Home
Class 12
MATHS
If the system of equation 2x-y+z=0, x-wy...

If the system of equation `2x-y+z=0, x-wy+z=0, lamdax-y+2z=0` has infinitely many solutions and `f(x)` be a continuous function such that `f(5+x)+f(x)=2,` then `int_0^(-2lamda)f(x)dx=` (A) 5 (B) 0 (C) lamda (D) `-2lamda`

Text Solution

AI Generated Solution

Promotional Banner

Similar Questions

Explore conceptually related problems

The system of equations x+py=0, y+pz=0 and z+px=0 has infinitely many solutions for

Let f(x) be a continuous function in R such that f(x)+f(y)=f(x+y) , then int_-2^2 f(x)dx= (A) 2int_0^2 f(x)dx (B) 0 (C) 2f(2) (D) none of these

If f(2a-x)=-f(x), prove that int_0^(2a)f(x)dx=0

Let f(x) be a continuous function such that f(a-x)+f(x)=0 for all x in [0,a] . Then int_0^a dx/(1+e^(f(x)))= (A) a (B) a/2 (C) 1/2f(a) (D) none of these

If the system of equations x+a y=0,a z+y=0,a n da x+z=0 has infinite solutions, then the value of equation has no solution is -3 b. 1 c. 0 d. 3

If the system of equations x+a y=0,a z+y=0 and a x+z=0 has infinite solutions, then the value of a is (a) -1 (b) 1 (c) 0 (d) no real values

Let f(x) be an integrable odd function in [-5,5] such that f(10+x)=f(x) , then int_x^(10+x) f(t)dt= (A) 0 (B) 2int_0^5 f(x)dx (C) gt0 (D) none of these

If f is continuous on [0,1] such that f(x)+f(x+1/2)=1 and int_0^1f(x)dx=k , then value of 2k is 0 (2) 1 (3) 2 (4) 3

If f(x) is a continuous function in [0,pi] such that f(0)=f(x)=0, then the value of int_(0)^(pi//2) {f(2x)-f''(2x)}sin x cos x dx is equal to

If the system of equation 14x-3y+z=12, x-2y=0 and x+2z=0 has a solution (x_(0), y_(0), z_(0)) , then the value of x_(0)^(2)+y_(2)^(2)+z_(2)^(2) is equal to