A box B1, contains 1 white ball, 3 red balls and 2 black balls. Another box B2, contains 2 white balls, 3 red balls and 4 black balls. A third box B3, contains 3 white balls, 4 red balls and 5 black balls.
From a point P(λ,λ,λ), perpendicular PQ and PR are drawn respectively on the lines y=x,z=1 and y=−x,z=−1.If P is such that ∠QPR is a right angle, then the possible value(s) of λ is/(are)
Suppose that p,qandr are three non-coplanar vectors in R3. Let the components of a vector s along p,qandr be 4, 3 and 5, respectively. If the components of this vector s along (−p+q+r),(p−q+r)and(−p−q+r) are x, y and z, respectively, then the value of 2x+y+z is
Let f:RRbe a differentiable function such that f(0),f(2π)=3andfprime(0)=1.If g(x)=∫x2π[fprime(t)cosect−cottcosectf(t)]dtforx(0,2π],then (lim)x0g(x)=
Let n1,andn2, be the number of red and black balls, respectively, in box I. Let n3andn4,be the number one red and b of red and black balls, respectively, in box II. One of the two boxes, box I and box II, was selected at random and a ball was drawn randomly out of this box. The ball was found to be red. If the probablity that this red ball was drawn from box II is 31 then the correct option(s) with the possible values of n1,n2,n3,andn4, is(are)
Let f:R→Rand g:R→Rbe two non-constant differentiable functions. If fprime(x)=(e(f(x)−g(x)))gprime(x)for all x∈R, and f(1)=g(2)=1, then which of the following statement(s) is (are) TRUE?f(2)<1−(log)e2(b) f(2)>1−(log)e2(c) g(1)>1−(log)e2(d) g(1)<1−(log)e2
Let fprime(x)=2+sin4πx192x3forallx∈Rwithf(21)=0.Ifm≤∫211f(x)dx≤M, then the possible values of mandM are (a)m=13,M=24 (b) m=41,M=21(c)m=−11,M=0 (d) m=1,M=12