একটি রম্বস তৈরি করুন যার কর্ণগুলি \r\nদৈর্ঘ্য 10 সেমি এবং 6 সেমি। | 8 | ফেজ-III বোঝা...

A plane surface A is at a constant temperature T_(1) = 1000 K . Another surface B parallel to A, is at a constant lower temperature T_(2) = 300 K . There is no medium in the space between two surfaces. The rate of energy transfer from A to B is equal to r_(1)(J/s) . In order to reduce rate of heat flow due to radiation, a heat shield consisting of two thin plates C and D, thermally insulated from each other, is placed between A and B in parallel. Now the rate of heat transfer (in steady state) reduces to r_(2) . Neglect any effect due to finite size of the surfaces, assume all surfaces to be black bodies and take Stefan’s constant sigma = 6 xx 10^(- )8 Wm^(- 2)K^(-4) . Area of all surfaces A = 1m^(2) . (i) Find r^(1) (ii) Find the ratio (r^(2))/(r^(1)) (iii)Find the ratio (r^E(2))/(r_(1)) if temperature of A and B were 2000 K 600 K respectively.

Find the area of the triangle whose vertices are: (i) A(3, 8), B(-4, 2) and C(5, -1) (ii) A(-2, 4), B(2, -6) and C(5, 4) (iii) A(-8, -2), B(-4, -6) and C(-1, 5) (iv) P(0, 0), Q(6, 0) and R(4, 3) (v) P(1, 1), Q(2, 7) and R(10, 8)

Use determinants to show that the following points are collinear. (i) A(2, 3), B(-1, -2) and C(5, 8) (ii) A(3, 8), B(-4, 2) and C(10, 14) (iii) P(-2, 5), Q(-6, -7) and R(-5, -4)

The firm of R, K and S was dissolved on 31.3.2019. Pass necessary journal entries for the following after various assets (other than cash and Bank) and the third party liabilities had been transferred to realisation account. (i) K agreed to pay off his wife’s loan of ₹ 6,000. (ii) Total Creditors of the firm were ₹ 40,000. Creditors worth ₹10,000 were given a piece of furniture costing ₹8,000 in full and final settlement. Remaining creditors allowed a discount of 10%. (iii) A machine that was not recorded in the books was taken over by K at ₹ 3,000 whereas its expected value was ₹ 5,000. (iv) The firm had a debit balance of ₹ 15,000 in the profit and loss A/c on the date of dissolution.

Direction : Resistive force proportional to object velocity At low speeds, the resistive force acting on an object that is moving a viscous medium is effectively modeleld as being proportional to the object velocity. The mathematical representation of the resistive force can be expressed as R = -bv Where v is the velocity of the object and b is a positive constant that depends onthe properties of the medium and on the shape and dimensions of the object. The negative sign represents the fact that the resistance froce is opposite to the velocity. Consider a sphere of mass m released frm rest in a liquid. Assuming that the only forces acting on the spheres are the resistive froce R and the weight mg, we can describe its motion using Newton's second law. though the buoyant force is also acting on the submerged object the force is constant and effect of this force be modeled by changing the apparent weight of the sphere by a constant froce, so we can ignore it here. Thus mg - bv = m (dv)/(dt) rArr (dv)/(dt) = g - (b)/(m) v Solving the equation v = (mg)/(b) (1- e^(-bt//m)) where e=2.71 is the base of the natural logarithm The acceleration becomes zero when the increasing resistive force eventually the weight. At this point, the object reaches its terminals speed v_(1) and then on it continues to move with zero acceleration mg - b_(T) =0 rArr m_(T) = (mg)/(b) Hence v = v_(T) (1-e^((vt)/(m))) In an experimental set-up four objects I,II,III,IV were released in same liquid. Using the data collected for the subsequent motions value of constant b were calculated. Respective data are shown in table. {:("Object",I,II,II,IV),("Mass (in kg.)",1,2,3,4),(underset("in (N-s)/m")("Constant b"),3.7,1.4,1.4,2.8):} A small sphere of mass 2.00 g is released from rest in a large vessel filled with oil. The sphere approaches a terminal speed of 10.00 cm/s. Time required to achieve speed 6.32 cm/s from start of the motion is (Take g = 10.00 m//s^(2) ) :

Let the circle C_(1):x^(2)+y^(2)=9 and C_(2):(x-3)^(2)+(y-4)^(2)=16 intersect at the point X and Y. Suppose that another circle C_(3):(x-h)^(2)+(y-k)^(2)=r^(2) satisfies the following conditions (i). Centre of C_(3) is collinear with the center of C_(1)&C_(2) (ii). C_(1)&C_(2) both lie inside C_(3) and (iii). C_(3) touches C_(1) at M and C_(2) at N Let hte line through X and Y intersect C_(3) at Z and W and let a common tangent of C_(1) & C_(3) be a tangent to the parabola x^(2)=8alphay There are some expressions given in the following lists {:("List I","List II"),((I)" "2h+k,(P)" "6),((II)" "("length of ZW")/("length of XY"),(Q)" "sqrt(6)),((III)" "("Area of "DeltaMZN)/("Area of "DeltaZMW),(R)" "(5)/(4)),((IV)" "alpha,(S)" "(21)/(5)),(,(T)" "2sqrt(6)),(,(U)" "(10)/(3)):} Q. Which of the following is the only correct combination? (A) (I)-(S) (B) (II)-(Q) ltBrgt (C) (I)-(U) (D) (II)-(T)

Let the circle C_(1):x^(2)+y^(2)=9 and C_(2):(x-3)^(2)+(y-4)^(2)=16 intersect at the point X and Y. Suppose that another circle C_(3):(x-h)^(2)+(y-k)^(2)=r^(2) satisfies the following conditions (i). Centre of C_(3) is collinear with the center of C_(1)&C_(2) (ii). C_(1)&C_(2) both lie inside C_(3) and (iii). C_(3) touches C_(1) at M and C_(2) at N Let hte line through X and Y intersect C_(3) at Z and W and let a common tangent of C_(1) & C_(3) be a tangent to the parabola x^(2)=8alphay There are some expressions given in the following lists {:("List I","List II"),((I)" "2h+k,(P)" "6),((II)" "("length of ZW")/("length of XY"),(Q)" "sqrt(6)),((III)" "("Area of "DeltaMZN)/("Area of "DeltaZMW),(R)" "(5)/(4)),((IV)" "alpha,(S)" "(21)/(5)),(,(T)" "2sqrt(6)),(,(U)" "(10)/(3)):} Q. Which of the following is the only incorrect combination?

Write each of the following in the product form: 15a^(9)b^(8)c^(6)( ii) 30x^(4)y^(4)z^(5) (iii) 43p^(10)q^(5)r^(15)17p^(12)q^(20)