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If a+b+c=0 and a,b,c are real, then prove that the eqn (b-x)2 - 4 (a-x)(c-x) = 0 has real roots and the roots will not be equal unless a=b=c. ...
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*Image* Ques) A smooth block of mass m is held stationary wedge of mass M and inclination theta. If the system is released from rest,will the normal reacn b/w wedge and block be less or greater than mgcos theta???? From my po ...
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Ques1) Show that the value of ∫ [(1 - cot n-2 x) / (tanx + cotx .cot n-2 x ) ]dx is equals to (1/n) log | sin n x + cos n x| + c. Ques2) If I1 =∫ sin -1 x dx and I 2 = ∫ sin -1 1-x 2 dx then show that I 1 +I 2 = pie x / ...
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Ques1) Prove that the sum of 1 st n odd natural numbers is n2 and hence or otherwise prove that the sum of next 'n' odd natural numbers is divisible by 3. Ques2) Show that the sum of 2/3 + 8/9 + 26/27 + 80/81 + .............u ...
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*Image* Ques1) In the above figure, an a meter bridge , two resistances in the gap are 5 ohms and 10 ohms. The wire resistance is 10 ohms. The emf of the cell connected at the neds of the wire is 5 volts and it's internal res ...
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Ques1) Show that the extremum value of the function f(x) = 1 / (sinx+4) - 1 / (cos x -4), where x belongs to R is 2 2 / (4 2 + 1). Ques2) If a2x4 + b2y4 = c6, then show that the max value of xy is c3 / 2ab . Ques3) If x7 - x5 ...
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Ques1) The lengths of three unequal rectangular block arein G.P. The volume of the block is 216 cm3 and the total surface area is 252 cm2 . Show that the length of the longest edge is 12 cm. Ques2)Show that 11 2 + 12 2 +13 2 ...
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*Image* Ques1) For the above pair of structures, identify the relation b/w them. Are thay enantiomers, diasterioisomers, structural isomers, or two molecules of the same compound? Ques2) *Image* How many optical active forms ...
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*Image* Ques1) The above figure shows an arrangement to measure the emf and internal resistance of the battery. Suppose the voltmeter reads 1.52 v when the switch S is open. When the switch is closed the voltmeter reading dro ...
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Ques1) Show that the sum of the series 1 / 1.3 + 2 / 1.3.5 + 3 / 1.3.5.7 + ........... upto n terms is 1/2. Ques2) Show that the sum of n terms for series 3/4 + 5/36 + 7/144 + 9/400 + 11 / 900 + ......... is 1. Ques3) If the ...
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Ques1) The eqn of tangen to the curve y = cos(x+y) where -2pie ≤ x ≤ 2 pie, that are parallel to the line x+2y = 0 (a) x+2y = pie/2 and x+2y = -3 pie/2 (b) x+2y = pie/2 and x+2y = 3 pie/2 (c) x+2y = 0 and x+2y = pie (d) n ...
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1) Find the values of a for which the eqn 3x4 + 4x3 -12x2 + a = 0 are real and distinct. 2) If f ' (sinx) < 0 and f '' (sinx) > 0 for x belonging to R, then find the intervals of monotonicity of the function g(x) = f(si ...
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1) If the equation x 4-4x 3+ax 2+bx+1=0 has four positive roots, then show that a=6 and b=-4 2) If S = a 1+a 2+a 3+..........+an then show that s/(s-a1) + s/(s-a2) +s/(s-a3) + ...............+ s/(s-a n) > n2 /( n-1). 3) If ...
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*Image* Is the compound opticaly active?? ...
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*Image* In the arrangement shown in the figure, the appreciable friction exisits b/w the wedge and body m. The friction coeff being equals to @.The masses of pulley and thread are negligible. Show that the acc of body m relat ...
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*Image* A block of mas m rests on a bracket of mass M. The coeff of friction b/w the block and bracket are @s and @k. The bracket rests on a frictionless surface. Show that the max force F that can be applied if the block is ...
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*Image* A block of mas m rests on a bracket of mass M. The coeff of friction b/w the block and bracket are @s and @k. The bracket rests on a frictionless surface. Show that the max force F that can be applied if the block is ...
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1) Let f(x) = x3+x2+100x+7sinx then show that the eqn 1 / [y-f(!)] + 2 / [y-f(2)] + 3 / [y-f(3)] = 0 has exactly one root lying in (f(1) , f(2)). 2) Let f(x) and g(x) be two functions which cuts each other orthogonally. At th ...
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1) Show that the least value of 2 log 100 a - log a 0.0001, for a > 0 is 4. 2) If the equation x 4-4x 3+ax 2+bx+1=0 has four positive roots, then show that a=6 and b=-4 3) If S = a 1+a 2+a 3+..........+an then show that s/ ...
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1) A potentiometer wire of length 100 cm has a resistance of 10 ohm. It is connected in series with a resistance and an accumulator of emf 2V and of negligible reistance.A source of emf 10 mV is balanced against a length of 4 ...
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*Image* 1) In the above figure A has a mass 40kg and B is of 15 kg and F is 500N parallel to the smooth inclined plane. The system is moving together.(a) Show that the acc of the system is 45/11 m/s2 (b) Show that the least c ...
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1) If a>1 , b>1 then show that the min value of log b a + log a b is 2. 2) Show that the least value of 2 log 100 a - log a 0.0001 for a >1 is 4. 3) If x,y,z are positive then show that the min value of X logy - logz ...
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Find the domain of the following:- (a) F(x) = sin -1{ (2-3[x] ) / 4 } (b) F(x) = sin |x| + sin -1 (tanx) + sin (sin -1 x) (c) F(x) = (x 2 - |x| - 2) 1/2 ...
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*Image* Ques1) In the above figure, show that the current in 3 ohm resistance is 1/7 A. Ques2) *Image* Find the current in branch CD of the circuit. Ques3) What would happen to the drift velocity of electrons in a wire and to ...
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Ques1) Let g(x) = {log(1+x)} -1 - x-1 , where x>0, then (a) 1<g(X)<2 (b) -1<g(x) <0 (c) 0<g(X)<1 (d) none of these Ques2) Show that the interval in which x3 increses more rapidly than 6x2+15x+5 is (5,infi ...
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Ques) A coil of current crrying Nichrome wire is immersed in aliquid. When the potetial difference across the coil is 12 V and the current through the coil is 5.2 A., the liquidm evaporated at the steady rate of 21mg/sec. Cal ...
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*Image* 1)In the figure, the wedge is acted on by a constant horizontal force F. The wedge is moving on a smooth horizontal surface. A ball of mass m is at rest relative to the wedge. Show that the ratio of the force exerted ...
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*Image* A charged capapcitor C1 is discharged through a resisitance R by Putting switch S in position 1 of circuit as shown in the figure. When discharge current reduces to I 0 , the switch is suddenly shifted to position2. C ...
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*Image* A charged capapcitor C1 is discharged through a resisitance R by Putting switch S in position 1 of circuit as shown in the figure. When discharge current reduces to I 0 , the switch is suddenly shifted to position2. C ...
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1) The value of x+y+z=15, if a,x,y,z,b are in A.P while the vlue of 1/x + 1/y + 1/z =5/3 if a,x,y,z,b are in H.P. , Find a and b. 2) If the (m+!)th,(n+1)th and (r+1)th terms of an A.P are in G.P. and m,n,r are in H.P. Then sh ...
