MATHEMATICS JEE MAIN ONLINE MOCK -II

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 $z_1$ and $z_2$ form an equilateral triangle. Then

$a^2=b$

$a^2=2b$

$a^2=3b$

$a^2=4b$

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

$p \bigwedge \sim q$

$\sim p \bigwedge q$

$\sim p \bigwedge q$

$p V \sim q$

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

$y^2$

$y^3/[latex]</span></label></div><div class='watupro-question-choice ' dir='auto' ><input type='radio' name='answer-129[]' id='answer-id-458' class='answer answerof-129 ' value='458' /><label for='answer-id-458' id='answer-label-458' class=' answer'><span>none of these </span></label></div></div></div></div><div class='watu-question ' id='question-5'><div id='questionWrap-5' class=' '> <div class='question-content' ><span class='watupro_num'>5. </span>The number of ways in which 6 men and 5 women can dine at a round table , if no two women are to sit together, is given by <input type='hidden' name='question_id[]' id='qID_5' value='130' /><input type='hidden' id='answerType130' value='radio'></div><div class='question-choices watupro-choices-columns '><div class='watupro-question-choice ' dir='auto' ><input type='radio' name='answer-130[]' id='answer-id-459' class='answer answerof-130 ' value='459' /><label for='answer-id-459' id='answer-label-459' class=' answer'><span>[latex]6! \times 5!$

<img src="https://mathstudy.in/wp-content/ql-cache/quicklatex.com-01a5f5cfd59d5d87936a34005f0fde20_l3.png" class="ql-img-inline-formula quicklatex-auto-format" alt="y^3/[latex]</span></label></div><div class='watupro-question-choice  ' dir='auto' ><input type='radio' name='answer-129[]' id='answer-id-458' class='answer   answerof-129 ' value='458'   /><label for='answer-id-458' id='answer-label-458' class=' answer'><span>none of these </span></label></div></div></div></div><div class='watu-question ' id='question-5'><div id='questionWrap-5'  class='  '> <div class='question-content' ><span class='watupro_num'>5. </span>The number of ways in which 6 men and 5 women can dine at a round table , if no two women are to sit together, is given by <input type='hidden' name='question_id[]' id='qID_5' value='130' /><input type='hidden' id='answerType130' value='radio'></div><div class='question-choices watupro-choices-columns '><div class='watupro-question-choice  ' dir='auto' ><input type='radio' name='answer-130[]' id='answer-id-459' class='answer   answerof-130 ' value='459'   /><label for='answer-id-459' id='answer-label-459' class=' answer'><span>[latex]6! \times 5! " title="Rendered by QuickLaTeX.com" height="395" width="880" style="vertical-align: -5px;"/>

$30$

$5! \times 4!$

$7! \times 5!$

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

$a=1,b=\frac{-1}{2}$

$a=-1,b=\frac{1}{2}$

$a=2,b=\frac{-1}{2}$

$a=2,b=\frac{-1}{3}$

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

$\frac{2b}{\sqrt{a^2-4b^2}}$

$\frac{b}{\sqrt{a^2+4b^2}}$

$\frac{2b}{\sqrt{a^2-b^2}}$

\item $\frac{2b}{\sqrt{2a^2-4b^2}}$

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

$log_e(\frac{4}{e})$

$2log_e2$

$log_e2$

$log_e2-1$

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

1+X

1-X

X-1

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

$\frac{a}{2}cot(\frac{\pi}{n})$

$\frac{a}{2}cot(\frac{\pi}{2n})$

$\frac{3a}{2}tan (\frac{\pi}{2n})$

$\frac{a}{3}cot(\frac{\pi}{2n})$

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

None of these

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

$(-1,0) \cup (0,2)\cup (2, \infty)$

$(-1,0) \cup (1,2)\cup (2, \infty)$

$(-3,0) \cup (1,2)\cup (2, 8)$

$(1,2)\cup (2, \infty)$

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

$\pm 1$

$\pm 2$

$\pm \frac{1}{2}$

none of these

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

$\frac{\pi}{6}$

$\frac{\pi}{3}$

$\frac{\pi}{2}$

none of these

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 $tan\alpha[latex] is <input type='hidden' name='question_id[]' id='qID_18' value='143' /><input type='hidden' id='answerType143' value='radio'></div><div class='question-choices watupro-choices-columns '><div class='watupro-question-choice ' dir='auto' ><input type='radio' name='answer-143[]' id='answer-id-499' class='answer answerof-143 ' value='499' /><label for='answer-id-499' id='answer-label-499' class=' answer'><span>[latex]\frac{1}{\sqrt{5}}$

1/2

$\frac{11}{\sqrt{3}}$

$\frac{12}{\sqrt{5}}$

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

$\frac{1}{2}$

$\frac{2}{3}$

$\frac{\sqrt{2}}{5}$

$\frac{3}{4}$

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

$\frac{n(n+1)}{2}$

$\frac{7n(n+1)}{2}$

$\frac{7n(n+2)}{2}$

$\frac{7n(2n+1)}{2}$

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

$\frac{1}{n+1}$

$\frac{1}{n+1}-\frac{1}{n+2}$

$\frac{1}{n+2}$

$\frac{1}{2n+1}+\frac{1}{n+2}$

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

$\frac{1}{5}$

$\frac{1}{3}$

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