A) 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) \[(A\,\,\times B)\,\,\bigcup \,\,(A\,\,\times C)\] done clear
B) \[(A\,\,\bigcup \,\,B)\,\,\times \,\,(A\,\,\bigcap \,\,C)\] done clear
C) \[(A\,\,\times B)\,\,\bigcap \,\,(A\,\,\times \,\,C)\] done clear
D) All of these done clear
E) None of these done clear
View Answer play_arrowA) 6 done clear
B) 9 done clear
C) 15 done clear
D) 22 done clear
E) None of these done clear
View Answer play_arrowA) 3 done clear
B) 9 done clear
C) 6 done clear
D) 18 done clear
E) None of these done clear
View Answer play_arrowquestion_answer5) The number of non-empty subsets of the set {1, 2, 3, 4} is
A) 15 done clear
B) 14 done clear
C) 16 done clear
D) 17 done clear
E) None of these done clear
View Answer play_arrowquestion_answer6) \[{{7}^{2{{\log }_{{{7}^{5}}}}}}\]is equal to
A) \[{{\log }_{7}}35\] done clear
B) 5 done clear
C) 25 done clear
D) \[{{\log }_{7}}25\] done clear
E) None of these done clear
View Answer play_arrowquestion_answer7) 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_arrowquestion_answer8) If n is a positive integer, then \[{{\left( \frac{1+i}{1-i} \right)}^{4n+1}}=\]
A) 1 done clear
B) \[-\,1\] done clear
C) i done clear
D) \[-\,i\] done clear
E) None of these done clear
View Answer play_arrowA) 1 done clear
B) \[-\,1\] done clear
C) \[{{c}^{2}}\] done clear
D) \[-\,{{c}^{2}}\] done clear
E) None of these done clear
View Answer play_arrowA) \[x=y=z\] done clear
B) \[x=y=-\,z\] done clear
C) \[x=1,\,\,y=2,\,\,z=3\] done clear
D) \[x=2,\text{ }y=4,\text{ }z=6\] done clear
E) None of these done clear
View Answer play_arrowA) 53 : 155 done clear
B) 27 : 77 done clear
C) 29 : 83 done clear
D) 31 : 89 done clear
E) None of these done clear
View Answer play_arrowA) 1, 3, 9 done clear
B) 2, 6, 18 done clear
C) 3, 9, 27 done clear
D) 2, 4, 8 done clear
E) None of these done clear
View Answer play_arrowA) \[\frac{1}{n\,(n+1)}\] done clear
B) \[\frac{n}{n+1}\] done clear
C) \[\frac{2\,n}{n+1}\] done clear
D) \[\frac{2n}{n\,(n+1)}\] done clear
E) None of these done clear
View Answer play_arrowA) No solution done clear
B) One solution done clear
C) Two solutions done clear
D) More than two solutions done clear
E) None of these done clear
View Answer play_arrowA) 0 and 6 done clear
B) 16 and 8 done clear
C) \[-\,16\text{ }and\text{ }0\] done clear
D) 16 and 0 done clear
E) None of these done clear
View Answer play_arrowquestion_answer16) In how many ways can mn letters be posted in n letter-boxes?
A) \[{{(mn)}^{n}}\] done clear
B) \[{{m}^{mn}}\] done clear
C) \[{{n}^{mn}}\] done clear
D) All of these done clear
E) None of these done clear
View Answer play_arrowquestion_answer17) \[{}^{47}{{C}_{4}}+\sum\limits_{r=1}^{5}{^{52-r}}{{C}_{3}}=\]
A) \[{}^{47}{{C}_{6}}\] done clear
B) \[{}^{52}{{C}_{5}}\] done clear
C) \[{}^{52}{{C}_{4}}\] done clear
D) All of these done clear
E) None of these done clear
View Answer play_arrowA) 7 done clear
B) 8 done clear
C) 9 done clear
D) 10 done clear
E) None of these done clear
View Answer play_arrowA) \[(n+2){{2}^{n-1}}\] done clear
B) \[(n+1){{2}^{n}}\] done clear
C) \[(n+1){{2}^{n-1}}\] done clear
D) \[(n+2){{2}^{n}}\] done clear
E) None of these done clear
View Answer play_arrowquestion_answer20) Which of the following relations is possible?
A) \[\sin \theta =\frac{5}{3}\] done clear
B) \[\tan 1125{}^\circ =1\] done clear
C) \[\cos \theta =\frac{1+{{p}^{2}}}{1-{{p}^{2}}},\,\,(P\ne \pm \,1)\] done clear
D) \[\sec \theta =\frac{1}{2}\] done clear
E) None of these done clear
View Answer play_arrowA) 2 done clear
B) 2m done clear
C) 2n done clear
D) mn done clear
E) None of these done clear
View Answer play_arrowA) 1 done clear
B) 3 done clear
C) 2 done clear
D) 4 done clear
E) None of these done clear
View Answer play_arrowA) 1 done clear
B) \[\frac{1}{2}\] done clear
C) \[-\frac{1}{2}\] done clear
D) \[\frac{1}{8}\] done clear
E) None of these done clear
View Answer play_arrowquestion_answer24) Which of the following number(s) is/are rational?
A) \[\sin 15{}^\circ \] done clear
B) \[\cos 15{}^\circ \] done clear
C) \[sin15{}^\circ \cos 15{}^\circ \] done clear
D) \[sin15{}^\circ \cos 75{}^\circ \] done clear
E) None of these done clear
View Answer play_arrowA) 1 : 2 internally done clear
B) 1 : 2 externally done clear
C) 2 : 1 internally done clear
D) 2 : 1 externally done clear
E) None of these done clear
View Answer play_arrowA) \[x-y=5\] done clear
B) \[x+y=5\] done clear
C) \[x+y=\text{1}\] done clear
D) \[xy=\text{1}\] done clear
E) None of these done clear
View Answer play_arrowA) \[x=\frac{1}{4}\] done clear
B) \[y=\frac{1}{4}\] done clear
C) \[y=\frac{1}{2}\] done clear
D) y = 1 done clear
E) None of these done clear
View Answer play_arrowA) \[2{{\tan }^{-1}}\frac{b}{a}\] done clear
B) \[{{\tan }^{-1}}\frac{2ab}{{{a}^{2}}+{{b}^{2}}}\] done clear
C) \[{{\tan }^{-1}}\frac{{{a}^{2}}-{{b}^{2}}}{{{a}^{2}}+{{b}^{2}}}\] done clear
D) \[2{{\tan }^{-1}}\frac{a}{b}\] done clear
E) None of these done clear
View Answer play_arrowquestion_answer29) The equation \[{{y}^{2}}-{{x}^{2}}-2x-1=0\] represents
A) A hyperbola done clear
B) An ellipse done clear
C) A pair of straight lines done clear
D) A rectangular hyperbola done clear
E) None of these done clear
View Answer play_arrowquestion_answer30) Which of the following points lie on the parabola\[{{x}^{2}}=4ay\]?
A) \[x=a{{t}^{2}},\,y=2\,at\] done clear
B) \[x=2\,at,\,y=at\] done clear
C) \[x=2\,a{{t}^{2}},\,y=at\] done clear
D) \[x=2\,at,\,y=a{{t}^{2}}\] done clear
E) None of these done clear
View Answer play_arrowquestion_answer31) The eccentricity of the hyperbola \[5{{x}^{2}}-4{{y}^{2}}+20x+8y=4\] is
A) \[\sqrt{2}\] done clear
B) \[\frac{3}{2}\] done clear
C) \[8\,\sqrt{2}\] done clear
D) \[4\,\sqrt{2}\] done clear
E) None of these done clear
View Answer play_arrowA) \[f\,\left( a \right)+a\,f'\left( a \right)\] done clear
B) \[f\left( a \right)a\text{ }f\left( a \right)\] done clear
C) \[f\left( a \right)\] done clear
D) \[-\text{ }f'\left( a \right)\] done clear
E) None of these done clear
View Answer play_arrowA) 3 done clear
B) 5 done clear
C) 0 done clear
D) \[-\,3\] done clear
E) None of these done clear
View Answer play_arrowA) \[\frac{2}{13}\] done clear
B) \[\frac{1}{169}\] done clear
C) \[\frac{1}{221}\] done clear
D) \[\frac{30}{221}\] done clear
E) None of these done clear
View Answer play_arrowquestion_answer35) If A and Bare two mutually exclusive events, then P (A + B) =
A) \[P\,\,\left( A \right)+P\,\,\left( B \right)-P\,\,\left( AB \right)\] done clear
B) \[P\,\,\left( A \right)-P\,\,\left( B \right)\] done clear
C) \[P\,\,\left( A \right)+P\,\,\left( B \right)\] done clear
D) \[P\,\,\left( A \right)+P\,\,\left( B \right)+P\,\,\left( AB \right)\] done clear
E) None of these done clear
View Answer play_arrowA) Father done clear
B) Sister done clear
C) Grandfather done clear
D) Grandmother done clear
E) None of these done clear
View Answer play_arrowA) 10 km done clear
B) 9 km done clear
C) 8 km done clear
D) 6 km done clear
E) None of these done clear
View Answer play_arrowquestion_answer38) Find the missing character from among the given alternatives.
A) 860 done clear
B) 1140 done clear
C) 2880 done clear
D) 3240 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_answer40) Which of the following sets is best represented in the given diagram?
A) Animals, Insects, Cockroaches done clear
B) Animals, Males, Females and Hermaphrodites done clear
C) States, Districts, Union Territories done clear
D) Country, States, Districts done clear
E) None of these done clear
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