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Let f (x) be a differentiable function a...

Let f (x) be a differentiable function and satisfying the equation
`f ' (x ) + f (x) = 4x e ^(-x) . sin 2 x and f (0) = 0` if
`lim _( n to oo) sum _( k =1) ^( n) f( k pi) = ( - p pi e ^(pi))/( (e ^(pi ) - 1) ^(2)) ` then p =

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NTA MOCK TESTS-NTA TPC JEE MAIN TEST 43 -MATHEMATICS
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  2. If the line (x - 2)/( 3) = (y +1)/(2) = (z -1)/(-1) intersects the pla...

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  3. If veca = veci + vecj + veck, vecb= 4 veci + 3 vecj + 4 veck and vec...

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  4. If f (x) = || sin (|x| - 2) | - 3|, then

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  5. Let f be a composite function of x defined by f (u) = (1)/( u ^(2) +...

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  6. int ( 3e ^(x) -5e ^(-x))/( 4e ^(x) + 5e ^(-x)) = ax + b ln then (4e ...

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  7. Let f (x+y) = f (x). f (y) for all x and y and f (1) = 2 . If in a tri...

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  8. Let f (x) = sin x + 2 sin^(2) x + 3 sin ^(3) x + 4 sin ^(4) x + .... o...

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  9. If theta = sin ^(-1) ((4)/(5)) + sin ^(-1) ((1)/(3)) and theta (2) = c...

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  11. Let x be the number of diagonal matrices A of rela etries and order 3 ...

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  13. If the function f (x) = x ^(3) + e ^((pi)/(2)) and g (x) = f ^(-1) (x)...

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  14. int (0) ^((1)/(2)) (1 + sqrt3)/( ((x + 1) ^(2) (1 - x ) ^(6) ) ^((1)/(...

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  15. Let f (x) be a differentiable function and satisfying the equation f...

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  16. The mean of 10 terms is 3. If the first term is increased by 1, second...

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  18. Let F (x) = int (x) ^((pi)/(3) + x ^(2)) 2 cos^(2) t dt, x in Rand f ...

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  19. If number of ways of arranging letters aaaabbbbccdd' in a line so that...

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  20. Consider the three vectors lamda hati + hatj + 2 hatk , hati + lamda...

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