Home
Class 12
MATHS
The number of points having position vec...

The number of points having position vector `a hat i + b hat j + c hatk `, where `1 leq a,b,cleq10` and `a,b,c in N`, such that `2^a + 3^b+5^c` is a multiple of 4 is

A

70

B

140

C

210

D

280

Text Solution

Verified by Experts

The correct Answer is:
A
`because 2^(a)+3^(b)+5^(c)=2^(a)+(4-1)^(b)+(4+1)^(c)`
`=2^(a)+4k+(-1)^(b)+(1)^(c)`
`=2^(a)+4k+(-1)^(b)+1`
I. a=1,b=even, c=any number
II. `a ne 1,b=`odd, c=any number
`therefore`Required number of ways`=1xx2xx5+4xx3xx5=70`
[`because`even numbers=2,4, odd numbers=1,3,5 and any numbers=1,2,3,4,5]
Promotional Banner

Similar Questions

Explore conceptually related problems

Find vec a +vec b if vec a = hat i - hat j and vec b =2 hat i

The three points whose position vectors are vec a - vec 2b + 3 vec c, vec 2a + vec 3b - 4 vec c and - 7 vec b + 10 vec c

Show that the points A,B and C having position vectors (3hati - 4hatj - 4hatk), (2hati - hatj + hatk) and (hati - 3hatj - 5hatk) respectively, from the vertices of a right-angled triangle.

Consider A, B, C or D with position vectors : 7 hati - 4 hatj + 7 hatk, hati - 6 hatj + 10 hatk, - hati - 3 hat + 4 hatk and 5 hati - hatj + 5 hatk respectively. Then ABCD is a:

The position vector of a point C with respect to B is hat i +hat j and that of B with respect to A is hati-hatj . The position vector of C with respect to A is

let vec a = 2hat i +3hat j and vec b = hat i +4hat j then find projection of vec a on vec b

Obtain the projection of the vector vec(a) = 2hat(i) + 3hat(j) + 2hat(k) on the vector vec(b) = hat(i) + 2hat(j) + hat(k) .

Find the value of lambda , if the point with position vectors 3hat(i) - 2hat(j) - hat(k), 2hat(i) + 3hat(j) - 4hat(k), -hat(i) + hat(j) + 2hat(k) and 4hat(i) + 5hat(j) + lambda hat(k) are coplanar.