1
GATE ECE 2015 Set 3
+1
-0.3
If x>y>1, which of the following must be true? $$\begin{array}{l}\mathrm i.\;\ln\left(\mathrm x\right)>\ln\left(\mathrm y\right)\;\;\;\;\;\;\;\;\;\;\mathrm{ii}.\;\;\mathrm e^\mathrm x>\mathrm e^\mathrm y\\\mathrm{iii}.\;\mathrm y^\mathrm x>\mathrm x^\mathrm y\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\mathrm{iv}.\;\cos\left(\mathrm x\right)>\cos\left(\mathrm y\right)\end{array}$$\$
A
(i) and (ii)
B
(i) and (iii)
C
(iii) and (iv)
D
(ii) and (iv)
2
GATE ECE 2015 Set 1
+1
-0.3
If $$\log_x\left(\frac57\right)=\frac{-1}3$$, then the value of x is
A
343/125
B
125/343
C
-25/49
D
-49/25
3
GATE ECE 2015 Set 1
+1
-0.3
Operators $$\square$$,◊,$$\rightarrow$$ are defined by : a $$\square$$ b = $$\frac{a-b}{a+b}$$; a ◊ b = $$\frac{a+b}{a-b}$$; a $$\rightarrow$$ b = ab. Find the value of (66 $$\square$$ 6) $$\rightarrow$$ (66 ◊ 6).
A
-2
B
-1
C
1
D
2
4
GATE ECE 2013
+1
-0.3
In the summer of 2012, in New Delhi, the mean temperature of Monday to Wednesday was 41ºC and of Tuesday to Thursday was 43ºC. If the temperature on Thursday was 15% higher than that of Monday, then the temperature in ºC on Thursday was
A
40
B
43
C
46
D
49
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