise (or) sudden fall of air pressure. From the given contour map in ‘R’ region only more changes in air pressure. So, the possibility of a thunderstorms in this region. So option C. is correct.Region Air pressure difference P 0.95 - 0.90 = 0.05 Q 0.80 - 0.75 = 0.05 R 0.85 - 0.65 = 0.20 S 0.95 - 0.90 = 0.05
10. The number of roots of ex + 0.5x2 - 2 =0 in the range [-5,5] is ______.
- Option : C
- Explanation : The given function is a continuous function in range [-5, 5]. The Intermediate Value Theorem states if a continuous function has values of opposite sign inside an interval, then it has a root in that interval. The function changes sign twice in range [-5, 5]. It becomes positive to negative in range [-5, 0] when ex + 0.5x2 becomes less than 2. It becomes positive to negative in range [0, 5] when ex + 0.5x2 becomes more than 2.
