A) \[\log \left( \frac{b}{a} \right)\] done clear
B) \[\log \left( \frac{a}{b} \right)\] done clear
C) \[\frac{a}{b}\] done clear
D) \[\log {{a}^{b}}\] done clear
E) None of these done clear
View Answer play_arrowA) A = B done clear
B) B = C done clear
C) A = C done clear
D) A = B = C done clear
E) None of these done clear
View Answer play_arrowA) Straight line done clear
B) circle done clear
C) Ellipse done clear
D) parabola done clear
E) None of these done clear
View Answer play_arrowA) \[\left( \frac{1}{3},\frac{7}{3} \right)\] done clear
B) \[\left( 1,\,\,\frac{7}{3} \right)\] done clear
C) \[\left( -\frac{1}{3},\frac{7}{3} \right)\] done clear
D) \[\left( -1,\,\,\frac{7}{3} \right)\] done clear
E) None of these done clear
View Answer play_arrowA) 5 done clear
B) 6 done clear
C) 7 done clear
D) 8 done clear
E) None of these done clear
View Answer play_arrowDirections: Based on the following paragraph. |
If \[\cos \,\,\frac{\pi }{7},\] \[cos\,\,\frac{3\pi }{7},\] \[\cos \,\,\frac{5\pi }{7}\] are the roots of the equation \[8{{x}^{3}}-4{{x}^{2}}-4x+1=0\] |
A) 2 done clear
B) 4 done clear
C) 8 done clear
D) All of these done clear
E) None of these done clear
View Answer play_arrowDirections: Based on the following paragraph. |
If \[\cos \,\,\frac{\pi }{7},\] \[cos\,\,\frac{3\pi }{7},\] \[\cos \,\,\frac{5\pi }{7}\] are the roots of the equation \[8{{x}^{3}}-4{{x}^{2}}-4x+1=0\] |
A) \[\frac{1}{4}\] done clear
B) \[\frac{1}{8}\] done clear
C) \[\frac{\sqrt{7}}{4}\] done clear
D) \[\frac{\sqrt{7}}{8}\] done clear
E) None of these done clear
View Answer play_arrowquestion_answer8) If in a triangle ABC, cosA cosB + sinA sinB sinC =1, then a:b:c is equal to
A) \[1:1:\sqrt{2}\] done clear
B) \[1:1:\sqrt{3}\] done clear
C) \[1:\sqrt{2}:1\] done clear
D) \[1:\sqrt{3}:1\] done clear
E) None of these done clear
View Answer play_arrowA) \[-\pi \] done clear
B) \[-\frac{\pi }{2}\] done clear
C) \[0\] done clear
D) \[\frac{\pi }{2}\] done clear
E) None of these done clear
View Answer play_arrowA) \[P\,\,\left( B/A \right)=P\left( B \right)-P\left( A \right)\] done clear
B) \[P\,\,\left( A'-B' \right)=P\,\,\left( A' \right)-P\,\,\left( B' \right)\] done clear
C) \[P\,(A\bigcup B)'=P\,\,(A')\,\,P\,\,(B')\] done clear
D) \[P\,\,\left( A/B \right)=P\,\,\left( A \right)-P\,\,\left( B \right)\] done clear
E) None of these done clear
View Answer play_arrowA) \[2ax+2by-({{a}^{2}}+{{b}^{2}}+{{k}^{2}})=0\] done clear
B) \[2ax+2by-({{a}^{2}}-{{b}^{2}}+{{k}^{2}})=0\] done clear
C) \[{{x}^{2}}+{{y}^{2}}-3ax-4by+{{a}^{2}}+{{b}^{2}}-{{k}^{2}})=0\] done clear
D) \[{{x}^{2}}+{{y}^{2}}-2ax-3by+({{a}^{2}}-{{b}^{2}}-{{k}^{2}})=0\] done clear
E) None of these done clear
View Answer play_arrowA) The length of whose transverse axis is \[2\sqrt{3}\] done clear
B) The length of whose conjugate axis is 8 done clear
C) Whose centre is (1, 2) done clear
D) Whose eccentricity is\[\sqrt{\frac{19}{3}}\] done clear
E) None of these done clear
View Answer play_arrowA) (0, 1) done clear
B) (1, 0) done clear
C) (1, 1) done clear
D) All of these done clear
E) None of these done clear
View Answer play_arrowA) \[x+y=0\] done clear
B) \[xy+a=0\] done clear
C) \[x+y+a=0\] done clear
D) All of these done clear
E) None of these done clear
View Answer play_arrowquestion_answer15) \[\frac{\tan x}{\tan \,\,3x}\] never lies between
A) \[-\frac{1}{3}\,\,and\,\,0\] done clear
B) \[\frac{1}{3}\,\,and\,\,3\] done clear
C) \[-\frac{1}{3}\,\,and\,\,\frac{1}{3}\] done clear
D) \[-\,3\,\,and\,\,3\] done clear
E) None of these done clear
View Answer play_arrowA) \[\frac{n}{{{[(n/2)!]}^{2}}}\] done clear
B) \[\frac{(2n)!}{{{[(n/2)!]}^{2}}}\] done clear
C) \[\frac{1.3.5...(2n+1)!}{n!}{{2}^{n}}\] done clear
D) \[\frac{(2n)!}{{{(n!)}^{2}}}\] done clear
E) None of these done clear
View Answer play_arrowA) \[2a\,f(a)+{{a}^{2}}f'(a)\] done clear
B) \[-{{a}^{2}}f'(a)\] done clear
C) \[af(a)-{{a}^{2}}f'(a)\] done clear
D) \[2af(a)-{{a}^{2}}f'(a)\] done clear
E) None of these done clear
View Answer play_arrowA) AP done clear
B) GP done clear
C) AGP done clear
D) All of these done clear
E) None of these done clear
View Answer play_arrowA) 40 done clear
B) 60 done clear
C) 80 done clear
D) 100 done clear
E) None of these done clear
View Answer play_arrowquestion_answer20) Negation of "Ram is in class X or Rashmi is in class XII" is
A) Ram is not in class X and Rashmi is not in class XII done clear
B) Ram is not in class X but Ram is class in XII done clear
C) Either Ram is not in class X or Rashmi is not in class XII done clear
D) All of these done clear
E) None of these done clear
View Answer play_arrowA) \[2n\pi \,\,\pm \,\,\frac{\pi }{4}\,\,+\,\,\frac{\pi }{12}\] done clear
B) \[n\pi +{{(-1)}^{n}}\,\,\frac{\pi }{4}\,\,+\,\,\frac{\pi }{12}\] done clear
C) \[2n\pi \,\,\pm \,\,\frac{\pi }{4}\,\,-\,\,\frac{\pi }{12}\] done clear
D) \[n\pi +\,\,{{(-1)}^{n}}\,\,\frac{\pi }{4}\,\,-\,\,\frac{\pi }{12}\] done clear
E) None of these done clear
View Answer play_arrowquestion_answer22) The two curves \[{{x}^{3}}-3x{{y}^{2}}+2=0\] and \[3{{x}^{2}}y-{{y}^{3}}-2=0\]
A) Cut at right angles done clear
B) touch each other done clear
C) Cut at an angle \[\frac{\pi }{3}\] done clear
D) Cut at an angle \[\frac{\pi }{4}\] done clear
E) None of these done clear
View Answer play_arrowquestion_answer23) If \[\frac{3x+4}{{{x}^{2}}-3x+2}=\frac{A}{x-2}-\frac{B}{x-1},\] then (A, B) =
A) (7, 10) done clear
B) (10, 7) done clear
C) \[\left( 10,-\,7 \right)\] done clear
D) \[\left( -\,10,7 \right)\] done clear
E) None of these done clear
View Answer play_arrowA) X done clear
B) Y done clear
C) N done clear
D) All of these done clear
E) None of these done clear
View Answer play_arrowA) A done clear
B) B done clear
C) D done clear
D) E done clear
E) None of these done clear
View Answer play_arrowquestion_answer26) If \[A={{\sin }^{2}}x+{{\cos }^{4}}x,\] then for all real x
A) \[\frac{13}{16}\,\,\le \,\,A\,\,\le \,\,1\] done clear
B) \[1\le A\le 2\] done clear
C) \[\frac{3}{4}\le A\le \frac{13}{16}\] done clear
D) \[\frac{3}{4}\le A\le 1\] done clear
E) None of these done clear
View Answer play_arrowA) equals \[\sqrt{2}\] done clear
B) equals \[-\sqrt{2}\] done clear
C) equals \[\frac{1}{\sqrt{2}}\] done clear
D) does not exist done clear
E) None of these done clear
View Answer play_arrowA) \[P\,(C|D)\ge P\,(C)\] done clear
B) \[P\,(C|D)<P\,(C)\] done clear
C) \[P\,(C|D)=\frac{P\,(D)}{P\,(C)}\] done clear
D) \[P\,(C|D)=P\,(C)\] done clear
E) None of these done clear
View Answer play_arrowA) \[\left( -\,1,1 \right]\] done clear
B) (0,\[\infty \]) done clear
C) [1,\[\infty \]) done clear
D) \[(-1,\infty )\] done clear
E) None of these done clear
View Answer play_arrowA) y = 0 done clear
B) y = 1 done clear
C) y = 2 done clear
D) y = 3 done clear
E) None of these done clear
View Answer play_arrowA) there is a regular polygon with \[\frac{r}{R}=\frac{1}{2}\] done clear
B) there is a regular polygon with \[\frac{r}{R}=\frac{1}{\sqrt{2}}\] done clear
C) there is a regular polygon with \[\frac{r}{R}=\frac{2}{3}\] done clear
D) there is a regular polygon with \[\frac{r}{R}=\frac{\sqrt{3}}{2}\] done clear
E) None of these done clear
View Answer play_arrowA) 24 min done clear
B) 34 min done clear
C) 125 min done clear
D) 135 min done clear
E) None of these done clear
View Answer play_arrowA) \[3\,\sqrt{5}\] done clear
B) \[10\,\sqrt{3}\] done clear
C) \[5\,\sqrt{3}\] done clear
D) \[3\,\sqrt{10}\] done clear
E) None of these done clear
View Answer play_arrowA) \[\frac{1}{4}\,\,{{n}^{2}}\,\,{{(n+1)}^{2}}+n\] done clear
B) \[\frac{1}{4}\,\,{{n}^{2}}\,\,{{(n+1)}^{2}}-n\] done clear
C) \[\frac{1}{4}\,\,n\,\,{{(n+1)}^{2}}-n\,\] done clear
D) \[\frac{1}{4}\,\,{{n}^{2}}\,\,{{(n-1)}^{2}}-n\] done clear
E) None of these done clear
View Answer play_arrowquestion_answer35) If \[x={{2}^{1/3}}-{{2}^{1/3}},\] then \[2{{x}^{3}}+6x=\]
A) 0 done clear
B) 2 done clear
C) 3 done clear
D) 4 done clear
E) None of these done clear
View Answer play_arrowquestion_answer36) If \[{}^{43}{{C}_{r-6}}={}^{43}{{C}_{3r+1}}\], then the value of r is
A) 6 done clear
B) 8 done clear
C) 10 done clear
D) 12 done clear
E) None of these done clear
View Answer play_arrowquestion_answer37) If A = {a, b, c}, B = {b, c, d} and C = {a, d, c} then \[(A-B)\times (B\cap C)=\]
A) {(a, c), (a, d)} done clear
B) {(a, b), (c, d)} done clear
C) {(c, a), (a, d)} done clear
D) {(a, c), (b, d)} done clear
E) None of these done clear
View Answer play_arrowA) \[20\sqrt{2}\] done clear
B) \[40\,\,\left( \sqrt{2}-1 \right)\] done clear
C) \[40\,\,\left( \sqrt{3}-\sqrt{2} \right)\] done clear
D) \[20\,\,\left( \sqrt{3}-1 \right)\] done clear
E) None of these done clear
View Answer play_arrowA) \[\frac{1}{2}\] done clear
B) \[\frac{\sqrt{3}}{\sqrt{2}}\] done clear
C) \[\frac{\sqrt{3}}{2}\] done clear
D) \[\frac{1}{4}\] done clear
E) None of these done clear
View Answer play_arrowA) \[{{\log }_{e}}3\] done clear
B) \[{{\log }_{e}}2\] done clear
C) \[({{\log }_{e}}3)\,\,({{\log }_{e}}2)\] done clear
D) \[\frac{{{\log }_{e}}5}{{{\log }_{e}}3}\] done clear
E) None of these done clear
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