1
GATE CSE 2017 Set 2
MCQ (Single Correct Answer)
+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 $${{16 \over \pi }}$$
2
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 $$b=$$ ______.
3
GATE CSE 2016 Set 2
Numerical
+1
-0
Let $$f(x)$$ be a polynomial and $$g\left( x \right) = f'\left( x \right)$$ be its derivative. If the degree of $$\left( {f\left( x \right) + f\left( { - x} \right)} \right)$$ is $$10,$$ then the degree of $$\left( {g\left( x \right) - g\left( { - x} \right)} \right)$$ is ___________.
4
GATE CSE 2016 Set 1
Numerical
+1
-0
$$\mathop {\lim }\limits_{x \to 4} {{\sin \left( {x - 4} \right)} \over {x - 4}} = \_\_\_\_\_\_\_.$$