Match the following:
(a) \[0.\overline{123}\] (i) An irrational number (b) \[0.23\overline{41}\] (ii) \[\frac{41}{333}\] (c) \[\frac{6}{\sqrt{7}+\sqrt{2}}\] (iii) \[\frac{1159}{4950}\] (d) \[\pi \] (iv) \[\frac{6}{5}\,\,(\sqrt{7}-\sqrt{2})\]
A)
A - (ii), B - (i), C - (iv), D - (iii)
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B)
A - (ii), B - (iii), C - (iv), D - (i)
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C)
A - (iv), B - (iii), C - (ii), D - (i)
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D)
A - (ii), B - (iv), C - (iii), D - (i)
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E)
None of these
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Thomas divides Rs. 6300 equally among certain number of persons. Had there been 20 more persons, each would have got Rs. 20 less. Find the original number of persons.
A)
60
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B)
70
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C)
50
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D)
80
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E)
None of these
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If k is the HCF of 56 and 72 satisfying \[k=56x+72y,\] then the value of x and y are respectively:
A)
2 and 3
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B)
\[4\,\,and\,\,-\,3\]
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C)
\[-\,3\,\,and\,\,2\]
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D)
\[-\,4\,\,and\,\,4\]
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E)
None of these
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If the number 117A49 is completely divisible by 7, then the smallest natural number in place of A will be:
A)
2
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B)
5
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C)
6
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D)
7
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E)
None of these
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Find the factors of \[{{x}^{2}}-{{y}^{2}}+x+y\].
A)
\[(x+y)\,\,and\,\,(x-y-1)\]
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B)
\[(x+y)\,\,and\,\,(x-y+1)\]
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C)
\[(x-y)\,\,and\,\,(x+y+1)\]
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D)
\[(x-y)\,\,and\,\,(x-y-1)\]
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E)
None of these
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In the following figure, \[I\parallel m\]. AC and BC are the bisectors of\[\angle \,ABP\]and\[\angle \,BAQ\]. If\[\angle \,ABP=60{}^\circ \]. Find the value of x.
A)
\[30{}^\circ \]
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B)
\[45{}^\circ \]
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C)
\[90{}^\circ \]
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D)
\[120{}^\circ \]
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E)
None of these
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Find the value of \[{{\alpha }^{2}}+{{\beta }^{2}},\] if a quadratic polynomial \[f(x)=2{{x}^{2}}-mx+n\] has \[\alpha \] and \[\beta \] as its two zeros.
A)
\[\frac{1}{4}\,\,({{m}^{2}}-4n)\]
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B)
\[4\,\,({{m}^{2}}-4n)\]
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C)
\[2\,\,(m-4n)\]
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D)
\[\frac{1}{2}\,\,(m-4n)\]
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E)
None of these
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The sum and the product of zeros of a quardratic polynomial are \[\frac{9}{2}\] and 2 respectively. The quardratic polynomial is:
A)
\[{{x}^{2}}-9x+4\]
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B)
\[2{{x}^{2}}-9x+4\]
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C)
\[{{x}^{2}}+9x+4\]
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D)
\[{{x}^{2}}+9x-2\]
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E)
None of these
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If \[{{\log }_{8}}x=\frac{2}{3},\] find the value of x.
A)
3
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B)
\[-\,4\]
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C)
4
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D)
2
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E)
None of these
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Which one of the following values does not satisfy\[\frac{x}{2}+\frac{y}{4}=15\]?
A)
(30, 0)
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B)
(0, 60)
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C)
(10, 40)
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D)
(20, 15)
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E)
None of these
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The types of solution the pair of linear equation \[5x+6y=7\] and \[8x-9y=7\] have:
A)
Unique solution
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B)
No solution
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C)
Infinitely many solution
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D)
All of these
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E)
None of these
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Amit is two years older than Yogesh who is twice as old as Suresh. If the sum of their ages is 27 years, then how old is Yogesh?
A)
5 years
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B)
6 years
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C)
10 years
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D)
12 years
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E)
None of these
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A number consists of 3 digits whose sum is 10. The middle digit is equal to the sum of the other two and the number increased by 99 if its digits are reversed. The number is:
A)
145
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B)
253
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C)
387
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D)
423
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E)
None of these
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A line segment is drawn between two parallel lines in such a way that its end points lies on the lines as shown in the figure given below. Let R is the mid-point of PQ. If any line segment which passes through R whose end points lies on parallel lines, then:
A)
PR = RU
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B)
TR = RU
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C)
\[\Delta \,PRU\cong \Delta \,QRT\]
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D)
Both (B) and (C)
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E)
None of these
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The perpendicular from the centre of a circle to a chord:
A)
Bisects the chord
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B)
Trisects the chord
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C)
Is equal to the length of the chord
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D)
All of these
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E)
None of these
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ABC is a right-angled triangle right-angled at C and \[AC=\sqrt{3}\,\,BC,\] then \[\angle \,ABC\]is equal to:
A)
\[30{}^\circ \]
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B)
\[45{}^\circ \]
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C)
\[60{}^\circ \]
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D)
\[90{}^\circ \]
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E)
None of these
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ABCD is a rectangle. Its diagonals meet at O. If \[OA=2x+4\] and \[OD=3x+1,\] then the value of x is:
A)
2
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B)
3
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C)
4
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D)
5
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E)
None of these
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The ratio of the corresponding sides of two similar squares is 1 : 4. What is the ratio of the area of the smaller square to the area of the larger square?
A)
1 : 2
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B)
1 : 4
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C)
1 : 8
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D)
1 : 16
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E)
None of these
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A dice is tossed once. What is the probability of the dice coming up with a number 8?
A)
This is an impossible event
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B)
This is a sure event
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C)
Both (A) and (B)
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D)
None of these
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In the figure given below PQRS is a quadrilateral in which\[PQ\parallel RS\]. A line segment ST which passes through the mid-point of QR meeting at point T when PQ produced, then:
A)
\[PT=PQ+SR\]
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B)
\[PS+SR+RQ>PT+ST+PQ\]
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C)
\[\angle \,P+\angle \,Q+\angle \,T+\angle \,S=360{}^\circ \]
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D)
\[PQ+QR=ST\]
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E)
None of these
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The area of a sector of a circle of radius 5 cm, formed by an arc of length 3.5 cm is:
A)
\[7.5\,c{{m}^{2}}\]
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B)
\[7.75\,c{{m}^{2}}\]
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C)
\[8.5\,c{{m}^{2}}\]
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D)
\[8.75\,c{{m}^{2}}\]
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E)
None of these
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The points \[(-\,2,-\,1),(1,\,\,0),(4,\,\,3),(1,\,\,2)\] are vertices of a:
A)
Parallelogram
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B)
Rectangle
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C)
Rhombus
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D)
Square
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E)
None of these
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Find the area of a triangle whose vertices are \[A\,(-\,5,-\,1),\] \[B\,(3,-\,5)\] and \[C\,(5,\,2)\].
A)
34 square units
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B)
32 square units
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C)
40 square units
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D)
46 square units
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E)
None of these
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If the points (k, 2k), (3k, 3k) and (3, 1) are collinear, then the value of k is:
A)
\[\frac{1}{3}\]
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B)
\[\frac{-\,1}{3}\]
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C)
\[\frac{2}{3}\]
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D)
\[\frac{-\,2}{3}\]
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E)
None of these
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A bridge across a river makes an angle of \[45{}^\circ \] with the river bank. If the length of the bridge across the river is 160 m, what is the width of the river?
A)
\[30\,\sqrt{3}\,\,m\]
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B)
\[90\,\sqrt{3}\]
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C)
\[80\,\sqrt{2}\,\,m\]
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D)
\[60\,\sqrt{3}\,\,m\]
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E)
None of these
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The value of \[2{{\sin }^{2}}90{}^\circ +2{{\cos }^{2}}60{}^\circ +2{{\sec }^{2}}45{}^\circ \] is given by:
A)
1
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B)
0
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C)
\[-\,1\]
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D)
\[\frac{13}{2}\]
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E)
None of these
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Two men on either side of a temple 75 m high observe the angles of elevation of the top of the temple to be \[30{}^\circ \] and \[60{}^\circ \] respectively. Find the distance between the two men.
A)
173.2 m
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B)
180.6 m
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C)
190.4 m
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D)
220.4 m
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E)
None of these
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\[\frac{\sin \theta -2si{{n}^{3}}\theta }{2\,{{\cos }^{3}}\theta -\cos \theta }\] can be reduced to:
A)
\[\sin \theta \]
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B)
\[\cos \theta \]
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C)
\[\tan \theta \]
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D)
\[\cot \theta \]
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E)
None of these
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A cone is 8.4 cm high and the radius of its base is 2.1 cm. It is melted and recast into a sphere. Find the radius of the sphere.
A)
5 cm
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B)
10 cm
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C)
8.5 cm
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D)
2.1 cm
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E)
None of these
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A toy is in the form of a cone mounted on a hemisphere of radius 3.5 cm. The total height of the toy is 15.5 cm. Find the total surface area of the toy.
A)
\[112.8\,\,c{{m}^{2}}\]
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B)
\[214\,\,c{{m}^{2}}\]
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C)
\[316.4\,\,c{{m}^{2}}\]
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D)
\[408.5\,\,c{{m}^{2}}\]
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E)
None of these
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A bag contains 7 black, 5 red and 3 white balls. A ball is drawn from the bag at random. Find the probability that the ball drawn is red.
A)
\[\frac{1}{3}\]
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B)
\[\frac{1}{2}\]
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C)
\[\frac{1}{5}\]
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D)
\[\frac{1}{4}\]
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E)
None of these
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Find the mean of the following frequency distribution.
Class interval 25-29 30-34 35-39 40-44 45-49 50-54 55-59 Frequency 14 22 16 6 5 3 4
A)
38.46
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B)
36.36
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C)
48.56
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D)
99.95
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E)
None of these
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The mean of the following frequency distribution is 57.6 and the sum of the observation is 50. Find the missing frequencies of \[{{f}_{1}}\] and \[{{f}_{2}}\].
Class interval 0-20 20-40 40-60 60-80 80-100 100-120 Frequency 7 \[{{f}_{1}}\] 12 \[{{f}_{2}}\] 8 5
A)
\[{{f}_{1}}=80\,\,and\,\,{{f}_{2}}=20\]
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B)
\[{{f}_{1}}=4\,\,and\,\,{{f}_{2}}=1\]
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C)
\[{{f}_{1}}=8\,\,and\,\,{{f}_{2}}=10\]
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D)
\[{{f}_{1}}=18\,\,and\,\,{{f}_{2}}=20\]
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E)
None of these
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The formula to calculate the median for grouped data is given below. What does letter I represent? \[{{M}_{e}}=I+\left\{ h\times \left( \frac{\frac{N}{2}-c}{f} \right) \right\}\]
A)
Lower limit of the median class
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B)
Cumulative frequency of the class preceding the median class.
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C)
Class size
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D)
All of these
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E)
None of these
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Which of the following formula is correct for the computation of mode for a continuous frequency distribution?
A)
\[I+\frac{f-{{f}_{1}}}{2f-{{f}_{1}}-{{f}_{2}}}\times h\]
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B)
\[I-\frac{f-{{f}_{1}}}{2f-{{f}_{1}}-{{f}_{2}}}\times h\]
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C)
\[I-\frac{f-{{f}_{1}}}{{{f}_{1}}+{{f}_{2}}}\times h\]
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D)
\[I+\frac{f-{{f}_{1}}}{f-{{f}_{2}}}\times h\]
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E)
None of these
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Find the value of: \[\frac{15}{5+\sqrt{2}}+\frac{16}{5-\sqrt{2}}\]
A)
\[\frac{155-\sqrt{2}}{23}\]
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B)
\[\frac{155+\sqrt{2}}{23}\]
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C)
\[\frac{155+\sqrt{3}}{23}\]
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D)
\[\frac{5-\sqrt{2}}{23}\]
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E)
None of these
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Robert tosses a coin three times. The probability that he gets atleast two heads is:
A)
\[\frac{1}{2}\]
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B)
\[\frac{1}{3}\]
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C)
\[\frac{1}{4}\]
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D)
\[\frac{1}{5}\]
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E)
None of these
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A number from 1 to 11 is chosen at random. What is the probability of choosing an odd number?
A)
\[\frac{6}{11}\]
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B)
\[\frac{5}{11}\]
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C)
\[\frac{4}{11}\]
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D)
\[\frac{3}{11}\]
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E)
None of these
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If \[\frac{x}{y}=\frac{4}{5},\] then \[\frac{8}{9}+\frac{y-x}{y+x}\] is equal to:
A)
0
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B)
1
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C)
\[-1\]
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D)
4
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E)
None of these
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If \[{{I}_{1}}\parallel {{I}_{2}}\] and \[{{I}_{3}}\parallel {{I}_{4}},\] then value of z in terms of \['\theta '\] is:
A)
\[\frac{\theta }{2}\]
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B)
\[90{}^\circ +\theta \]
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C)
\[90{}^\circ +\frac{\theta }{2}\]
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D)
\[90{}^\circ -\frac{\theta }{2}\]
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E)
None of these
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