Which one of the following statements is false?
A)
The product of three consecutive integers is divisible by 2
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B)
The product of three consecutive integers is divisible by 3
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C)
The product of three consecutive even integers is divisible by 4
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D)
The product of three consecutive integers is divisible by 5
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E)
None of these
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Find the greatest number which divides 1531 and 1222 leaving remainder 1 and 7 respectively.
A)
45
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B)
35
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C)
55
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D)
90
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E)
None of these
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If polynomials \[(2{{a}^{3}}+p{{a}^{2}}+3a-5)\] and \[({{a}^{3}}+{{a}^{2}}-2a+p)\] on dividing by \[(a-2)\] leaves the same remainder, then the value of p will be:
A)
\[-\,3\]
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B)
0
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C)
\[-\,2\]
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D)
2
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E)
None of these
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Write the value of\[{{2}^{{{\log }_{2}}5}}\].
A)
5
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B)
1
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C)
0
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D)
2
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E)
None of these
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The centroid of a triangle whose vertices are \[(-\,1,\,0),\]\[\,(6,\,-\,6)\] and \[(-\,2,\,3)\] is:
A)
(5, 0)
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B)
\[(1,\,-\,1)\]
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C)
\[(-\,3,\text{ }3)\]
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D)
(4, 3)
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E)
None of these
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One card is drawn from a well shuffled deck of 52 cards. What is the probability of getting a red card?
A)
\[\frac{1}{4}\]
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B)
\[\frac{1}{52}\]
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C)
\[\frac{1}{2}\]
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D)
\[\frac{1}{26}\]
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E)
None of these
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For any acute angle\[\theta \], which one of the following relation is incorrect?
A)
\[\tan \theta =\frac{\sin \theta }{\cos \theta }\]
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B)
\[{{\sec }^{2}}q-{{\tan }^{2}}q=1\]
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C)
\[\tan q\cot q=1\]
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D)
\[\sec q\tan q=1\]
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E)
None of these
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When \[(4{{a}^{3}}+4{{a}^{2}}-a-1)\] is divided by \[(2a+1),\] the remainder will be:
A)
2
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B)
\[-1\]
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C)
1
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D)
0
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E)
None of these
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If \[x+y=2,\]then the value of \[{{x}^{3}}+6xy+{{y}^{3}}-8\]is equal to:
A)
1
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B)
0
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C)
3
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D)
5
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E)
None of these
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Factorise: \[{{(a-b)}^{3}}+{{(b-c)}^{3}}+{{(c-a)}^{3}}\]
A)
\[3\,(a+b)\,\,(b+c)\,\,(c-a)\]
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B)
\[3\,(a-b)\,\,(b-c)\,\,(c+a)\]
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C)
\[3\,(a-b)\,\,(b+c)\,\,(c+a)\]
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D)
\[3\,\,(a-b)\,\,(b-c)\,\,(c-a)\]
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E)
None of these
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Each side of an equilateral triangle measures 10 cm. Calculate the height of the triangle. \[(Take\sqrt{3}=1.732)\]
A)
18.65 cm
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B)
8.66 cm
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C)
10.64 cm
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D)
16.85 cm
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E)
None of these
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Which one of the following is the condition for infinitely many solutions?
A)
\[{{a}_{1}}{{a}_{2}}={{b}_{1}}{{b}_{2}}\]
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B)
\[\frac{{{a}_{1}}}{{{a}_{2}}}\ne \frac{{{b}_{1}}}{{{b}_{2}}}\]
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C)
\[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{b}_{1}}}{{{b}_{2}}}\ne \frac{{{c}_{1}}}{{{c}_{2}}}\]
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D)
\[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{b}_{1}}}{{{b}_{2}}}=\frac{{{c}_{1}}}{{{c}_{2}}}\]
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E)
None of these
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The sum of a two digit number and the number formed by interchanging the digits is 143. The number becomes 6 times the sum of digits if 11 is added to the number. Find the number.
A)
76
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B)
67
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C)
35
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D)
87
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E)
None of these
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Consider the following statements:
1. Product of two irrational number is an irrational number 2. Product of any two rational numbers is a rational number 3. Product of any two natural numbers is a natural number Which of the above statements are correct?
A)
1 and 2
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B)
2 and 3
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C)
1 and 3
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D)
1, 2 and 3
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E)
None of these
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\[{{\log }_{2}}8+{{\log }_{4}}8+{{\log }_{16}}8\] equals:
A)
\[\frac{21}{4}\]
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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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The inner diameter of a glass is 7 cm and it has a raised portion at the bottom in the shape of a hemisphere as shown in the figure. If the height of the glass is 16 cm then find the apparent capacity of the glass. \[\left[ Take\,\pi \,=\,\frac{22}{7} \right]\]
A)
\[484.33\,c{{m}^{3}}\]
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B)
\[616.00\,c{{m}^{3}}\]
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C)
\[526.67c{{m}^{3}}\]
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D)
\[632.20\,c{{m}^{3}}\]
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E)
None of these
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The cars shown on the graph below are moving towards each other at the same speed and on a straight line. The cars start from points \[A(-\,2,\,5)\] and\[B\,(8,\,-5)\]. How far will each car move before they collide, if each grid on the graph represents a square of side 5 km?
A)
38.35 km
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B)
25.35 km
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C)
35.35 km
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D)
43.35 km
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E)
None of these
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In the figure given below perimeter and length of two sides of a triangle are 42 cm, 12 cm and 14 cm respectively. Find the length of the third side.
A)
16 cm
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B)
10 cm
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C)
12 cm
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D)
9 cm
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E)
None of these
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In the given figure find the value of y if\[\angle \,AOC=120{}^\circ \].
A)
\[135{}^\circ \]
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B)
\[45{}^\circ \]
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C)
\[120{}^\circ \]
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D)
\[115{}^\circ \]
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E)
None of these
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The mean of 30 observations was found to be 45. Later on, it was detected that a number 46 was misread as 76. Find the correct mean of the given numbers.
A)
43
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B)
46
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C)
42
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D)
44
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E)
None of these
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A bag contains 5 red, 2 black and 3 white balls. One ball is drawn at random. What is the probability that the ball drawn is green?
A)
\[\frac{2}{15}\]
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B)
\[\frac{13}{15}\]
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C)
\[\frac{8}{15}\]
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D)
0
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E)
None of these
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In the figure given below\[KN\parallel LM\]. Find the value of x.
A)
5
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B)
7
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C)
9
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D)
11
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E)
None of these
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The diagonals PR and QS of a parallelogram PQRS intersect each other at the point O. If \[\angle \,SPR=32{}^\circ \] and \[\angle \,POQ=70{}^\circ ,\], then find the value of\[\angle SQR\].
A)
\[24{}^\circ \]
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B)
\[32{}^\circ \]
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C)
\[38{}^\circ \]
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D)
\[86{}^\circ \]
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E)
None of these
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If \[{{10}^{x}}={{x}^{50}},\] then x is equal to:
A)
100
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B)
200
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C)
\[\sqrt{10}\]
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D)
\[\sqrt{15}\]
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E)
None of these
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If \[\text{cosec}\theta -\cot \theta =a,\] then the value of \[\cot \theta \] is:
A)
\[\frac{a-1}{2a}\]
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B)
\[\frac{1-{{a}^{2}}}{2a}\]
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C)
\[{{a}^{2}}-1\]
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D)
\[\frac{{{a}^{2}}-1}{{{a}^{2}}+1}\]
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E)
None of these
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The value of \[2\,({{\cot }^{2}}45{}^\circ +{{\sec }^{2}}30{}^\circ )\]\[-\,6\,({{\tan }^{2}}45{}^\circ -\cos e{{c}^{2}}60{}^\circ )\] is:
A)
\[\frac{4}{7}\]
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B)
\[\frac{20}{3}\]
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C)
\[\frac{3}{20}\]
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D)
\[\frac{1}{3}\]
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E)
None of these
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The minute hand of a clock is \[\frac{x}{2}cm\] long. Find the area of the face of the clock described by the minute hand in 35 minutes.
A)
\[\frac{11{{x}^{2}}}{24}\]
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B)
\[\frac{7{{x}^{2}}}{24}\]
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C)
\[\frac{5{{x}^{2}}}{24}\]
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D)
\[\frac{13{{x}^{2}}}{24}\]
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E)
None of these
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Find the mean of the following data:
Class Interval Frequency 0 - 10 7 10 - 20 8 20 - 30 12 30 - 40 13 40 - 50 10
A)
25.60
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B)
24.80
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C)
23.30
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D)
27.20
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E)
None of these
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Find the value of \[{{f}_{2}}\] in the following frequency distribution table, if N = 100, median is 33.75 and median class is 30 - 40.
Marks 0-10 10-20 20-30 30-40 40-50 50-60 Total No. of Student 10 \[{{f}_{1}}\] 15 \[{{f}_{2}}\] 30 10 100
A)
16
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B)
13
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C)
14
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D)
15
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E)
None of these
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Simplify:\[\left( \frac{\sqrt{3}-1}{\sqrt{3}+1}+\frac{\sqrt{3}+1}{\sqrt{3}-1} \right)\]
A)
\[2-\sqrt{3}\]
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B)
\[2+\sqrt{3}\]
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C)
4
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D)
2
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E)
None of these
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In a trapezium ABCD shown below, \[AB\parallel CD.\]If the diagonal AC and BD intersect at point O, then find the ratio of areas of \[\Delta \,AOB\] and\[\Delta \,COD,\] where OA = 15 cm and OC = 12 cm.
A)
\[\frac{16}{25}\]
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B)
\[\frac{36}{48}\]
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C)
\[\frac{25}{16}\]
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D)
\[\frac{5}{16}\]
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E)
None of these
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In the figure given below find the measure of angle y.
A)
\[150{}^\circ \]
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B)
\[90{}^\circ \]
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C)
\[100{}^\circ \]
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D)
\[110{}^\circ \]
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E)
None of these
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If the coordinates of the mid-points of the sides of a triangle are (1, 1), (2, 3) and (3, 4), then its centroid will be:
A)
\[\left( \frac{8}{3},2 \right)\]
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B)
\[\left( \frac{-\,8}{3},-\,2 \right)\]
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C)
\[\left( 2,\frac{8}{3} \right)\]
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D)
\[\left( -\,2,\frac{-\,8}{3} \right)\]
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E)
None of these
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A carton contains 44 bulbs out of which 2 are defective and others are good. Peter will buy one bulb if it is good, but will not buy if it is defective. The shopkeeper draws one bulb at random and gives it to him. The probability that he will not buy it is:
A)
\[\frac{19}{22}\]
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B)
\[\frac{1}{22}\]
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C)
\[\frac{13}{22}\]
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D)
\[\frac{15}{22}\]
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E)
None of these
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If the mode of the following data is 36 and the modal class is 30-40, then find the value of missing frequency.
Class Interval 0-10 10-20 20-30 30-40 40-50 50-60 60-70 Frequency 8 10 f 16 12 6 7
A)
9
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B)
10
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C)
12
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D)
15
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E)
None of these
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In the following figure, S, T and U are the mid points of PQ, PR and QR respectively. If the line joining QT and RS intersect SU and TU at L and M respectively, then LM is:
A)
\[\frac{1}{16}\,QR\]
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B)
\[\frac{1}{4}\,QR\]
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C)
\[\frac{1}{2}\,QR\]
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D)
\[\frac{1}{8}\,QR\]
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E)
None of these
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A conical vessel is lying on a table with its base downwards. The capacity of the vessel is 500 litre and its vertical height is 150 cm. If 244 litre of water is put in the vessel, then what is the height of the water level in the conical vessel above the table?
A)
25 cm
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B)
30 cm
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C)
35 cm
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D)
40 cm
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E)
None of these
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A right circular cylinder and a right circular cone have equal bases and equal volumes. But the lateral surface area of the right circular cone is 15/8 times the lateral surface area of the right circular cylinder. What is the ratio of radius to height of the cylinder?
A)
3 : 4
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B)
9 : 4
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C)
15 : 8
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D)
8 : 15
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E)
None of these
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On increasing the radius of a cylinder by 6 units, the volume increases by x cubic units. On increasing the altitude of the cylinder by 6 units, the volume also increases by x cubic units. If the original altitude is 2 units, what is the original radius?
A)
2 units
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B)
4 units
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C)
6 units
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D)
8 units
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E)
None of these
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In the figure given below the height of two poles are 10 metre and 15 metre. If the poles are 30 metre apart then the height of point of intersection of the lines joining the top of each pole from opposite foot of the other pole is:
A)
18 m
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B)
8 m
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C)
6 m
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D)
9 m
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E)
None of these
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