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Please post a brief soln to the problem 1) The no. of right triangles with integer sides and inradius r=2013 2)Let a,b,c,d be non zero digits. If n is the no. of 4 digit no.s abcd such that ab+cd is even, then last digit of n ...
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If f(x) is an invertible func such that f(x) + f(-x)=2a then ∫a-xa+x f-1(t)dt equals : ...
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f(x) is defined for x > −1 and has a continuous derivate. If f satisfies f(0) = 1, f′(0) = 0; (1 + f(x)) f′′(x) = 1 + x. If x is positive then f′(x) is (A) always positive (B) always negative (C) always non-negat ...
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Why is Pb+2 kept in both Gr1 and Gr2? ...
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The value of i log(x – i) + i2+i3 log(x +i) + i4( 2 tan-1x), x> 0 is (A) 0 (B) 1 (C) 2 (D) 3 ...
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Let f(x+y)=f(x).f(y) and f(x)=1+sin(3x).g(x) where g(x) is cont. , then f'(x) is a) f(x).g(0) b)3g(0) c) f(x).cos(3x) d)3f(x).g(0) e)3f(x).g(x) ...
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If f(x+y)=f(x)f(y) for all x and y and f'(0) exists show that f'(x)=f'(x).f'(0) for all x ...
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1)If α and β are ends of a focal chord of an ellipse of eccentricity e, find tan(α/2).tanβ(/2) 2)Normals drawn to ellipse x2/a2 + y2/b2 =1 at P meet the coordinate axes at A, B. Find the locus of mid point of A and B. 3)A ...
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Solid Cylinder, rolls over horizontal surface Find the max value of v which still permits it to roll over incline plane without a jump, sliding is absent. *Image* ...
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The minimum are of triangle formed by any tangent to ellipse x2/a + y2/b =1 with the coordinate axes is : ...
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Convert ethanal to cyclohexylcarbaldehyde ...
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Dehydrobromination of A and B yield the same compound alkene C. C can regenerate A and B by addn of Hbr in the presence and absence of peroxide. 1,2 diphenyl ethane is obtained on reaction of C in presence of H+. Give structu ...
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Convert ethanol to 2 methoxy propane ...
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A mark placed on the surface of a glass sphere is viewed through a glass prism form an oppositely directed position. If the diameter of the glass sphere is 20 cm, find the position of image if refractive index of glass is 1.5 ...
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How can we convert Anniline to phenyl isocyanide? ...
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Why are pentahalides of Gr 15 elements more covalent than trihalides? ...
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Find the greatest integer k for which 1991^k divides 1990^1991^1992 + 1992^1991^1990 ...
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When an uncharged CONDUCTING ball of radius R is placed in a uniform electric field, surface charge density σ=σ°cosθ is induced on ball's surface where σ° is a constant What is the magnitude of resultant ELECTRIC FORCE ...
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Masses of the pulley and thread are negligible C is the angle of inclination. What is the accn of Wedge? *Image* ...
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A uniform disc of radius R is spinned to angular vel ω and then carefully placed on a horizontal surface. How long will the disc be rotating on the surface if coefficient of friction is μ? The pressure by the disc on the su ...
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AB and CD are the plates of a parallel plate capacitor, having 2 dielectrics inserted between them as shown, of constants K1 and K2. Separation between the plates is d and edge length a. Find the capacitance *Image* ...
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For n >=4 points in a plane , such that distance between any 2 points is an integer, prove that there are at least 1/6 distances , which are divisible by 3 ...
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There is a circular wire loop carrying current i, of radius a. It is placed in a perpendicular magnetic field B. What is the force of compression in the wire? ...
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How much ice will separate if a solution containing 25g of ethylene glycol[C2How much ice will separate if a solution containing 25g of ethylene glycol[C2H4(OH)2 in 100g of water is cooled to -10°C? Kf for water is 1.86 - Af ...
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The standard reduction potential of a calomel half cell is 0.28 V at 25°The standard reduction potential of a calomel half cell is 0.28 V at 25°C. Calculate half cell potential when 0.1N KCL soln is used ...
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While deriving an expression for resultant capacitance or resistance in a parallel combination, how do we reach to the conclusion that potential difference across each capacitor is same?? ...
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2.5g of BaO and CaO when heated with excess H2 SO4 , produced 4.713g of mixed sulphates. Find the percentage of BaO present in mixture ...
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A small block of mass m is placed on the top of a right triangular block of mass M, which in turn is placed on a horizontal surface. All the surfaces are frictionless. Angle of inclination is α. Height of the triangular bloc ...
