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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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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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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, a smooth block loosely fits in a circular tube placed on a horizontal surface. The block moves in an uniform circular motion along the tube. Which wall (inner or outer) will exert a non zer ...
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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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*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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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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*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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*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 ...
