Questions asked by Tony

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• Carbon disulphide 'CS2' . Can be made from by product SO2. The overall reaction is 5C + 2SO2 -------> CS2 + 4CO How much CS2 can be produced from 450kg of waste SO2 with excess of coke if the SO2 conversion is 82%?
  
• `"50 g"` of `"ZnS"` are strongly heated in air to effect partial oxidation and the resultant mass weighed `"44 g"`. What is the ratio of `"ZnO"` to `"ZnS"` in the resulting mixture?
  
• Mole fraction of ethanol in ethanol and water mixture is 0.25. Hence percentage concentration of ethanol by weight of mixture is?
  
• The molality of a 1L solution with x% H2SO4 is 9. The weight of solvent is 910 grams. The value of x is?
  
• An aqueous solution of concentrated hydrobromic acid contains 48% HBr by mass. If the density of the solution is 1.5 g / mL, What is its concentration?
  
• For the equation `sin(3θ) + cos(3θ) = 1 - sin(2θ)` then?
  
• If 0 < x < π, and cos x + sin x = 1/2, then tan x is?
  
• Differentiate `y^2 = 4ax` w.r.t `x` (Where a is a constant)?
  
• The real number x when added to its inverse gives the maximum value of the sum at x equal to?
  
• `y = sec^2theta + cos^2theta`, `theta != 0`, then?(Solve it without A.M - G.M inequality method)
  
• If the roots of the equation `bx^2 + cx + a = 0` be imaginary, then for all real values of x , the expression `3b^2x^2 + 6bcx + 2c^2` is?
  
• A particle is moving vertically upward and reaches the maximum height H in T seconds. The height of the particle at any time t ( t > T) will be?
  
• A particle starts from rest and has a constant acceleration of `4m/s^2` for `4sec`. It then retards uniformly for next `8sec` and comes to rest. Average speed of the particle during the motion is?
  
• The length of a seconds hand in a watch is 1 cm. Magnitude of change in velocity of its tip in 15 sec is?
  
• If a,b,c are in GP and a + x , b + x, c + x are in HP. Find x where a,b,c are distinct numbers?
  
• How high a column of air would be necessary to cause the barometer to read 76 cm of Hg, if the atmosphere were of uniform density `1.2Kg/m^3`? The density of Hg = `13.6*10^3Kg/m^3`
  
• A closed beaker of circular cross section radius 4 cm is filled with Hg up to height 10 cm. Find the force exerted by the mercury on the bottom of the beaker?
  
• Calculate the molality of a sulfuric acid solution of specific gravity 1.2 containing 27% `H_2SO_4` by **weight**?
  
• A projectile is fired with velocity u making angle `theta` with the horizontal. What is the change in velocity( from initial ) when it is at the highest point?
  
• A projectile is fired with a speed u at an angle `theta` with the horizontal. Its speed when its direction of motion makes an angle `alpha` with the horizontal is?
  
• For the equation sin 3θ + cos 3θ = 1 - sin2θ then? Please note that the question has multiple answers, i.e. one or more options may be correct.
  
• The velocity of a particle moving along x - axis is given as `v = x^2 - 5x + 4`(in m/s), where x denotes the x-coordinate of the particle in meters. Find the magnitude of acceleration of the particle when the velocity of particle is zero?
  
• The length of a seconds hand in a watch is 1 cm. Magnitude of change in velocity of its tip in 15 sec is?
  
• A particle is moving in x - axis according to relation `x= (4t - t^2 - 4)` m then? **The question has multiple answers**.
  
• What atomic number of an element "X" would have to become so that the 4th orbit around X would fit inside the 1st Bohr orbit of H-atom?
  
• Find the number of integral value of `m` for which exactly one root of the equation `x^2-2mx+m^2-1 = 0` lies in the interval `(-2,4)`?
  
• If `sin x + sin^2 x = 1` then the value of `cos^2x + cos^4x + cot^4x - cot^2x` is?
  
• Let `alpha,beta` be such that `pi < alpha - beta < 3pi`. If `sinalpha + sinbeta = -21/65` and`cosalpha + cosbeta = -27/65`, then the value of `cos(alpha - beta)/2` is?
  
• If `alpha` and `beta` are the roots of the equation `x^2 - x +1 = 0`, then `alpha^2009 + beta^2009` is?
  
• Find the sum of `1^2 - 2^2 + 3^2 - 4^2 + 5^2 - 6^2........`? ( Please find out the #n^(th) term and then use the sigma method)
  
• The pollution in a normal atmosphere is less than 0.01%. Due to leakage of a gas from a factory, the pollution is increased to 20%. If everyday 80% of the pollution is neutralized , in how many days the atmosphere will be normal( `log_2 = 0.3010`)?
  
• If the quadratic equation `ax^2 + 2cx + b = 0` and `ax^2 +2bx + c = 0, (b != c)`, have a common root then a + 4b + 4c is equal to?
  
• If x is satisfied the inequality `log_(x+3)(x^2-x) < 1`, the x may belongs to the set?
  
• If `p^th` , `q^th` , and `r^th` terms of a H.P are a,b,c respectively, then prove that #(q-r) / (a) + (r-p) / (b) + (p-q)/(c) = 0?
  
• Find the sum of `2 + 2^2 + 2^3 + 2^4 + 2^5....... 2^n`?
  
• If the `p^(th), q^(th), and r^(th)` of a H.P is a,b,c respectively, then prove that`(q-r) /a + (r-p) / b + (p-q)/c = 0`?
  
• If `(a^n + b^n)/(a^(n-1) + b^(n-1))` is the G.M between a & b find the value of'n'?
  
• If a, b, c are positive such that `ab^2c^3 = 64` then the least value of `(1/a + 2/b + 3/c)` is?
  
• The of the first n terms of the series `1^2 + 2.2^2 + 3^2 + 4.4^2......` is `(n(n+1)^2) / 2`, where n is even. When n is odd, the sum is?
  
• The `p^th` term `T_p` of H.P (Harmonic Progression) is `q(p+q)` and `q^th` term `T_q` is `p(p+q)` when p>1, q>1 then? The question has multiple answers.
  
• If (1+3+5+...... +a ) + (1+3+5+ .......... +b) = (1+3+5......... +c), where each set of parentheses contains the sum of consecutive odd integers as shown such that a+b+c = 21, a>6. If G = Max{a,b,c} and L = Min{a,b,c}, then? The question has multiple ans
  
• If `a,a_1, a_2,.....a_10,b` are in A.P and `a,g_1,g_2,g_3................g_10,b` are in G.P and h is the H.M between a and b, then find the value of below given expression?
  
• Given that `a^x = b^y = c^z = d^u` and a,b,c,d are in G.P, show that x,y,z,u are in H.P?
  
• Express the recurring decimal `0.1bar576` as rational number using the concept of geometric series?
  
• Find the sum of the first n terms of the series : `1+2*(1+1/n) + 3*(1+1/n)^2 + 4*(1+1/n)^3........`?
  
• If the sum to first n terms of a series, the `r^(th)` term of which is given by `(2r + 1)^(2r)` can be expressed as `R(n*2^n) + S*2^n + T`, then find the value of (R+T+S)?
  
• Let `a_1,a_2,a_3......a_n` be an A.P . Prove that: `1/(a_1*a_n) + 1/(a_2*a_(n-1)) + 1/(a_3*a_(n-2)) + ......... + 1/(a_n*a_1) = 2/(a_1 + a_n)[1/a_1 + 1/a_2 + 1/a_3 +....... + 1/a_n]`?
  
• If there be 'm' A.P's beginning with unity whose common difference is 1,2,3......m. Show that the sum of their `n^(th)` terms is `(m/2)(mn-m+n+1)`?
  
• Prove that the sum of the infinite series `(1*3)/2 + (3*5)/(2^2) + (5*7)/(2^3) + (7*9)/(2^4) ........ oo = 23`?
  
• If an arithmetic progression & a geometric progression have the same first term, the last term & the same number of terms, prove that [ . . . ] (see description)?
  
• Find the sum of the first n terms of the series : `1 + 2(1+1/n) + 3(1+1/n)^2 + 4(1+1/n)^3.......`?
  
• Find the sum of the first n terms of the series `1+2(1+1/n) +3(1+1/n)^2 + 4(1+1/n)^3.......` Using the agp ( arithmerico - geometrico progression ) sum formula?
  
• Find the distance of point A(2,3) measured parallel to the line x- y = 5 from the line 2x + y + 6 = 0?
  
• A triangle ABC is formed by three lines x + y +2 = 0, x - 2y + 5 = 0 and 7x + y - 10 = 0. P is a point inside the triangle ABC such that areas of the triangles PAB, PBC, and PCA are equal?
  
• A line passes through `(2,2)` and cuts a triangle of area `9 " units"^2` from the first quadrant. The sum of all possible values for the slope of such a line, is?
  
• A variable line passing through the origin intersects two given straight lines 2x + y = 4 and x + 3y = 6 at R and S respectively. A point P is taken on this variable line. Find the equation to the locus of the point P if?A
  
• What is the density of wet air with 75% relative humidity at 1atm and 300K? Given : vapour pressure of `H_2O` is 30 torr and average molar mass of air is 29g/mol?
  
• Find the distance of point A(2,3) measured parallel to the line x- y = 5 from the line 2x + y + 6 = 0?
  
• A variable line passing through the origin intersects two given straight lines 2x + y = 4 and x + 3y = 6 at R and S respectively. A point P is taken on this variable line. Find the equation to the locus of the point P if?
  
• A certain volume of argon gas ( Mol.wt = 40) requires 45 s to diffuse through a hole at a certain pressure and temperature. The same volume of another gas of unknown molecular weight requires 60 s to pass through the same hole under same conditions?
  
• Find the reading of the spring balance shown in fig. The elevator is going up with an acceleration g/10, the pulley and the string are light and the pulley is smooth?( The mass of the blocks are 1.5 Kg and 3.5 Kg)
  
• Acceleration of a particle varies as `a = v^2`, where v is the velocity of particle. If initially the particle was at rest, then?
  
• If mass % of Oxygen in a monovalent metal carbonate is 48. Then find the number of atoms of metal present in 5mg of this metal carbonate sample?`( N_a = 6.022 * 10^23)`
  
• Prove that `log_(2/3)(5/6)` is less that one greater than zero? Also explain your answer?
  
• For a body starting off with an initial velocity of `vec u = 16hati + 12hatj m/s` and moving with a uniform acceleration of `vec a = -2.5hati m/s^2`, if after time 't' seconds the velocity `vec V` becomes perpendicular to it's initial velocity, then t= ?
  
• Calculate `int_0^(2pi) cos^2x .dx`?
  
• Find the sum upto infinite terms of the series: `1/(1*3) + 2/(1*3*5) + 3/(1*3*5*7) + 4/(1*3*5*7*9).......` Using partial fractions?
  
• Find the sum of the series `(1+1/3)(1+1/3^2)(1+1/3^4)(1+1/3^8)...... oo`?
  
• A line passes through (2,2) and cuts a triangle of area 9 from the first quadrant. The sum of all possible values for the slope of such a line, is?
  
• A variable line passing through the origin intersects two given straight lines 2x + y = 4 and x + 3y = 6 at R and S respectively. A point P is taken on this variable line. Find the equation to the locus of the point P if?
  
• If the straight lines `ax + by + c = 0` and `x cos(alpha) + y sin(alpha) = c` enclose an angle `pi/4` between them and meet the straight line `x sin(alpha) - y cos(alpha) = 0` in the same point between them, then?
  
• The equation of a straight line passing through the point (-5,4) and which cuts off an intercept of `sqrt2` units between the lines `x + y + 1 = 0` and `x + y - 1 = 0` is?
  
• If `sinA + cosecA + 2 = 0` then, `sin^(2017)(A) + cosec^(2016)(A) + 1` is equal to?
  
• The number of possible integral values of the parameter `k` for which the inequality `k^2x^2 < (8k -3)(x+6)` holds true for all values of `x` satisfying `x^2 < x+2` is?
  
• A ray of light is sent along the line `x-2y-3=0`. Upon reaching the line`3x-2y-5=0`, the ray is reflected from it. If the equation of the line containing reflected ray is `ax-2y = b`, then find the value of`(a+b)`?
  
• With what minimum acceleration mass M be moved on frictionless surface so that m remains stick to it. The co-efficient of friction between M and m is u?
  
• `100 ml` of `H_2SO_4`solution having molarity `1 M` and density `"1.5 g/ml"` is mixed with `400 ml` of water. Calculate final molarity of `H_2SO_4` solution, if final density is `"1.25 g/ml"`?
  
• What is number of real solutions of x which satisfies `(x-1)(2x+1)(x+1)(2x-3) = 15`?
  
• Find the sum of the series `1/(2sqrt1 + 1sqrt2) + 1/(3sqrt2 + 2sqrt3) + 1/(4sqrt3 + 3sqrt4) ........ 1/(100sqrt99 + 99sqrt100)`? ( Please solve without differentiation )
  
• A pair of straight lines is represented by `2y^2 +5xy -3x^2 = 0`. Another line having an equation `x+y = k`. These lines form a triangle whose centroid is `(1/18,11/18)`. Find the value of k?
  
• Q,R and S are point on the line joining the point P and T. `P(a,x), T(b,y)` such that `TQ=QR=RS=SP`. Then the co-ordinates `((5a + 3b)/8,(5x+3y)/8)` is the mid-point of which segment?
  
• Why is the Lattice energy of `MgO` greater than `MgF_2` even though the size of Oxygen is greater than Fluorine?
  
• What is the difference between donation and transfer of electrons?
  
• Why is `AlF_3` ionic while `AlCl_3` covalent compound?
  
• Why is `F_2, Cl_2` gaseous room temperature while `I_2` is a solid? Please give an answer relating to bond strength.
  
• There are two separate fixed frictionless inclined planes making angle `60^o` and `30^o` with the horizontal. Two blocks A and B are kept on both of them. Find the relative acceleration of A with respect to B?
  
• Find the sum of the n terms of the series `1*4*7 + 2*5*8 + 3*6*9.....`?
  
• On the portion of the straight line `x+2y=4` intercepted between the axes , a square is constructed on the side of the line away from the origin. The the point of intersection of its diagonals has co-ordinates is?
  
• Given the family of lines, `a(3x+4y+6) + b(x+y+2)=0`. The line of the family situated at the greatest distance from the point `P(2,3)` has the equation?
  
• If one diagonal of a square is along the line `x=2y` and one of its vertex is `(3,0)`, then its sides through the vertex are given by the equations?
  
• Let P be `(5,3)` and a point R on `y=x` and Q on x-axis are such that `PQ + QR + RP` is minimum. The the coordinates of Q are?
  
• Find the sum till infinity `1*3*5 + 3*5*7 + 5*7*9...`?
  
• Find the sum of the series till n terms `1*3*2^2 + 2*4*3^2 + 3*5*4^2...`?
  
• The equations of two sides AB and AC of an isosceles triangle ABC are x + y = 5 and 7x - y = 3 respectively. Find the equations of the side BC is the area of the triangle is 5 sq. units?
  
• Simplify `30+114n -114 +81{(n-1)(n-2)} + 17{(n-1)(n-2)(n-3)} + (n-1)(n-2)(n-3)(n-4)`?
  
• If O be the origin and if the co-ordinates of any two points `P_1` and `P_2` be respectively `(x_1,y_1) ,(x_2,y_2)`, prove that `OP_1 * OP_2 cosP_1OP_2 = x_1x_2 + y_1y_2`?
  
• Find the area of the triangle with the coorinates a) `(acostheta_1,bsintheta_1 , (acostheta_2,bsintheta_2 (acostheta_3,bsintheta_3` B) `(am_1^2, 2am_1) , (am_2^2, 2am_2), (am_3^2, 2am_3)`?
  
• All the points lying inside the triangle with coordinates `(1,3),(5,0),(-1,2)` satisfy?
  
• If the equation `ax^2-6xy+y^2+bx+cy+d=0` represents a pair of straight lines whose slopes are `m` and `m^2`, then value(s) of a is/are?
  
• Let `A(3,2)` and `B(5,1)`. ABP is an equilateral triangle constructed on the side of AB remote from origin then the orthocentre of triangle ABP is?
  
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