If \[A=(5\sqrt{2}+6\sqrt{3})(4\sqrt{2}-5\sqrt{3})\] & \[B=(7\sqrt{2}+5\sqrt{3})(8\sqrt{2}-5\sqrt{3})\] then find the value of A + B.
A)
\[4\sqrt{6}-13\]
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B)
\[7\sqrt{6}-13\]
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C)
\[5\sqrt{6}-13\]
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D)
\[3\sqrt{6}-13\]
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E)
None of these
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Find the product of \[(a+b-c)\] \[({{a}^{2}}+{{b}^{2}}+{{c}^{2}}-ab+bc+ca)\].
A)
\[{{a}^{3}}+{{b}^{3}}+{{c}^{3}}-ab+bc+ca\]
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B)
\[{{a}^{3}}+{{b}^{3}}+{{c}^{3}}+3abc\]
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C)
\[{{a}^{3}}+{{b}^{3}}-{{c}^{3}}+3abc\]
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D)
\[{{a}^{3}}-{{b}^{3}}-{{c}^{3}}+3abc\]
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E)
None of these
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The exponential form of \[{{\log }_{10}}\]\[(0.001)=-3\] is:
A)
\[{{(-3)}^{10}}=0.001\]
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B)
\[({{10}^{-3}})=0.001\]
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C)
\[({{0.001}^{-3}})=10\]
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D)
\[{{(0.01)}^{-2}}=1\]
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E)
None of these
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The area bounded by y-axis, \[x+y=1\]and \[x-y=1\]is:
A)
7.5 square units
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B)
13.5 square units
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C)
1 square unit
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D)
75 square units
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E)
None of these
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In a triangle DEF, G and H are points on sides DE and DF respectively. If DF = 5.6 cm and\[\frac{DG}{GE}=1\], then the value of HF is equal to:
A)
2.80cm
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B)
3.36cm
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C)
3.35cm
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D)
2.24cm
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E)
None of these
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Read the statements given below : Statement 1: In a trapezium adjacent sides are parallel Statement 2: In a trapezium one pair of opposite sides are parallel Statement 3: The line joining the mid points of the diagonal is parallel to the parallel sides and equal to half of their difference Which one of the following options represent the correct statements?
A)
Statement 1 and 2 are true whereas statement 3 is false
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B)
Statement 1 and 3 are false whereas statement 2 is true
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C)
Statement 2 and 3 are true whereas statement 1 is false
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D)
Statement 1 and 3 are true whereas statement 2 is false
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E)
None of these
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PA and PB are tangents from P to the circle with centre O. At point M, a tangent is drawn cutting PA at K and PB at N. Then AK + BN is equal to:
A)
KM
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B)
KN
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C)
PN
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D)
PA
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E)
None of these
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P(4, 3) and Q lies on the same straight line which is parallel to the x- axis. If Q is 3 units from the x-axis, then the possible coordinates of Q are:
A)
\[(4,0)\]
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B)
(\[3,-4\])
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C)
(\[-2,-3\])
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D)
(\[4,-3\])
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E)
None of these
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If \[\sin \alpha =\sin \beta \] and\[\cos \alpha =\cos \beta \], then which one of the following option satisfies the given equation?
A)
\[\alpha =\beta \]
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B)
\[\alpha =-\beta \]
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C)
\[\alpha =-2\beta \]
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D)
\[\alpha +\beta =\pi \]
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E)
None of these
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The volume of a right circular cylinder of height 7 cm is 567\[\pi c{{m}^{3}}\]. Find its curved surface area.
A)
\[148\,\,c{{m}^{2}}\]
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B)
\[272\,\,c{{m}^{2}}\]
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C)
\[396\,\,c{{m}^{2}}\]
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D)
\[408\,\,c{{m}^{2}}\]
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E)
None of these
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Find the median of the following data given in the boxes:
A)
25
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B)
23
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C)
17
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D)
11
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E)
None of these
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A cartoon contains 144 bulbs out of which 20 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 buy it is
A)
\[\frac{5}{36}\]
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B)
\[\frac{31}{36}\]
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C)
\[\frac{13}{36}\]
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D)
\[\frac{15}{36}\]
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E)
None of these
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Evaluate: \[{{2}^{55}}\times {{2}^{60}}-{{2}^{97}}\times {{2}^{18}}\]
A)
0
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B)
1
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C)
3
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D)
2
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E)
None of these
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Evaluate: \[(27)\frac{2}{3}\]
A)
27
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B)
9
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C)
18
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D)
12
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E)
None of these
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Simplify: \[\frac{16\times {{2}^{n+1}}-4\times {{2}^{n}}}{16\times {{2}^{n+2}}-2\times {{2}^{n+2}}}\]
A)
1
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B)
\[\frac{1}{2}\]
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C)
\[\frac{3}{2}\]
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D)
\[\frac{1}{5}\]
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E)
None of these
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If \[\frac{\sqrt{3}-1}{\sqrt{3}+1}=a-b\sqrt{3}\]then
A)
\[a=2,\text{ }b=-1\]
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B)
\[a=2,\text{ }b=1\]
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C)
\[a=-2,\text{ }b=-1\]
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D)
\[a=-2,\text{ }b=1\]
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E)
None of these
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Which of the following is the factor of \[a-b-{{a}^{2}}+{{b}^{2}}\]
A)
\[(a+b)\,\,(1-a-b)\]
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B)
\[(a-b)\,\,(a-b)\]
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C)
\[(a+b)\,\,(1+a+b)\]
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D)
\[(a-b)\,\,(1-a-b)\]
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E)
None of these
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Which one of the following is equal to a?
A)
\[{{a}^{\frac{7}{5}}}-{{a}^{\frac{12}{7}}}\]
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B)
\[{{a}^{\frac{5}{7}}}+\,\,{{a}^{\frac{12}{7}}}\]
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C)
\[{{\left( \sqrt{{{a}^{3}}} \right)}^{\frac{2}{3}}}\]
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D)
\[{{a}^{\frac{12}{7}}}\times \,\,{{a}^{\frac{7}{12}}}\]
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E)
None of these
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Simplify: \[{{({{1}^{3}}+{{2}^{3}}+{{3}^{3}})}^{\frac{1}{2}}}\]
A)
14
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B)
36
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C)
6
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D)
42
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E)
None of these
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Find the value of \[\frac{4}{{{(216)}^{-\,\,\frac{2}{3}}}}\]+ \[\frac{1}{{{(256)}^{-\,\,\frac{3}{4}}}}\]+\[\frac{2}{{{(243)}^{-\,\,\frac{1}{5}}}}\]
A)
216
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B)
234
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C)
261
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D)
214
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E)
None of these
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If the mean of five observations x, x +2, x + 4, x + 6 and x + 8 is 13, find the value of x.
A)
8
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B)
3
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C)
6
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D)
9
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E)
None of these
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Find the slope of the line \[2x+3y-4=0\]
A)
\[\frac{2}{3}\]
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B)
\[-\frac{2}{3}\]
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C)
\[\frac{3}{2}\]
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D)
\[-\frac{3}{2}\]
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E)
None of these
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Find the remainder when the polynomial \[f(x)={{x}^{3}}-3{{x}^{2}}+4x+50\] is divided by \[(x+3)\]
A)
16
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B)
\[-16\]
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C)
18
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D)
\[-18\]
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E)
None of these
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