1
GATE CSE 2020
+1
-0.33
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]?
A
III only
B
II and III only
C
II only
D
I and III only
2
GATE CSE 2019
+1
-0.33
Compute $$\mathop {\lim }\limits_{x \to 3} {{{x^4} - 81} \over {2{x^2} - 5x - 3}}$$
A
1
B
Limit does not exits
C
$${{53} \over {12}}$$
D
$${{108} \over {7}}$$
3
GATE CSE 2017 Set 2
+1
-0.3
If $$f\left( x \right)\,\,\, = \,\,\,R\,\sin \left( {{{\pi x} \over 2}} \right) + S.f'\left( {{1 \over 2}} \right) = \sqrt 2$$ and $$\int_0^1 {f\left( x \right)dx = {{2R} \over \pi }} ,$$ then the constants $$R$$ and $$S$$ are respectively.
A
$${{2 \over \pi }}$$ and $${{16 \over \pi }}$$
B
$${{2 \over \pi }}$$ and $$0$$
C
$${{4 \over \pi }}$$ and $$0$$
D
$${{4 \over \pi }}$$ and $${{16 \over \pi }}$$
4
GATE CSE 2017 Set 2
Numerical
+1
-0
Consider a quadratic equation $${x^2} - 13x + 36 = 0$$ with coefficients in a base $$b.$$ The solutions of this equation in the same base $$b$$ are $$x=5$$ and $$x=6$$. Then $$b=$$ ______.
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