question

of three numbers, second is twice the first and is also thrice the third. if the average of the three numbers is 44, the largest number is:

option 1) 24                              option 2) 56option 3) 72               option 4) 108option 5)    36
of three numbers, second is twice the first and is also thrice the third. if the average of the three numbers is 44, the largest number is:

option 1) 24                              option 2) 56option 3) 72               option 4) 108option 5)    36
we know that- - - - - (i)taking 3 as common, we get3; solving only bracket term first,here a = 2a, b = 3b; putting values in eq.i}applying }}ans: - 3}note: must memorize cubes upto 12 Total no. of possible outcomes = 30 {1, 2, 3, … 30}  

  

E ⟶ event of getting no. divisible by 3.  

  

No. of favourable outcomes = 10 {3, 6, 9, 12, 15, 18, 21, 24, 27, 30}  

  

Probability, P(E) = (No.of favorable outcomes)/(Total no.of possible outcomes)  

  

P(E) = 10/30 = 1/3  

  

Bar E ⟶ event of getting no. not divisible by 3.  

  

P(Bar E) = 1 – P(E)  

  

= 1 - 1/3 = 2/3 [readmore]typed answer2no + o2 → 2no2rate=knomo2n2nd order in no → m = 23rd order overall → m + n = 3so 2 + n = 3n = 1rate=k[no]2[o2] * If the number ends with a $0$ then there are $9$ choices for the first digit, $8$ for the second and $7$ for the third, which makes $1\times9\times8\times7= 504$ possibilities.
* If the number is even ending with something else than $0$ then there are $4$ choices for the last digit, $8$ choices for the first digit (no $0$ nor the last digit), $8$ for the second digit and $7$ for the third digit, which makes $4\times8\times8\times7 =1792$


Together, this gives $2296$ numbers with $4$ distinct digits that are even. Note that this does not allow leading $0$, as you see to want it based from the question.


Correct Answer: $B$ By Pythagoras, if the sum of squares of two sides is equal to the square of the largest side then the triangle is said to be right-angled


Here given sides of the triangle are 7, 24 and 25


Largest side = 25


252 = 625  Sum of squares of remaining two sides 72 + 242 = 49 + 576 = 625


∴ 72 + 242 = 252 Therefore triangle having sides 7,24 and 25 is a right-angled triangle finding the correct answer here is important, but perhaps equally important is finding it using the method of matrix reduction, since those are the instructions.the augmented matrix is4 -2 -5 -514 -1 -2 -364 -2 4 -24you'll have to forgive the poor formatting. this answer box doesn't have a proper math symbol editor.using elementary row operations, the reduced row echelon form of the augmented matrix is1 0 0 -60 1 0 60 0 1 3from which we conclude that the system has a unique solution (-6,6,3). if a number is divisible by 55 than it must alsobe divisible by factors of 55 that is 5 and 11.∵ aabb is divisible by 5∴ by divisibility test of 5 b must be 0 or 5.therefore (c) option is correct. a - ii, b - iv, c - i, d - iii switch x and y, then solve again for y:

x = 3y+12
x-12 = 3y
(x-12)/3 = y

or,

y = x/3 - 4 we know that dividend = divisor × quotient + remainderaccording to the problem :dividend 1 = 245dividend 2 = 1029dividend - remainder = divisor × quotientso dividend 1- remainder = 240 = divisor × quotient 1prime factor of 240 = 24 × 3 × 5dividend 2 – remainder = 1024 = divisor × quotient 2prime factor of 1024 = 24 × 26since, the divisor is common for both the numbers we need to find the highest common factor between both the numbers. from the prime factors, we find thehighest common factor between the two numbers is 24 = 16