If \[\frac{\sqrt{\sqrt{\sqrt{\sqrt{5+{{2}^{x}}}}}}}{{{2}^{x}}-1}=\frac{1}{{{3}^{{}^{7}/{}_{8}}}},\]then find the value of x.
A)
4
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B)
1
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C)
2
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D)
3
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E)
None of these
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\[\sqrt{11+4\sqrt{7}}-\sqrt{8-2\sqrt{7}}\] is equal to ____.
A)
0
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B)
3
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C)
1
done
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D)
\[\sqrt{7}\]
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E)
None of these
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If P and Q are two polynomials of degree 5 and 4, respectively, then find the degree of\[P-Q\].
A)
1
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B)
5
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C)
4
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D)
Cannot be determined
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E)
None of these
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If \[\sqrt{3{{x}^{2}}-4\sqrt{3}{{x}^{2}}-2{{x}^{2}}+4\sqrt{3}x+3}=(a{{x}^{2}}+bx+c),\] then which one of the following is incorrect?
A)
A and B are of different sign
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B)
\[{{b}^{2}}+2\,ac=2\]
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C)
\[2bc=4\sqrt{3}\]
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D)
\[ab=-\,2\sqrt{3}\]
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E)
None of these
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Two circles with centres O and O? and of radii 6 cm and 4 cm touch each other internally. If the perpendicular bisector of line segment OO? meets the bigger circle in M and N, then the length of MN is________.
A)
1 cm
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B)
\[2\,\sqrt{35}\,cm\]
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C)
\[3\,\sqrt{5}\,cm\]
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D)
\[\sqrt{35}cm\]
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E)
None of these
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In the shown figure, PQRS is a trapezium where \[PQ\parallel RS\] and M and N are the mid-points of PR and SQ, respectively. If PQ = 7 cm and RS = 3 cm then the length of MN is _________.
A)
1 cm
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B)
2 cm
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C)
3 cm
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D)
4 cm
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E)
None of these
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Find the area of the shaded region where each circle is of radius 7 cm as shown in the figure.
A)
\[126\,\,c{{m}^{2}}\]
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B)
\[252\,\,c{{m}^{2}}\]
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C)
\[342\,\,c{{m}^{2}}\]
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D)
\[378\,\,c{{m}^{2}}\]
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E)
None of these
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A cylinder is within the cube touching all the vertical faces. A cone is inside the cylinder. If their heights are same with the same base, then the ratio of their volumes is_____. \[\left( Use\,\pi =\frac{22}{7} \right)\]
A)
21 : 33 : 11
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B)
42 : 23 : 11
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C)
42 : 33 : 22
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D)
42 : 33 : 11
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E)
21 : 22 : 11
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The mean of 18 items was found to be 25. On rechecking it was found that two items were wrongly taken as 23 and 20 instead of 26 and 30, respectively. The correct mean is _________.
A)
25.60
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B)
25.32
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C)
25.72
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D)
25.52
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E)
None of these
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A bag contains x white balls, 15 red balls and y black balls. A ball is drawn at random from the bag. If the probability that the drawn ball is white, is \[\frac{4}{15}\] and the probability that the drawn ball is red, is \[\frac{1}{3},\] then the values of x and y are respectively ________.
A)
18, 12
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B)
12, 18
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C)
14, 16
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D)
16, 14
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E)
None of these
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The ratio of the present ages of Mr. Abhimanyu and Mr. Yuvraj is 4 : 3. Which of the following cannot be the ratio of their ages 4 years ago?
A)
3 : 2
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B)
2 : 1
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C)
7 : 8
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D)
10 : 7
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E)
None of these
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If\[\cos ec\theta +\cot \theta =p\], then \[\cos ec\theta \] is equal to:
A)
\[\frac{{{p}^{2}}-1}{2p}\]
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B)
\[\frac{{{p}^{2}}-1}{{{p}^{2}}+1}\]
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C)
\[\frac{{{p}^{2}}+1}{2p}\]
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D)
\[\frac{{{p}^{2}}+1}{{{p}^{2}}-1}\]
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E)
None of these
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If \[\cos ec\theta -\sin \theta =m\] and, \[\sec \theta -\cos \theta \]\[=n\] then _______.
A)
\[{{\left( {{m}^{2}}n \right)}^{\frac{2}{3}}}+{{\left( m{{n}^{2}} \right)}^{\frac{2}{3}}}=1\]
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B)
\[{{\left( {{m}^{2}}{{n}^{2}} \right)}^{\frac{1}{3}}}+{{\left( m{{n}^{2}} \right)}^{\frac{1}{3}}}=1\]
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C)
\[{{\left( m{{n}^{2}} \right)}^{\frac{1}{3}}}+{{\left( {{m}^{2}}{{n}^{2}} \right)}^{\frac{2}{3}}}=1\]
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D)
\[{{\left( {{m}^{2}}{{n}^{2}} \right)}^{\frac{1}{3}}}+{{\left( {{m}^{2}}{{n}^{2}} \right)}^{\frac{1}{3}}}=1\]
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E)
None of these
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Find the ratio in which two milk solutions of milk to water ratio 1 : 3 and 1 : 5 should be mixed to get milk to water ratio of 1 : 4.
A)
1 : 1
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B)
3 : 5
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C)
2 : 3
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D)
3 : 4
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E)
None of these
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Solve for y. \[y=\frac{1}{2-\frac{1}{2-\frac{1}{2-y}}}\]
A)
1
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B)
2
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C)
3
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D)
4
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E)
None of these
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A triangle BAC is right angled at A, if BD = 16 cm, CD = 25 cm then AD=______.
A)
17 cm
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B)
7.5 cm
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C)
18 cm
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D)
20 cm
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E)
None of these
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Pipe A can fill a tank in 20 minutes and pipe B can fill the tank in 50 minutes. Both the pipes can fill at the rate of 14 litres per second. The capacity of the tank (in litres) is _______.
A)
10000 litres
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B)
13200 litres
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C)
12000 litres
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D)
55000 litres
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E)
None of these
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A bag contains 12 balls out of which x are red. If three more red balls are put in the bag, then probability of drawing a red ball becomes twice. Find the value of x.
A)
2
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B)
4
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C)
6
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D)
5
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E)
None of these
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Let \[(k-1)\] be the mid-point and ?m? be the lower class limit of a class in a continuous frequency distribution. The upper class-limit of the class is ________.
A)
\[(k-1)-m\]
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B)
\[(k-1)+m\]
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C)
\[2\,(k-1)-m\]
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D)
\[2\,\,(k+1)-m\]
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E)
None of these
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P, Q and R are on ML, NL and MN of the equilateral triangle MLN, respectively. If MP : PL = NQ : QL = 1 : 2 and G is the centroid of the triangle PQL and S is the mid-point of MN. Find LG : GS.
A)
2 : 3
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B)
4 : 5
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C)
3 : 4
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D)
1 : 3
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E)
None of these
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If \[A=\sqrt{13}-\sqrt{5}\] and \[B=\sqrt{17}-\sqrt{13},\] then ____.
A)
A > B
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B)
B > A
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C)
A = B
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D)
A < 2B
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E)
None of these
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The graph of the linear equation \[3x+5y=-\,5\,\] cuts ________.
A)
\[x-axis\,at\left( \frac{-3}{5},0 \right)\]
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B)
\[y-axis\,at\left( -1,\,0 \right)\]
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C)
\[x-axis\,at\left( \frac{5}{3},\,0 \right)\]
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D)
\[y-axis\,at\left( 0,\,-1 \right)\]
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E)
None of these
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The graph of the equation represented by a straight line which is parallel to the y-axis and is 3 units left from the origin is______.
A)
\[x=3\]
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B)
\[x=\,-\,\,3\]
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C)
\[y=3\]
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D)
\[y=-\,3\]
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E)
None of these
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Solve: \[\frac{7\sqrt{3}}{\sqrt{10}+\sqrt{3}}-\frac{2\sqrt{5}}{\sqrt{6}+\sqrt{5}}-\frac{3\sqrt{2}}{\sqrt{15}+3\sqrt{2}}\]
A)
0
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B)
2
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C)
\[-\,2\]
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D)
\[-\,1\]
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E)
None of these
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In the shown figure, determine the value of x.
A)
60
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B)
15
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C)
20
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D)
30
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E)
None of these
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The area of the triangle formed by the points (0, 1), (0, 7) and (5, 4) is _______.
A)
12 sq units
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B)
15 sq units
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C)
18 sq units
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D)
10 sq units
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E)
None of these
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In a \[\Delta \,PQR,\] right angled at Q, if \[PR-QR=6\,cm\] and \[PQ=12\,cm,\] then which one among the following is true?
A)
\[\text{cosec}\,R=\cot p+\sin \,30{}^\circ \]
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B)
\[\cos \,60{}^\circ =\text{cosec}\,R+\tan p\]
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C)
\[\sec \,\,(90{}^\circ -R)=\cot \,R+\cos \,60{}^\circ \]
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D)
All the above
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E)
None of these
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If \[\sec \theta +\tan \theta =\frac{3}{4},\] then find the value of\[\operatorname{cosec}\theta .\]
A)
\[\frac{25}{24}\]
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B)
\[\frac{25}{12}\]
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C)
\[\frac{25}{7}\]
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D)
\[\frac{12}{25}\]
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E)
None of these
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Two coins are tossed 1000 times and the outcomes are recorded as below:
Number of heads 0 1 2 Frequency 312 320 368
Based on this information, the probability for at most 1 tail is ________.
A)
\[\frac{86}{125}\]
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B)
\[\frac{79}{125}\]
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C)
\[\frac{96}{125}\]
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D)
\[\frac{97}{125}\]
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E)
None of these
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If \[m\cos \theta +n\,\sin \theta =r,\] then find the value of\[{{(m\,\,\sin \theta -n\,\,\cos \theta )}^{2}}\].
A)
\[{{m}^{2}}+{{n}^{2}}-{{r}^{2}}\]
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B)
\[{{r}^{2}}+{{m}^{2}}-{{n}^{2}}\]
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C)
\[{{n}^{2}}+{{r}^{2}}-{{m}^{2}}\]
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D)
\[-\,{{m}^{2}}+{{r}^{2}}-{{n}^{2}}\]
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E)
None of these
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In a certain code, BREAKTHROUGH is written as EAOUHRBRGHKT. How is DISTRIBUTION written in that code?
A)
TISTBUONDIRI
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B)
STTIBUONRIDI
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C)
STTIBUDIONRI
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D)
RISTTIBUDION
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E)
None of these
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P is the brother of Q and R. S is R?s mother. T is P?s father. Which one of the following statements is incorrect?
A)
T is Q?s father
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B)
S is P?s mother
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C)
P is S?s son
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D)
T is R?s husband
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E)
None of these
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A, B, C, D, E and F are sitting around a round table. A is between E and F, E is opposite to D and C is not in either of the neighbouring seats of E. Who is opposite to B?
A)
C
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B)
D
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C)
F
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D)
All of these
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E)
None of these
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How many triangles are there in the given figure?
A)
21
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B)
22
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C)
24
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D)
19
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E)
None of these
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Direction: In the following questions, the symbols @, ©, , % and # are used as the following illustrated meanings. 'p@q' means 'p is neither smaller than nor equal to q'. 'p#q' means 'p is not smaller than q'. 'p©q' means 'p is not greater than q'. ?p%q? means 'p is neither greater than nor equal to q'. means 'p is neither smaller than nor greater than q' In each of the following questions assuming the given statements to be true, find out which of the three conclusions I, II and III given below is/are definitely true.
Statements: , H@E, E©K Conclusions. I. K@H II. K@B III. E%B
A)
Only III
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B)
Only II
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C)
Only I
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D)
Only I and III
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E)
None of these
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View Answer play_arrow
Direction: In the following questions, the symbols @, ©, , % and # are used as the following illustrated meanings. 'p@q' means 'p is neither smaller than nor equal to q'. 'p#q' means 'p is not smaller than q'. 'p©q' means 'p is not greater than q'. ?p%q? means 'p is neither greater than nor equal to q'. means 'p is neither smaller than nor greater than q' In each of the following questions assuming the given statements to be true, find out which of the three conclusions I, II and III given below is/are definitely true.
Statements: M#W, , N@B Conclusions: I. II. N%M III. M@B
A)
Either I or II
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B)
Either I or III
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C)
Either I or II and III
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D)
Only III
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E)
None of these
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View Answer play_arrow
Direction: In the following questions, the symbols @, ©, , % and # are used as the following illustrated meanings. 'p@q' means 'p is neither smaller than nor equal to q'. 'p#q' means 'p is not smaller than q'. 'p©q' means 'p is not greater than q'. ?p%q? means 'p is neither greater than nor equal to q'. means 'p is neither smaller than nor greater than q' In each of the following questions assuming the given statements to be true, find out which of the three conclusions I, II and III given below is/are definitely true.
Statements: M%T, T#J, J@K Conclusions: I. K%T II. M%J III. K©M
A)
Only III
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B)
Only II
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C)
Only I
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D)
Only I and II
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E)
None of these
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Which number indicates married graduates who are doctors?
A)
2
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B)
3
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C)
5
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D)
7
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E)
None of these
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Direction: In each of the following question, which one of the alternative figures will complete the given figure pattern?
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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Direction: In each of the following question, which one of the alternative figures will complete the given figure pattern? Which one of the alternative figures will complete the figure pattern?
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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If \[\frac{{{2}^{3n}}}{64}+\frac{27}{4}{{.2}^{n}}+\frac{{{9.2}^{2n}}}{16}=6832,\] then find the value of n.
A)
3
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B)
4
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C)
5
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D)
6
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E)
None of these
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\[\frac{\sqrt{\sqrt{\sqrt{\sqrt{{{5}^{x-3}}-{{2}^{x-4}}}}}}}{{{\left( {{3}^{x-2}}+{{2}^{x-1}}+8 \right)}^{\frac{3}{2}}}{{.11}^{\frac{-21}{8}}}}=\frac{1}{{{\left( 121 \right)}^{\frac{1}{8}}}},\] then what will be the value of x?
A)
8
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B)
5
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C)
6
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D)
4
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E)
None of these
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In figure shown below X is a point in the interior of square PQRS. PXYZ is also a square. If PZ = 4 cm and SY = 5 cm, then find the length of QY.
A)
12 cm
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B)
11 cm
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C)
13 cm
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D)
14 cm
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E)
None of these
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If \[3\sin \theta .\cos \theta =2-{{\cos }^{2}}\theta ,\] where \[\sin \theta \] is not equal to\[\cos \theta \], then find the value of\[\tan \theta \].
A)
1
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B)
\[\frac{1}{2}\]
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C)
\[\frac{1}{3}\]
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D)
\[\frac{2}{3}\]
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E)
None of these
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If \[\left( a+1 \right)\,\,\left( a+2 \right)\,\,\left( a+3 \right)\,\,\left( a+m \right)+1\] is a perfect square where a and m are any natural numbers, then find the value of \[\left( m+\text{1} \right)\,\,\left( m+2 \right)\,\,\left( m+3 \right)\,\,\left( m+4 \right)\].
A)
3024
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B)
1680
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C)
360
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D)
24
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E)
None of these
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If \[a+b:b+c:c+a=6:7:8\] and \[a+b+c=14,\] then find the value of c.
A)
7
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B)
14
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C)
6
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D)
12
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E)
None of these
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A three digit number was chosen at random. What will be the probability that its hundred's digit, ten's digit and unit's digit are consecutive integers in ascending order and the number is divisible by 6.
A)
\[\frac{1}{450}\]
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B)
\[\frac{7}{900}\]
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C)
\[\frac{1}{100}\]
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D)
\[\frac{1}{225}\]
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E)
None of these
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If \[{{2}^{a}}={{(0.02)}^{b}}=100,\] then find the value of \[\frac{1}{a}-\frac{1}{b}.\]
A)
0
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B)
\[\frac{1}{2}\]
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C)
\[\frac{1}{4}\]
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D)
2
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E)
None of these
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A number when divided by 31 gives remainder 29. If this same number is divided by 62, the remainder will be_______.
A)
either 29 or 60
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B)
either 33 or 58
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C)
only 60
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D)
only 58
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E)
None of these
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Find the number of ways in which 1008 can be resolved as the product of two factors.
A)
12
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B)
15
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C)
13
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D)
16
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E)
None of these
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