The number of points having position vector a -b -c k- where a- b- c -1-2-3-4-5 such that 2a -3b -5c is divisible by 4- isA- 140B- 70C- 100D- 150

The correct option is B 70If the number is divisible by 4 then, 4k = 2^a +3^b +5^c ⇒ 4k = 2^a +(4 1)^b +(4+1)^c ⇒ 4k = 4n + 2^a + ( 1)^b +(1)^c Case1: a = 1 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Fundamental Principle of Counting

The number of...

Question

The number of points having position vector $a^i + b^j + c^k$ where $a, b, c \in {1, 2, 3, 4, 5}$ such that $2^{a} + 3^{b} + 5^{c}$ is divisible by $4,$ is

140

No worries! We‘ve got your back. Try BYJU‘S free classes today!

70

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

100

No worries! We‘ve got your back. Try BYJU‘S free classes today!

150

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $70$
If the number is divisible by $4$ then,
$4 k = 2^{a} + 3^{b} + 5^{c} \Rightarrow 4 k = 2^{a} + (4 - 1)^{b} + (4 + 1)^{c} \Rightarrow 4 k = 4 n + 2^{a} + (- 1)^{b} + (1)^{c}$

Case1:
$a = 1$ then,
$b - should be even and c - can be any number$
Total possible ways
$= 1 \times 2 \times 5 = 10$
Case2:
$a \neq 1$ then,
$b - odd c - any$
Total possible ways
$= 4 \times 3 \times 5 = 60$

Total ways
$= 60 + 10 = 70$

Suggest Corrections

Similar questions

Q. Number of points having position vector

a^i + b^j + c^k,

where

a, b, c \in {1, 2, 3, 4, 5}

such that

2^{a} + 3^{b} + 5^{c}

is divisible by

4

Q. If the position vectors of the plane

A, B, C

^i +^j,^i -^j

and

a^i + b^j + c^k

respectively, then the points

A, B, C

are collinear if

Q. The three points A, B, C with position vectors

- 2 a + 3 b + 5 c, a + 2 b + 3 c, 7 a - c

Q. If

\to p =^i +^j +^k

and

\to q = a^i + b^j + c^k,

where

a, b, c \in {- 2, - 1, 0, 1, 2},

then the number of vectors

\to q

perpendicular to

\to p

Q. Let

a, b, c

be distinct non-negative numbers. If the vectors

^i + a^j + c^k

^i +^k

and

c^i + b^j + b^k

lie in a plane, then

c

Join BYJU'S Learning Program

The number of points having position vector a^i+b^j+c^k where a,b,c∈{1,2,3,4,5} such that 2a+3b+5c is divisible by 4, is

The number of points having position vector $a^i + b^j + c^k$ where $a, b, c \in {1, 2, 3, 4, 5}$ such that $2^{a} + 3^{b} + 5^{c}$ is divisible by $4,$ is