1. Let z_1 and z_2 be two roots of the equation z^2+az+b=0, z being complex. Further assume that the origin z_1and z_2 form an equilateral triangle. Then

2. Let p and q be two statements. Amongst the following the statement that is equivalent to p \to q is

3. (Integer Answer ) Number of integral values of \alpha for which the equatin \frac{x^3}{3}-x=\alpha has 3 distinct solutions is

4. If y =2^{1/log_x8} then x equal to

6. (Integer Answer ) The number of integral terms in the expansion of (\sqrt{3} +\sqrt[8]{5})^{256} is

7. If y =aln x +bx^2+x has its extremum values at x=-1 and x=2 then

8. If a > 2b >0 then the positive value of m for which y =mx -b\sqrt{1+m^2} is a common tangent to x^2+y^2 =b^2/[latex] and [latex](x-a)^2 +y^2= b^2 is

9. The sum of the series \frac{1}{1.2} -\frac{1}{2.3} +\frac{1}{3.4} -..... upto \infty is equal to

10. If x =\frac{2sin\alpha}{1+cos\alpha + sin\alpha}, then \frac{1-cos\alpha +sin\alpha}{1+sin\alpha} is equal to

11. The sum of the radii of inscribed and circumscribed circles for an n sided regular polygon of side a , is

12. If in \triangle ABC acos^2(\frac{C}{2}) +c cos^2(\frac{A}{2}) =\frac{3b}{2} then the sides a,b and c are in

13. (Integer Answer) If f(x) =x^n then the value of f(1) -\frac{f'(1)}{1!}+\frac{f''(1)}{2!}-\frac{f'''(1)}{3!}+......+ \frac{(-1)^n f^n (1)}{n!} is

14. Domain of definition of function f(x) =\frac{3}{4-x^2}+log_{10}(x^3-x) is

15. The slope of one of the common tangents to the hyperbolas (x^2/a^2)-(y^2/b^2)=1 and (y^2/a^2)-(x^2/b^2)=1 is

16. If the angle between the lines whose direction cosines are connected by the relations l+m+n=0 and 2lm+2nl-mn=0 is \alpha , then the value of 4sin^2\alpha is

17. (Integer Answer) Let f(a) =g(a) =k and their nth derivatives f^n(a), g^n (a) exist and are not equal for some n. Further , if \lim_{x \to a} \frac{f(a) g(x) -f(a) -g(a) f(x) +g(a)}{g(x) -f(x) }=4 then value of k is equal to

18. If \alpha is the angle between the pair of tangents from point (1,2) to the ellipse 3x^2+2y^2=5 then the value of tan\alpha[latex] is <input type='hidden' name='question_id[]' id='qID_18' value='143' /><input type='hidden' id='answerType143' value='radio'><!-- end question-content--></div><div class='question-choices watupro-choices-columns '><div class='watupro-question-choice  ' dir='auto' ><input type='radio' name='answer-143[]' id='answer-id-499' class='answer   answerof-143 ' value='499'   /><label for='answer-id-499' id='answer-label-499' class=' answer'><span>[latex]\frac{1}{\sqrt{5}}

19. If \int x log(1+1/x)dx = f(x) log(x+1) +g(x) x^2 +Ax +C then A =

20. If f: R \to R satisfies f(x+y) =f(x) +f(y), for all x,y \in R and f(1) =7 then \sum^n_{r=1} f(r) is

21. (Integer Answer) The value of the \lim_{x \to 0} \frac{\int^{x^2}_0 sec^2t dt}{x sinx} is

22. The value of the integral I = \int^1_0 x(1-x)^n dx is

23. \lim_{n \to \infty} \frac{1+2^4 +3^4 +....+n^4}{n^5} -\lim_{n \to \infty} \frac{1+2^3+3^3+...+n^3}{n^5}

24. (Integer Answer) Let \frac{d}{dx}F(x) =(\frac{e^{sinx}}{x}) ,x >0 If \int^4_1 \frac{3}{x}e^{sinx^3}dx =F(k)-F(1) then one of the possible values of k is

25. The solution of the differential equation (1+y^2) +(x-e^{tan^{-1}y})\frac{dy}{dx}=0 is


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