The correct statement(s) pertaining to the adsorption of a gas on a solid surface is (are)
Let `f(x)``=x+log_ex-xlog_ex ,x(0,oo)dot`Column 1 contains information about zeros of `f^(prime)(x)f^(prime)(x)a n df^(x)dot`Column 2 contains information about the limiting behaviour of `f^(prime)(x)f^(prime)(x)a n df^(x)`at infinity.Column 2 contains information about the increasing/decreasing nature of `f(x)a n df^(prime)(x)dot`Column I, Column 2, Column 3I, `f(x)=0forsom ex(l , e^2)`, (i), `("lim")_("x"vecoo"")f^(prime)(x)=0`, (P), `f`is increasing in (0,1)II, `f'(x)=0forsom ex(l , e)`, (ii), `("lim")_("x"vecoo"")f^(x)=-oo`, (Q), `f`is decreasing in `(e ,e^2)`III, `f'(x)=0forsom ex(0,1)`, , `("lim")_("x"vecoo"")f^(prime)(x)=-oo`, (R), `f`is increasing in (0,1)IV, `f^(' '(x))=0forsom ex(1, e)`, , `("lim")_("x"vecoo"")f^prime^'(x)=0`, (S), `f`is decreasing in (`e , e^2`)Which of the following options is the only CORRECT combination?(I) (ii) (P) (b) (IV) (iv) (S) (III) (iii) (R) (d) (II) (ii) (Q)Which of the following option is the only incorrect combination?(III) (i) (R) (b) (I) (iii) (P)(II) (iii) (P) (d) (II) (iv) (Q)Which of the following options is the only CORRECT combination?(I) (ii) (R) (b) (II) (iii) (S)(III) (iv) (P) (d) (IV) (i) (S)
Let a, b, cbe three non-zero real numbers such that the equation 3 acosx+2 bsinx=c, x∈[−2π,2π], has two distinct real roots αand βwith α+β=3π. Then, the value of abis _______.
Let Obe the origin and let PQR be an arbitrary triangle. The point S is such thatOPO˙Q+ORO˙S=ORO˙P+OQO˙S=OQ.OR+OPO˙SThen the triangle PQ has S as its:circumcentre (b) orthocentre (c) incentre (d) centroid
Let y(x) be a solution of the differential equation (1+ex)yprime+yex=1. If y(0)=2 , then which of the following statements is (are) true? (a)y(−4)=0 (b)y(−2)=0 (c)y(x) has a critical point in the interval (−1,0) (d)y(x) has no critical point in the interval(−1,0)
A cylindrica container is to be made from certain solid material with the following constraints: It has a fixed inner volume of Vm3, has a 2 mm thick solid wall and is open at the top. The bottom of the container is a solid circular disc of thickness 2mm and is of radius equal to the outer radius of the container. If the volume the material used to make the container is minimum when the inner radius of the container is 10mm. then the value of 250πV is
Consider the hyperbola H:x2−y2=1 and a circle S with centre N(x2,0) Suppose that H and S touch each other at a point (P(x1,y1) with x1>1andy1>0 The common tangent to H and S at P intersects the x-axis at point M. If (l,m) is the centroid of the triangle ΔPMN then the correct expression is (A) dx1dl=1−3x121 for x1>1 (B) dx1dm=3(x12−1)x!)forx1>1 (C) dx1dl=1+3x121forx1>1 (D) dy1dm=31fory1>0
Suppose that the foci of the ellipse 9x2+5y2=1are (f1,0)and(f2,0)where f1>0andf2<0.Let P1andP2be two parabolas with a common vertex at (0, 0) and with foci at (f1.0)and(2f_2 , 0), respectively. LetT1be a tangent to P1which passes through (2f2,0)and T2be a tangents to P2which passes through (f1,0). If m1is the slope of T1and m2is the slope of T2,then the value of (m121+m22)is