Let f1:R→R, f2:(−2π,2π)→R f3:(−1, e2π−2)→Rand f4:R→Rbe functions defined by
The equation of the plane passing through the point (1,1,1) and perpendicular to the planes 2x+y−2z=5 and 3x−6y−2z=7 , is (A) 14x+2y+15z=3 (B) 14x+2y−15z=1 (C) 14x+2y+15z=31 (D) 14x−2y+15z=27
Let u^=u1i^+u2j^+u3k^ be a unit vector in be a unit vector in R3andw^=61(i^+j^+2k^).Given that there exists vector v^ in R3 such that ∣u^×v∣=1andw^.(u^×v)=1. Which of the following statement(s) is(are) correct?
Let Pbe a point in the first octant, whose image Qin the plane x+y=3(that is, the line segment PQis perpendicular to the plane x+y=3and the mid-point of PQlies in the plane x+y=3)lies on the z-axis. Let the distance of Pfrom the x-axis be 5. If Ris the image of Pin the xy-plane, then the length of PRis _______.
A curve passes through the point (1,6π) . Let the slope of the curve at each point (x,y) be xy+sec(xy),x>0. Then the equation of the curve is
Let f:R0,1 be a continuous function. Then, which of the following function (s) has (have) the value zero at some point in the interval (0,1)? ex−∫0xf(t)sintdt (b) f(x)+∫02πf(t)sintdt(c)x−∫02π−xf(t)costdt (d) x9−f(x)
Let n be the number of ways in which 5 boys and 5 girls can stand in a queue in such a way that all the girls stand consecutively in the queue. Let m be the number of ways in which 5 boys and 5 girls can stand in a queue in such a way that exactly four girls stand consecutively in the queue. Then the value of m/n is