A)
\[-\,1\]
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B)
0
done
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C)
1
done
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D)
2
done
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E)
None of these
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Find the value of k if the points \[A\,\,\left( k+3,\text{k}-1 \right),\] \[B\,\,\left( 2k-3,k-3 \right)\] and \[C\,\,\left( 5k+1,2k \right)\] are collinear.
A)
2
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B)
5
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C)
7
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D)
\[-\,1\]
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E)
None of these
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A)
28
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B)
45
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C)
49
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D)
60
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E)
None of these
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Statement (A): If \[\tan \theta +\cot \theta =2,\] then for all \[n\in N,\]\[ta{{n}^{n}}\theta +{{\cot }^{n}}\theta =2\] Reason (R): For all \[n\in N,\]\[tan\theta +\cot \theta ={{\tan }^{n}}\theta +{{\cot }^{n}}\theta \]
A)
Both A and R are correct and R is the correct explanation of A.
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B)
Both A and R are correct but R is not a correct explanation of A.
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C)
A is correct, R is incorrect.
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D)
A is incorrect, R is correct
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E)
None of these
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Let \[D\,\,\left( 3,-2 \right),\]\[E\,\,\left( -3,\,\,1 \right)\] and \[F\,\,\left( 4,-\,3 \right)\] be the midpoints of the sides BC, CA and AB respectively of\[\Delta \,ABC\]. Find the coordinates of the vertex A of the \[\Delta \]ABC.
A)
\[\left( 10,-\,6 \right)\]
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B)
\[\left( -\,2,0 \right)\]
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C)
\[\left( -\,4,\,\,2 \right)\]
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D)
\[\left( 5,-\,3 \right)\]
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E)
None of these
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A)
5
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B)
\[-\,6\]
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C)
\[-\,8\]
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D)
12
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E)
None of these
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Directions: Basis of the information given below: A punching machine is used to punch a circular hole of diameter two units from a square sheet of aluminium of width 2 units, as shown below. The hole is punched such that the circular hole touches one corner P of the square sheet and the diameter of the hole originating at P is in line with a diagonal of the square.
The proportion of the sheet area that remains after punching is:
A)
\[\frac{(\pi +2)}{8}\]
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B)
\[\frac{(6-\pi )}{8}\]
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C)
\[\frac{(4-\pi )}{4}\]
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D)
\[\frac{(\pi -2)}{4}\]
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E)
None of these
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View Answer play_arrow
Directions: Basis of the information given below: A punching machine is used to punch a circular hole of diameter two units from a square sheet of aluminium of width 2 units, as shown below. The hole is punched such that the circular hole touches one corner P of the square sheet and the diameter of the hole originating at P is in line with a diagonal of the square.
Find the area of the part of the circle (round punch) falling outside the square sheet:
A)
\[\frac{\pi }{4}\]
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B)
\[\frac{(\pi -1)}{2}\]
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C)
\[\frac{(\pi -1)}{4}\]
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D)
\[\frac{(\pi -2)}{2}\]
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E)
None of these
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View Answer play_arrow
A)
\[3\,\sqrt{7\,}cm\]
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B)
\[2\,\sqrt{7\,}cm\]
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C)
\[4\,\sqrt{7\,}cm\]
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D)
\[\sqrt{7\,}cm\]
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E)
None of these
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View Answer play_arrow
A)
\[416.88\,{{m}^{2}}\]
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B)
\[412.69\,{{m}^{2}}\]
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C)
\[418.88\,{{m}^{2}}\]
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D)
\[512.68\,{{m}^{2}}\]
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E)
None of these
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A)
\[46\,c{{m}^{2}}\]
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B)
\[44\,c{{m}^{2}}\]
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C)
\[48\,c{{m}^{2}}\]
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D)
\[42\,c{{m}^{2}}\]
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E)
None of these
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View Answer play_arrow
A)
\[-\,12\,\,and\,\,-6\]
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B)
\[-\,14\,\,and\,\,-4\]
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C)
\[-\,16\,\,and\,\,-2\]
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D)
\[-\,8\,\,and\,\,-4\]
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E)
None of these
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A)
\[65{}^\circ \,and\,\,135{}^\circ \]
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B)
\[85{}^\circ \,and\,\,115{}^\circ \]
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C)
\[55{}^\circ \,and\,\,145{}^\circ \]
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D)
\[75{}^\circ \,and\,\,125{}^\circ \]
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E)
None of these
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View Answer play_arrow
A)
\[1\,\,\frac{10}{17}\]
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B)
\[\frac{10}{17}\]
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C)
\[\frac{16}{27}\]
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D)
\[\frac{17}{27}\]
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E)
None of these
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A)
0
done
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B)
1
done
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C)
2
done
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D)
3
done
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E)
None of these
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A)
\[300\,\sqrt{3\,}m\]
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B)
\[300\,\,(1+\sqrt{3})\,m\]
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C)
\[300\,m\]
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D)
\[500\,\,(1+\sqrt{3})\,m\]
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E)
None of these
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A)
\[q=5,\text{ }a=-\,7\]
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B)
\[q=1,\text{ }a=2\]
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C)
\[q=2,\text{ }a=-\,5\]
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D)
\[q=1,\text{ }a=-\,2\]
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E)
None of these
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View Answer play_arrow
A)
1060 km
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B)
1080 km
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C)
1205 km
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D)
1030 km
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E)
None of these
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View Answer play_arrow
A)
\[\frac{19}{50}\]
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B)
\[\frac{29}{50}\]
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C)
\[\frac{31}{50}\]
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D)
\[\frac{21}{50}\]
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E)
None of these
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View Answer play_arrow
A)
Rs. 40 and Rs. 170
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B)
Rs. 20 and Rs. 160
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C)
Rs. 30 and Rs. 180
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D)
Rs. 50 and Rs. 250
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E)
None of these
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A)
4
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B)
\[\frac{3}{4}\]
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C)
19
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D)
18
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E)
None of these
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A)
14
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B)
16
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C)
12
done
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D)
10
done
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E)
None of these
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View Answer play_arrow
A)
\[\frac{1}{a}+\frac{1}{b}=\frac{1}{c}\]
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B)
\[\frac{1}{b}+\frac{1}{c}=\frac{1}{a}\]
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C)
\[\frac{1}{a}+\frac{1}{c}=\frac{1}{b}\]
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D)
All of these
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E)
None of these
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A)
11th
done
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B)
12th
done
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C)
14th
done
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D)
16th
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E)
None of these
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View Answer play_arrow
A)
\[\frac{4}{z}\,\,(2z-1)\]
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B)
\[\frac{4}{z}\,\,(z+1)\]
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C)
\[\frac{2}{z}\,\,(z+2)\]
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D)
\[\frac{2}{z}\,\,(2z-1)\]
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E)
None of these
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A)
\[\frac{5}{2}\,\,cm\]
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B)
\[\frac{3}{2}\,\,cm\]
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C)
\[\frac{5}{3}\,\,cm\]
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D)
\[\frac{5}{4\,}\,\,cm\]
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E)
None of these
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View Answer play_arrow
A)
9.76 km /hr
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B)
29. 28 m/s
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C)
9.76 m/s
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D)
29.28 km/hr
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E)
None of these
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A)
4
done
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B)
3
done
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C)
2
done
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D)
1
done
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E)
None of these
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View Answer play_arrow
A)
\[5,-\,5\]
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B)
\[-\,5,\text{ }5\]
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C)
\[5,-\,7\]
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D)
\[7,-\,5\]
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E)
None of these
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View Answer play_arrow
A)
\[170.3\,c{{m}^{2}}\]
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B)
\[122.8\,c{{m}^{2}}\]
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C)
\[180.6\,c{{m}^{2}}\]
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D)
\[192.5\,c{{m}^{2}}\]
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E)
None of these
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View Answer play_arrow
A)
39
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B)
40
done
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C)
41
done
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D)
42
done
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E)
None of these
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View Answer play_arrow
A)
daabbc
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B)
bdbcba
done
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C)
adabcd
done
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D)
cdbbca
done
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E)
None of these
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A)
done
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B)
done
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C)
done
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D)
done
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E)
None of these
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View Answer play_arrow
A)
64
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B)
60
done
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C)
58
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D)
56
done
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E)
None of these
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View Answer play_arrow
A)
Only conclusions I and III follows
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B)
Either conclusion II or IV follows
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C)
Only conclusions I, II and III follows
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D)
Either conclusion I or II or III follow
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E)
None of these
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View Answer play_arrow
A)
J15
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B)
K8
done
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C)
K15
done
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D)
L10
done
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E)
None of these
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A)
done
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B)
done
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C)
done
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D)
done
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E)
None of these
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Directions: In each of the following questions a number series is given. After the series below it in the next line a number is given and is followed by (a), (b), (c), (d) and (e). You have to complete the series starting with the given number following the pattern of the given series. Then answer the questions given below it.
\[\begin{matrix} 140, & 68, & 36, & 16, & 10, & 3 \\ 284, & (A) & (B) & (C) & (D) & (E) \\ \end{matrix}\] Which number will come in place of (B)?
A)
38
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B)
72
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C)
84
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D)
91
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E)
None of these
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View Answer play_arrow
Directions: In each of the following questions a number series is given. After the series below it in the next line a number is given and is followed by (a), (b), (c), (d) and (e). You have to complete the series starting with the given number following the pattern of the given series. Then answer the questions given below it.
\[\begin{matrix} 25, & 194, & 73, & 154, & 105, & {} \\ 14, & (A) & (B) & (C) & (D) & {} \\ \end{matrix}\] Which number will come in place of (D)?
A)
143
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B)
84
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C)
102
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D)
94
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E)
None of these
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View Answer play_arrow
Directions: In each of the following questions a number series is given. After the series below it in the next line a number is given and is followed by (a), (b), (c), (d) and (e). You have to complete the series starting with the given number following the pattern of the given series. Then answer the questions given below it.
\[\begin{matrix} 6, & 9, & 18, & 45, & 135 \\ 20, & (\text{A}) & (B) & (C) & (D) \\ \end{matrix}\] Which number will come in place of (C)?
A)
324
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B)
81
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C)
175
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D)
150
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E)
None of these
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View Answer play_arrow
Match the following: (A) The points \[\left( -\,3,0 \right),\] \[\left( 1,-\,3 \right)\] and (4,1) are the vertices of I Equilateral triangle (B) The points (a, a) \[\left( -\,a,-\,a \right)\]\[(-\sqrt{3}a,\sqrt{3}a)\] are the vertices of II Right triangle (C) The points (3,2) \[\left( 2,-\,3 \right)\]and (2,3) are the vertices of III Isosceles right - angled triangle (D) The points\[\left( -\,5,6 \right),\]\[\left( -\,4,-\,2 \right)\]and (7, 5) are the vertices of. IV Scalene triangle
A)
A- I, B-II, C-III, D-IV
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B)
A-II, B-II, C- I, D-IV
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C)
A - III, B - I, C - II, D-IV
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D)
A-III, B-I, C-IV, D-II
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E)
None of these
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A)
\[82.3\,c{{m}^{2}}\]
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B)
\[70.7\,c{{m}^{2}}\]
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C)
\[94.5\,c{{m}^{2}}\]
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D)
\[62.1\,c{{m}^{2}}\]
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E)
None of these
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A)
756
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B)
576
done
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C)
563
done
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D)
257
done
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E)
None of these
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View Answer play_arrow
A)
\[{{f}_{1}}=18\,\,\And \,\,{{f}_{2}}=29\]
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B)
\[{{f}_{1}}=22\,\,\And \,\,{{f}_{2}}=25\]
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C)
\[{{f}_{1}}=14\,\,\And \,\,{{f}_{2}}=33\]
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D)
\[{{f}_{1}}=24\,\,\And \,\,{{f}_{2}}=23\]
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E)
None of these
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View Answer play_arrow
A)
5 m
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B)
7 m
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C)
12 m
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D)
10 m
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E)
None of these
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View Answer play_arrow
A)
\[{{\log }_{3}}4\]
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B)
\[1-{{\log }_{3}}4\]
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C)
\[1-{{\log }_{4}}3\]
done
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D)
\[{{\log }_{4}}3\]
done
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E)
None of these
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View Answer play_arrow
A)
3169
done
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B)
2884
done
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C)
2820
done
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D)
3441
done
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E)
None of these
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View Answer play_arrow
A)
(16, 17)
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B)
(7, 16)
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C)
(25, 16)
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D)
(16, 7)
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E)
None of these
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View Answer play_arrow
A)
\[x=3\]
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B)
\[x=2\]
done
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C)
\[x=\frac{3}{2}\]
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D)
\[x=\frac{2}{3}\]
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E)
None of these
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View Answer play_arrow
A)
\[\frac{{{n}^{3}}\,{{(n+1)}^{3}}+(n+3)}{6}\]
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B)
\[\frac{n\,(n+1)\,\,(3{{n}^{2}}+7n+2)}{12}\]
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C)
\[\frac{n\,(n+1)}{6}\,\,[n\,(n+1)+(2n+1)]\]
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D)
\[\frac{n\,(n+1)}{18}\,\,[6n\,(n+1)+2\,(2n+1)]\]
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E)
None of these
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