Higher Level Maths ( also useful for PGDCM )

[rahul4IIMA]

@anil_sharma
Let f(x)=ax^3+bx^2+cx
f(0)=0
f(1)=0 Given...
and as we know f(x) is a function..so between these 2 values, the slope of f(x)
must have become 0,to put it in a different way,f(x) must have reached a local maxima or local minima between f(0) and f(1) ..for that local maxima and minima to occur...we can say f'(x) must have been 0 at that point ..hence
3x"2+2x+c must have been 0 , hence f'(x) has at least one root between 0 and 1

[sushanttare]

Hey guys I went thru all the posts...really nice initiative.... I am looking forward for more interesting posts.

[gauravbrills]

Hi can anybody help me on the following Q'n ?

The function f(x) = mx + sin x will have an inverse if and only if
a. – 1 <= m <=1 b. m < – 1 c. m > 1 d. |m| > 1

Cheers

[STALWART]

Originally Posted by gauravbrills

Hi can anybody help me on the following Q'n ?

The function f(x) = mx + sin x will have an inverse if and only if
a. – 1 <= m <=1 b. m < – 1 c. m > 1 d. |m| > 1

Cheers

Its |m| > 1

Just draw the two separate graphs of sinx and mx and analyse .

... Sayonara

[STALWART]

From digits 1,2,3...... 9 , Seven digit number is formed without any repitition . What is the probability that it will be divisible by 9 ?


..... Sayonara

[g_nik]

The probability is 1/9.

Out of the ninedigits we need to choose seven such that the sum of chosen digits is a multiple of 9.

Lowest sum = 1+2+3+4+5+6+7 = 28
Highest sum = 3+4+5+6+7+8+9 = 42

Now between 28 n 42, only 36 is divisible by9.

2+3+4+5+6+7+9 = 36

Remaining digits are 1 and 8 which sum upto 9.
so we can replace 2 digits from 2,3,4,5,6,7,9 having sum 9 with numbers 1 and 9........such 2 numbers can be 2,7 ; 3,6 ; 4,5

So in all we have 4 ways in which sum total is 36

Total no. of ways is 9c2 = 36

So prob = 1/9.

[shemz]

Originally Posted by neo_leo53

..explaination needed.

.. A man leaves office daily at 7pm.a driver with car comes from his home to pick him from office and bring back home. One day he gets free at 5.30 and instead of waiting for driver he starts walking towards home. In the way he meets the car and returns home on car. He reaches home 20 minutes earlier than usual. In how much time does the man reach home usually?

(A) 1 hr 20 min (B) 1 hr (C) 1 hr 10 min (D) 55 min

Do you think its possible to answer precisely? I feel that all the answer choices are possible. To solve for n variables, we need to have atleast n equations. Here the problem is we get only 1 equation to solve for 2 variables. (From the given data: y = x + 1.17...; x = time on any normal day, y = time when he left the office at 5:30. Infinite pairs of (x,y) can successfull satisfy the above equation, in absence of another condition, or another equation.)

[sujit singh]

find the hundred place digit of 9to power 77?

[PaglaMota]

Got 1 doubt when solving some geometry problem?

Why do all 3 angle bisectors, medians, altitudes, and perpendicular bisector is sides meet at same point?(of course diff. point for diff. parameters )

[PaglaMota]

Got 1 doubt when solving some geometry problem?

In a triangle why do all 3 angle bisectors, medians, altitudes, and perpendicular bisector is sides meet at same point?(of course diff. point for diff. parameters )

Sorry for double post...ehh