Express \[0.25\overline{62}\] in the form\[\frac{m}{n}\].
A)
\[\frac{2537}{9900}\]
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B)
\[\frac{2437}{9800}\]
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C)
\[\frac{9900}{2537}\]
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D)
\[\frac{9900}{-\,2537}\]
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E)
None of these
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Which one of the following is irrational number?
A)
\[-\,\sqrt{0.64}\]
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B)
\[(\sqrt{5}+1)(\sqrt{5}-1)\]
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C)
\[\sqrt{100}\]
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D)
\[\sqrt{\frac{9}{27}}\]
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E)
None of these
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If \[2a-9=b+a,\] then the value of \[\left( \left| a-b \right|+\left| b-a \right| \right)\] is:
A)
18
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B)
11
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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 \[\left( {{x}^{4}}+\frac{1}{{{x}^{4}}} \right)=34,\] then the value of \[\left( x-\frac{1}{x} \right)\] is:
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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The three numbers are in the ratio 1 : 2 : 3 and their HCF is 12. These numbers are :
A)
4, 8, 12
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B)
5, 10, 15
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C)
24, 48, 72
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D)
12, 24, 36
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E)
None of these
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The value of the expression \[\frac{{{4}^{n}}\times {{20}^{m-1}}\times {{12}^{m-n}}\times {{15}^{m+n-2}}}{{{16}^{m}}\times {{5}^{2m+n}}\times {{9}^{m-1}}}\] is :
A)
500
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B)
1
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C)
200
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D)
\[\frac{1}{500}\]
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E)
None of these
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Find the length of the longest rod that can be placed in a room 16 m long, 12 m broad and \[10\,\,\frac{2}{3}\] m high.
A)
\[22\,\,\frac{1}{3}\,\,m\]
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B)
\[22\,\,\frac{2}{3}\,\,\,m\]
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C)
23 m
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D)
68 m
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E)
None of these
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If m, n are the positive integers (n > 1) such that\[{{m}^{n}}=121\], then value of \[{{(m-1)}^{n+1}}\] is:
A)
12321
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B)
1
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C)
1000
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D)
11
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E)
None of these
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Which of the following is/are correct?
(i) \[{{a}^{x+y}}=ax+ay\] (ii) \[{{({{a}^{x}})}^{y}}=y{{a}^{x}}\] (iii) \[a\,(x.y)=ax.ay\] (iv) \[\frac{{{a}^{x}}}{{{a}^{y}}}={{a}^{x-y}}\]
A)
(i) Only
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B)
(ii) & (iii) only
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C)
(iv) only
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D)
All of these
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E)
None of these
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Which one of the following sets of surds is in correct sequence of ascending order of their values?
A)
\[\sqrt[4]{10},\sqrt[3]{6},\sqrt[{}]{3}\]
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B)
\[\sqrt{3},\sqrt[4]{10},\sqrt[3]{6}\]
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C)
\[\sqrt{3},\sqrt[3]{6},\sqrt[4]{10}\]
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D)
\[\sqrt[4]{10},\sqrt{3},\sqrt[3]{6}\]
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E)
None of these
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Which one of the following statement is not correct:
A)
Every integer is a rational number
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B)
Every natural number is an integer
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C)
Every natural number is real number
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D)
Every real number is a rational number
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E)
None of these
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If \[\left( \sqrt{a}+\sqrt{b} \right)=17\] and \[\left( \sqrt{a}-\sqrt{b} \right)=1,\] then the value of \[\sqrt{ab}\]is :
A)
12
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B)
27
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C)
35
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D)
72
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E)
None of these
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The numerator of a fraction is 4 less than its denominator. If the numerator is decreased by 2 and the denominator is increased by 1, then the denominator is eight times the numerator. Find the fraction.
A)
\[\frac{2}{7}\]
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B)
\[\frac{3}{7}\]
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C)
\[\frac{4}{8}\]
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D)
\[\frac{3}{8}\]
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E)
None of these
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Five years ago, A was three times as old as B and ten years later, A shall be twice as old as B. What are the present ages of A and B (in years)?
A)
45, 15
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B)
30, 40
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C)
50, 30
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D)
50, 20
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E)
None of these
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The value of \[{{\log }_{\sqrt{6}}}216\] is:
A)
\[\frac{1}{6}\]
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B)
\[\sqrt{6}\]
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C)
3
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D)
6
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E)
None of these
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Find the value of k for which the given polynomial \[({{x}^{4}}-{{x}^{3}}+11{{x}^{2}}-x+k)\] is divisible by \[(x-3)\].
A)
35
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B)
150
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C)
\[-150\]
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D)
\[-\,35\]
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E)
None of these
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Find the remainder where \[2{{x}^{4}}-6{{x}^{3}}+3{{x}^{2}}+3x-2\] is divided by\[{{x}^{2}}-3x+2\].
A)
\[-\,3\]
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B)
0
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C)
1
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D)
3
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E)
None of these
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If \[{{\log }_{x}}4=\frac{1}{4},\] then x is equal to :
A)
16
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B)
64
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C)
128
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D)
256
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E)
None of these
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Which one of the following system of linear equations has unique solution?
A)
\[x-2y+14=0\,\,\,and\,\,\,3x-6y+42=0\]
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B)
\[x-2y+14=0\,\,\,and\,\,\,3x-4y+42=0\]
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C)
\[x-2y+14=0\,\,\,and\,\,\,x-2y+18=0\]
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D)
\[x-2y+14=0\,\,\,and\,\,\,4x-8y+52=0\]
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E)
None of these
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The difference between altitude and base of a right angled triangle is 17 cm and its hypotenuse is 25 cm. What is the sum of the base and altitude of the triangle?
A)
24 cm
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B)
31 cm
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C)
34 cm
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D)
Can't be determine
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E)
None of these
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In the triangle ABC, side BC is produced to D. \[\angle \,ACD=100{}^\circ \] if \[BC=AC,\] then \[\angle \,ABC\] is:
A)
\[40{}^\circ \]
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B)
\[50{}^\circ \]
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C)
\[80{}^\circ \]
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D)
Can't be determine
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E)
None of these
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In the given figure, AB = BC and \[\angle BAC=15{}^\circ \], AB = 10 cm. Find the area of\[\Delta ABC\].
A)
\[50\,c{{m}^{2}}\]
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B)
\[40\,c{{m}^{2}}\]
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C)
\[25\,c{{m}^{2}}\]
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D)
\[32\,c{{m}^{2}}\]
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E)
None of these
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The measures of the angles of a quadrilateral taken in order are proportional to 1 : 2 : 3 : 4, then the quadrilateral is:
A)
Parallelogram
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B)
Trapezium
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C)
Rectangle
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D)
rhombus
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E)
None of these
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Diagonals of a parallelogram are 8 cm and 6 cm respectively. If one side is 5 cm, then the area of parallelogram is:
A)
\[18\,c{{m}^{2}}\]
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B)
\[30\,c{{m}^{2}}\]
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C)
\[24\,c{{m}^{2}}\]
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D)
\[48\,c{{m}^{2}}\]
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E)
None of these
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Area of quadrilateral ACDE is \[36\,c{{m}^{2}},\] B is the mid-point of AC. Find the area of \[\Delta \,ABE\] if \[AC\parallel DE\] and \[BE\parallel DC.\]
A)
\[10\,c{{m}^{2}}\]
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B)
\[9\,c{{m}^{2}}\]
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C)
\[12\,c{{m}^{2}}\]
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D)
\[24\,c{{m}^{2}}\]
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E)
None of these
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If each interior angle of a regular polygon is 3 times its exterior angle, the number of sides of the polygon is:
A)
4
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B)
5
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C)
6
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D)
8
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E)
None of these
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In the given figure the two chords AC and BC are equal. The radius OC intersect, AB at M, then AM : BM is:
A)
1 : 1
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B)
\[\sqrt{2}\,:\,3\]
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C)
\[3\,:\,\sqrt{2}\]
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D)
\[2\,:\,\sqrt{2}\]
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E)
None of these
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DABC and DDBC have a common base and drawn towards one side.\[\angle \,BAC=\angle \,BDC=90{}^\circ \]. If AC and DB intersect at P, then:
A)
\[AP\times PC=BP\times PD\]
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B)
\[AP\times BP=PC\times PD\]
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C)
\[AP\times PD=PC\times BP\]
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D)
All of these
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E)
None of these
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In the given figure, ABCD is a cyclic quadrilateral and diagonals bisect each other at P. If \[\angle \,DBC=60{}^\circ \] and \[\angle \,BAC=30{}^\circ ,\] then \[\angle \,BCD\] is:
A)
\[90{}^\circ \]
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B)
\[80{}^\circ \]
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C)
\[60{}^\circ \]
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D)
\[45{}^\circ \]
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E)
None of these
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Find the total number of prime factors in \[{{2}^{17}}\times {{6}^{31}}\times {{7}^{5}}\times {{10}^{11}}\times {{11}^{10}}\times {{(323)}^{23}}\]:
A)
162
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B)
161
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C)
346
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D)
97
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E)
None of these
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Direction: \[p*q={{p}^{2}}-{{q}^{2}}\] \[p\,\$\,q={{p}^{2}}+{{q}^{2}}\] \[pq=pq+p+q\] \[p\Delta q=\text{Remainder}\,of\,\,\frac{p}{q}\] p © q = greatest integers less than or equal to \[\frac{p}{q}\]
If p = 11 and q = 7, then the value of \[(p*q)\,\,\,\,(p\$q)\] is:
A)
14641
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B)
12482
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C)
12243
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D)
12458
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E)
None of these
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Direction: \[p*q={{p}^{2}}-{{q}^{2}}\] \[p\,\$\,q={{p}^{2}}+{{q}^{2}}\] \[pq=pq+p+q\] \[p\Delta q=\text{Remainder}\,of\,\,\frac{p}{q}\] p © q = greatest integers less than or equal to \[\frac{p}{q}\]
If p = 8 and q = 10, then the value of\[[(p\$q)\,\,\Delta\,\,(pq)]*[(q*p)\,\,\,\,(qp)]\] is:
A)
5329
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B)
5239
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C)
12100
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D)
\[-973\]
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E)
None of these
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Direction: \[p*q={{p}^{2}}-{{q}^{2}}\] \[p\,\$\,q={{p}^{2}}+{{q}^{2}}\] \[pq=pq+p+q\] \[p\Delta q=\text{Remainder}\,of\,\,\frac{p}{q}\] p © q = greatest integers less than or equal to \[\frac{p}{q}\]
If p = 15 and q = 25, then the value of the expression \[[(qp)(p\$q)]\,\,[(q*p)\,\,\Delta\,\,(p\$q)]\] is:
A)
4
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B)
5
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C)
101
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D)
6
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E)
None of these
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The sides of a triangle are 3 cm, 4 cm and 5 cm. The area \[(in\,\,c{{m}^{2}})\] of the triangle formed by joining the mid-points of the sides of this triangle is:
A)
\[\frac{3}{4}\]
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B)
\[\frac{3}{2}\]
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C)
3
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D)
6
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E)
None of these
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If the height of a triangle is decreased by 40 % and its base is increased by 40 %, what will be the effect on its area?
A)
No change
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B)
8 % decrease
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C)
16 % decrease
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D)
16 % increase
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E)
None of these
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Four equal sized maximum circular plates are cut off from a square paper sheet of area \[784\,c{{m}^{2}}\]. The circumference of each plate is:
A)
22 cm
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B)
44 cm
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C)
66 cm
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D)
88 cm
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E)
None of these
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If \[\frac{{{9}^{n}}\times {{3}^{2}}\times {{({{3}^{-n/2}})}^{-2}}-{{(27)}^{n}}}{{{3}^{3m}}\times {{2}^{3}}}=\frac{1}{27},\] then the value of \[(m-n)\] is:
A)
\[-\,1\]
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B)
1
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C)
2
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D)
\[-\,2\]
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E)
None of these
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If a right circular cone of height 24 cm has a volume of \[1232\,\,c{{m}^{3}}\], then the area of its curved surface is:
A)
\[154\,c{{m}^{2}}\]
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B)
\[550\,c{{m}^{2}}\]
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C)
\[704\,c{{m}^{2}}\]
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D)
\[1254\,c{{m}^{2}}\]
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E)
None of these
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A card is drawn at random from a well-shuffled pack of 52 cards. Find the probability that the card drawn is neither a red card nor a queen.
A)
\[\frac{1}{2}\]
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B)
\[\frac{6}{13}\]
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C)
\[\frac{23}{52}\]
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D)
\[\frac{5}{16}\]
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E)
None of these
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Which of the following interchange of signs would make the equation correct? \[49-7+7=14\]
A)
\[\div \,\,and\,\,-\]
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B)
\[+\,\,and\,\,-\]
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C)
\[-\,\,and\,\,\div \]
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D)
\[-\,\,and\,\,+\]
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E)
None of these
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