CAT Questions

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kl>k+1l+1 for (k,l) > 0 and  k > l 

Let     k = x+1    and   l = x

Therefore, x+1x>(x+1)+1(x)+1

 (x + 1) > x

Therefore, log(x+1)log(x)>log(x+2)log(x+1)

⇒logxx+1 >logx+1x+2

DPI [Dots Per Inch] is a measurement of output quality of printer resolution. It represents number of ink dots the printer can place in an area of one square inch. The lesser the DPI the less sharper the image and vice versa.

Therefore, a printer that may have 400 DPI, a printer that can print 400 x 400 per square inch or 1,60,000 dots per inch.

Now, take percentage of milk and applying mixture rule

25          100

       50

50            25  = 2 : 1

Hence required answer =  1/3 or 33.33%

Let the three numbers be x, y, z.

From the gien data,

x = 2y ....(1)

x = z/2 => z = 2(2y) = 4y .....(From 1)  ...........(2)

Given average of three numbers = 56

Then,

$$\begin{gathered} x + y + z3 = 56 \\ 2y + y + 4y3 = 56 (From 1 & 2) \\ 7y = 56 x 3 \\ y = 24 \end{gathered}$$

Now,

x = 2y => x = 2 x 24 = 48

z = 4y = 4 x 24 = 96

Now, the highest number is z = 96 & smallest number is y = 24

Hence, required sum of highest number and smallest number

= z + y

= 96 + 24

= 120.

Area = (l + b – d) d

= (80 + 60 – 10)10

=> 1300 sq.mts

=> 1300 x 3 = Rs.3900

The order of basicity in ammonia is different in gaseous phases vs. aqueous phases due to hydrogen bonding.

So in gaseous phases it's the well known: 3' > 2' > 1'> NH3. Just so we're on the same page, this is due to the inductive effect of electron donating alkyl groups--they destabilize the lone pair on nitrogen atom, making nitrogen more basic.

But in aqueous phase, the order is slightly different: 2'> 1'> 3' > NH3.