Maths-
General
Easy
Question
The value of
is
The correct answer is: ![a open parentheses x to the power of 2 end exponent plus fraction numerator 1 over denominator x to the power of 2 end exponent end fraction close parentheses minus fraction numerator a to the power of 2 end exponent over denominator 2 end fraction open parentheses x to the power of 4 end exponent plus fraction numerator 1 over denominator x to the power of 4 end exponent end fraction close parentheses plus fraction numerator a to the power of 3 end exponent over denominator 3 end fraction open parentheses x to the power of 6 end exponent plus fraction numerator 1 over denominator x to the power of 6 end exponent end fraction close parentheses minus.....](data:image/png;base64,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)
![log subscript e end subscript invisible function application open square brackets 1 plus a x to the power of 2 end exponent plus a to the power of 2 end exponent plus fraction numerator a over denominator x to the power of 2 end exponent end fraction close square brackets](data:image/png;base64,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)
![equals log subscript e end subscript invisible function application left parenthesis 1 plus a x to the power of 2 end exponent right parenthesis open parentheses 1 plus fraction numerator a over denominator x to the power of 2 end exponent end fraction close parentheses](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALcAAAArCAYAAAA6yhmnAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAZpE86XgAABNpJREFUeNrtXV1kHUEUPqKuqCgREVdViIqoiFBRERGlKqIqL1V96EOEiIqK6ktVVeUl+pCHiFIVUVUhoiKqSlVVRJSKqKq8RPWhD3FfqqriCrdz7Lm6mczu3d+7M7Pn40h2bzLmzDl75vzNXgCG7bglaMFi/uaJR0bOMChoR9AJi3lE3r4IGmJx5wcnBX0X1JsDXruJ1yYWez4wI+hJjvidJ54ZlqNV0C9Bp3PEc1HQb+KdYTHuC3phyFwbBD0StC+oTDFCe8SxFgU9YPHbjW8UTJqA1+RSNJOirwgajTjWgKBdFr+96BRUMmSuN0iZ3XguaCTGmLgDdLEa2IkxQS8NmesHQf3SvY8x3BIg3sdYDfRHhQh90U1BZwP8D1q+SUP4+0uuiNv//hNzzHFaA4ZBQRdW4bYD+rAjhvBVUvjM2zHHHBb0xmZlQEWYtZCvA9fvs6AuO6PCmJIO+ymo0XWNmY7VmGM2GRRzhEaPoC0L+Roif9SNTeLXb6vXGVh0eUrzbSd/Oa7VbaA1SMVHzBoo8F6PLAJahh0DFbtIfHVI988L2oggA53WAnPyKzSfRsp2jMYcs2yjcveSEqiARY0JTR7AMOgkP7ro8fkGKXkYGei8Fq266mHWi/VY0FQKc8yKryJt06d8/ua2FF9UUubLBONQN+W+Ak7FrEw/r3r8L+Y7P1PQtAdOrjLsJN9C7cpc2gINUk4e9wh4Z+izKlCxaxUkcN3es3IHm2MlAAUd9AIpajddd9O1nLjvovtVxeyg4CLsQmLjTCFjgQYtJ2PKq811jQ/zQgBZyCgQ36zcdbbcq2S5ZUu+Jt1bIh8w7iQPMxZomHIy5mPn6PdLkvWNE0CxctdJuVWWVLY0iBJZOl2UO+ruFbac/A6cFB+6Li2aKnfcnTwtytwtqQRM1VQSegKzdkvClpOnaS16Yig2uyWaW26vwkPYSaIlHMhQoGHKyQPkts2ROxMVHFBm6HPL2REMrl4pshzydt4cYZJZpwKDlpMxYF4H55xjE2WJorolU8Q3K3edlbuPsiDn6LqHrmXrigHXBmUPGijY+gRHeyncmCXr/8OViUH4FXHqIdAg5eRWutciBdlRT85EKeKwcic0KApul3zLr+BdWh0ny1cmxe5TuC+IefifC0afdVH6fMvDhw0blESFXzm5QLuW6mzjMj3UYRC1/F6vtYijR2FbfY16ANvgeHqsSA9AFZcV275ujVNpduipGqdMay/wQ5hWX63XYJ2sdVWJ8Vo+UXFdYXGWFGNNgp0tr3J8MWGCYBPAgenKfQ2cNwdVy+/Tir9RVfEYdiu3qtXXyjXAcv4a629ulNur1dfaNbgDzquzysREgfX5CA4t4aNWq68fyqwGdsKkkzh+FrtWq68XTkBKJ3EY2QOzSc2azi3JVl8vYP2gxGpgJ3ArH9Z4fkm1+nphBCw//Z5nLIHeL6VJstVXhQlQp4cZFuAm6P8SzKRafVVYBn7jlLXALMO+5nNMotXXCyXgdwVaDSyG9Ws6t6RafVW4CPyWV+txF443lOmAJFt9VUB37B6L326gwuj2zQpJt/rKOAPOqacWFr/9eAj69OEk3eqrwjNwXqnByAFw699LKWjTDXhIhb/NLGfA4M3276EsUAA9yOLOH7CoYfNX9qHrpXzZ/j/A5p7bF+Pf1wAAAVp0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bW8+PTwvbW8+PG1yb3c+PG1zdWI+PG1pPmxvZzwvbWk+PG1pPmU8L21pPjwvbXN1Yj48bW8+JiN4MjA2MTs8L21vPjxtbz4oPC9tbz48L21yb3c+PG1uPjE8L21uPjxtbz4rPC9tbz48bWk+YTwvbWk+PG1zdXA+PG1pPng8L21pPjxtbj4yPC9tbj48L21zdXA+PG1vPik8L21vPjxtZmVuY2VkIHNlcGFyYXRvcnM9InwiPjxtcm93Pjxtbj4xPC9tbj48bW8+KzwvbW8+PG1mcmFjPjxtaT5hPC9taT48bXN1cD48bWk+eDwvbWk+PG1uPjI8L21uPjwvbXN1cD48L21mcmFjPjwvbXJvdz48L21mZW5jZWQ+PC9tYXRoPgbWmoEAAAAASUVORK5CYII=)
![equals log subscript e end subscript invisible function application left parenthesis 1 plus a x to the power of 2 end exponent right parenthesis plus log subscript e end subscript invisible function application open parentheses 1 plus fraction numerator a over denominator x to the power of 2 end exponent end fraction close parentheses](data:image/png;base64,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)
=
![plus open square brackets fraction numerator a over denominator x to the power of 2 end exponent end fraction minus fraction numerator 1 over denominator 2 end fraction a to the power of 2 end exponent open parentheses fraction numerator 1 over denominator x to the power of 4 end exponent end fraction close parentheses plus fraction numerator 1 over denominator 3 end fraction a to the power of 3 end exponent open parentheses fraction numerator 1 over denominator x to the power of 6 end exponent end fraction close parentheses minus..... close square brackets](data:image/png;base64,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)
![equals a open parentheses x to the power of 2 end exponent plus fraction numerator 1 over denominator x to the power of 2 end exponent end fraction close parentheses minus fraction numerator 1 over denominator 2 end fraction. a to the power of 2 end exponent open parentheses x to the power of 4 end exponent plus fraction numerator 1 over denominator x to the power of 4 end exponent end fraction close parentheses plus fraction numerator 1 over denominator 3 end fraction a to the power of 3 end exponent open parentheses x to the power of 6 end exponent plus fraction numerator 1 over denominator x to the power of 6 end exponent end fraction close parentheses minus...](data:image/png;base64,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)
Related Questions to study
Maths-
The sum of the products of the elements of any row of a determinant A with the same row is always equal to
The sum of the products of the elements of any row of a determinant A with the same row is always equal to
Maths-General
Maths-
is divisor of
is divisor of
Maths-General
Maths-
If
,then the value of k is
If
,then the value of k is
Maths-General
Maths-
The value of the determinant
is
The value of the determinant
is
Maths-General
Maths-
If
the value of t is
If
the value of t is
Maths-General
Maths-
If
are unequal what is the condition that the value of the following determinant is zero ![capital delta equals open vertical bar table row a cell a to the power of 2 end exponent end cell cell a to the power of 3 end exponent plus 1 end cell row b cell b to the power of 2 end exponent end cell cell b to the power of 3 end exponent plus 1 end cell row c cell c to the power of 2 end exponent end cell cell c to the power of 3 end exponent plus 1 end cell end table close vertical bar](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAIcAAABHCAYAAAAtD1S+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAo9ZE6ZAAABEhJREFUeNrtnT9oFEEUxocQQooghJBCRAQJIpJOJIiIjViIiK2FiAgWVhIEkSNICAGxsBAbsRAREYIECwk2EoKITZBgJYKFhcgREBGREIT1DfuCy7q3uzPzdnbu5vvgFXfI++Zmfzt/1n0ZpaAdJRzbFG8ppjx5bVCcQvf/30EhaojiKsV7T34HKb7g2vQHHDva8gjjd8DRP3CcoFjz4DNBcZ/iUoMeByjmePoCHI7azWuO/Z7WOBca9nlCccWwvwFHj7vsJQPiQ7soFvniNd1vAwWHnovnKbqZVf0+h3m9KpcGYoUvmOsawrTdW4DDrAH6Dr5HMc4dvkRxztKrTq4V3jm4yrTdxynWAUf9BpznTs3qMcVpC5+6uZKCaNpLjxivDEfE6OFYpTia+27NclqRzNWGV1IjooLjNw/J2Xn8l6WPZK4QvKIfOTZzn48p+yeWkrlC8Ioejq8Uo5nP+iHOc0sfyVwheEUPxwLFAx6W9Xz9lHcTNpLMFYIXtrKkDq/85/hu7DpsZSVzheRlu6DtezjymhT0nvT4OydV/wmPzyHAAQEOCHBAgAMCHBDgAByAA3AADsABOAAH4AAcuTah6g1wlCr2qrekTge9jnxaibXqrfLa3OIhbyZSOAap6k302kxTvGNAFlqEI/9OpotMcrlWvdX18lX1ZloSmZQNceuc8DDFh5bgmBL0NsnlWvVm2m6bqjdTmZZE9vx3mrCbmc/fKlbttq/OVzVUvz31TKhz6uaSqHqzbXdIVW9Jr+kkX331kGK2hZFDT2n6lbt5BlR33qrlHV03l0TVm027Q6t6S3pNJ4dy359taGFW1VD9HuZnihvqX2nhXcu7sm4uiao3U68Qq96SoumkU/APh/kHTHieVj4VgKqH+58WnSKZKwQvr3BMVwxrLyguehw5hnjFn9eoRSdL5mrLy3dJZFI1nWSlV7o+i3NmeJ7OS9ehmj6Yk8wVipe3kaPDU0rVKn6bpxgfP1BXqz8q+H62RlubzBWKlzc4ftQctnSMePqB+u9b5J8YjvDzA9PdimSuULxa2cr6VFkDlnlhd5I/7+HvbB4xS+YKxStqOLq8hdYd/Uelj31tSwolc4Xk5bqg7Vs4oMivDeAAHIADcAAOwAE4AAfgAByAAwIcEOCAAAcEOCDAEVKHoBQScJQKBwACjkrhAEDAUaiYSyEBR4kG7QBAnA4p2JGhHwBoKpwOKTRiSBwA2PT6BqcmZDRGcUelZ5norZ9+J3Pc0rMsl9QBgKbtxgGAlg0Y4y3lIt/R+k3u6xRnLC9WWS6JUkhTLxwA6NCA2yp93V9Ckrna9AIcvP/fdJhCmsrl2wunQxboCMUbIS/JXG17YeRQ6UG9y0Jekrna9gIcKv2TUx+FvCRzte0FOFgbvOIf5lX/NZWe1WojyVxtegEO1l6V/h+HLi3UxciXHfwkc4XkZbOgHQg4oEivDeAIHI6/8vxDE6Y0ZW4AAAJDdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1pPiYjeDM5NDs8L21pPjxtbz49PC9tbz48bWZlbmNlZCBjbG9zZT0ifCIgb3Blbj0ifCIgc2VwYXJhdG9ycz0ifCI+PG10YWJsZT48bXRyPjxtdGQ+PG1pPmE8L21pPjwvbXRkPjxtdGQ+PG1zdXA+PG1pPmE8L21pPjxtbj4yPC9tbj48L21zdXA+PC9tdGQ+PG10ZD48bXN1cD48bWk+YTwvbWk+PG1uPjM8L21uPjwvbXN1cD48bW8+KzwvbW8+PG1uPjE8L21uPjwvbXRkPjwvbXRyPjxtdHI+PG10ZD48bWk+YjwvbWk+PC9tdGQ+PG10ZD48bXN1cD48bWk+YjwvbWk+PG1uPjI8L21uPjwvbXN1cD48L210ZD48bXRkPjxtc3VwPjxtaT5iPC9taT48bW4+MzwvbW4+PC9tc3VwPjxtbz4rPC9tbz48bW4+MTwvbW4+PC9tdGQ+PC9tdHI+PG10cj48bXRkPjxtaT5jPC9taT48L210ZD48bXRkPjxtc3VwPjxtaT5jPC9taT48bW4+MjwvbW4+PC9tc3VwPjwvbXRkPjxtdGQ+PG1zdXA+PG1pPmM8L21pPjxtbj4zPC9tbj48L21zdXA+PG1vPis8L21vPjxtbj4xPC9tbj48L210ZD48L210cj48L210YWJsZT48L21mZW5jZWQ+PC9tYXRoPmLjWokAAAAASUVORK5CYII=)
If
are unequal what is the condition that the value of the following determinant is zero ![capital delta equals open vertical bar table row a cell a to the power of 2 end exponent end cell cell a to the power of 3 end exponent plus 1 end cell row b cell b to the power of 2 end exponent end cell cell b to the power of 3 end exponent plus 1 end cell row c cell c to the power of 2 end exponent end cell cell c to the power of 3 end exponent plus 1 end cell end table close vertical bar](data:image/png;base64,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)
Maths-General
Maths-
If – 9 is a root of the equation
then the other two roots are
If – 9 is a root of the equation
then the other two roots are
Maths-General
Maths-
If
is a cube root of unity, then ![open vertical bar table row cell x plus 1 end cell omega cell omega to the power of 2 end exponent end cell row omega cell x plus omega to the power of 2 end exponent end cell 1 row cell omega to the power of 2 end exponent end cell 1 cell x plus omega end cell end table close vertical bar equals](data:image/png;base64,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)
If
is a cube root of unity, then ![open vertical bar table row cell x plus 1 end cell omega cell omega to the power of 2 end exponent end cell row omega cell x plus omega to the power of 2 end exponent end cell 1 row cell omega to the power of 2 end exponent end cell 1 cell x plus omega end cell end table close vertical bar equals](data:image/png;base64,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)
Maths-General
Maths-
Maths-General
Maths-
In the expansion of
the coefficient of
will be
In the expansion of
the coefficient of
will be
Maths-General
Maths-
The value of
is equal to
The value of
is equal to
Maths-General
Maths-
The sum to infinity of the given series
is
The sum to infinity of the given series
is
Maths-General
Maths-
is defined for ![left parenthesis a greater than 0 right parenthesis](data:image/png;base64,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)
is defined for ![left parenthesis a greater than 0 right parenthesis](data:image/png;base64,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)
Maths-General
Maths-
The sum of the series![fraction numerator 1 over denominator 2.3 end fraction plus fraction numerator 1 over denominator 4.5 end fraction plus fraction numerator 1 over denominator 6.7 end fraction plus... equals](data:image/png;base64,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)
The sum of the series![fraction numerator 1 over denominator 2.3 end fraction plus fraction numerator 1 over denominator 4.5 end fraction plus fraction numerator 1 over denominator 6.7 end fraction plus... equals](data:image/png;base64,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)
Maths-General
Maths-
Maths-General