How many five digit numbers can be formed using the digits from 1 to 9, such that the first three digits are in increasing order and the last three digits are in decreasing order?
1 and 8 are the first two natural numbers for which 1+2+3+......+n is a perfect square. Which number is the 4th such number?
23 people are there, they are shaking hands together, how many hand shakes possible, if they are in pair of cyclic sequence?
For a set of particular distinct integral values of a,b,c and d the equation (n+a)(n+b)(n+c)(n+d)=25 holds.for how many disticnt values of n does it hold?
- 0
- 1
- 2
- more than 2
0 voters
20 cubical blocks are arranged in the following manner: First 10 are arranged in a triangular pattern, then a layer of 6, arranged in a triangular pattern, is centered on the 10; then a layer of 3, arranged in a triangular pattern is centered on the 6; and finally one block is centered on the third layer. The blocks in the bottom layer are numbered 1 through 10 in some order. Each block in layers 2,3 and 4 is assigned the number which is the sum of the numbers assigned to the three blocks on which it rests. Find the smallest possible number which could be assigned to the smallest block.
(How to approach such questions?)
AB is hypotenuse of right triangle ABC. N is point inside ABC such that it divides triangle into 3 equal parts (Triangles ABN, CAN, BCN) Distance btw ths point N and circumcentre S od triangle ABC? Options: AB/4, AB/6, AB/3, 2/(1 + sqrt3)
a^2-a+1=0
Then value of
(a-1/a)^2 + (a+1/a)^2 + (a^2+(1/a)^2)^2 + (a^3 + (1/a)^3)^2 + ...... + (a^2015+(1/a)^2015)^2 is equal to
What is the remainder when 1^7+ 2^7+3^7+.........100^7 is divided by 7
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- 3
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0 voters
Remainder when 50! is divided by 16^15
remainder when 50!/47^2
The HCF of how many distinct pairs of factors of 18000 is 75?
A)38 B)40 C) 41 D)42
The sum of lengths of hypotenuse and one of the perpendicular sides of a right angled triangle is L. The area of triangle s maximum when angle between those two sides is ____
Options: 45, 22.5, 60, None
Soln: Let sides be a,b,c. So, a+c=L. Let angle between a and c is 'X'.
=> cosX=a/c => a=c cosX and b=c sinX. Hence, L =a+c = c cosX + c = c(1+cosX) => C = L / (1+cosX) ---- (1)
Now, Area (A) = 1/2 (a) (b) = 1/2 (c cosX) (c sinX) = 1/2 (c^2sinXcosX)
Now from (1), A = L^2 sinXcosX / 2(1+cosX)^2
For A (max) => Do, d/dx (A) => After long procedure => (cosX+1)(2cosX-1) = 0 => cosX= 1/2 => X = 60 degree.
My doubt is - Is there any shortcut way to deal with it?
@Rahul-Srivastava sir please help.
9 parallel chords are drawn in a circle of diameter 10 cm. If the distance between any 2 adjacent chords is 1 cm, which of the statements is always true? (a) One of the chords is diameter of circle (b) Atleast 2 of the chords must be of equal length (c) The difference between the lengths of any 2 adjaent chords on same side of diameter is > 1 cm. (d) none
There is a six-letter word having distinct letters. The first two letters are horizontally symmetrical, the last two are vertically symmetrical and the remaining two are both horizontally and vertically symmetrical.
- The two letters in the middle are vowels and they are arranged in alphabetical order.
- The last two letters are consecutive letters and comprise one vowel and one consonant.
- The first two letters are consecutive letters.
How many combinations of the three statements above can uniquely determine exactly four letters of the given word?
A.0
B.1
C.2
D.3
182000 + 122000 - 52000 - 1 is divisible by:
The number 2013 has the property that its units digit is the sum of its other digits, that is 2+0+1=3. How many integers less than 2013 but greater than 1000 share this property?
Find the smallest number which when divided by 7,8,9 leaves remainder 2,4,6
any good book for DI LR practice ?
I want to subscribe to an online course ( all encompassing), which would be better, CL / IMS / oliveboard. I have know the basics and just need extensive practice. CAT 2014 : 93%ile. Calls: IIFT, SPJIMR (Fin).