Which of the following in an irrational number?
A)
\[\sqrt{2}\]
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B)
\[\sqrt{5}\]
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C)
\[\sqrt{7}\]
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D)
All of these
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E)
None of these
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If \[q\,(x)=3{{x}^{4}}-5{{x}^{3}}+8,\] then \[q\,(-\,1)\] is equal to:
A)
17
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B)
11
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C)
13
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D)
16
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E)
None of these
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If a = 1, b = 4 and \[c=-1,\] then find the value of\[{{a}^{3}}+{{b}^{3}}+{{c}^{3}}\].
A)
\[-12\]
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B)
64
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C)
32
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D)
48
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E)
None of these
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The factors of \[-10{{a}^{2}}+31a-24\]________.
A)
\[(2a-3)\,\,(5a-8)\]
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B)
\[(3-2a)\,\,(8-5a)\]
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C)
\[(2a+3)\,\,(5a-8)\]
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D)
\[-(2a-3)\,\,(5a-8)\]
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E)
None of these
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If \[a+b+c+d=4,\] \[ab+bc+ca=5,\] \[a+b+c=0,\] then \[{{a}^{3}}+{{b}^{3}}+{{c}^{3}}\] is equal to:
A)
0
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B)
3abc
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C)
4
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D)
2
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E)
None of these
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Find the values of x from the figure given below.
A)
\[x=1\]
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B)
\[x=5\]
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C)
\[x=-\,1\]
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D)
\[x=2\]
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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. Its area is:
A)
\[12\,c{{m}^{2}}\]
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B)
\[15\,c{{m}^{2}}\]
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C)
\[6\,c{{m}^{2}}\]
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D)
\[9\,c{{m}^{2}}\]
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E)
None of these
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The height of a cylinder is 15 cm. Its curved surface area is \[660\,c{{m}^{2}}\]. Find the radius.
A)
5 cm
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B)
7 cm
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C)
8 cm
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D)
9 cm
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E)
None of these
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In \[\Delta \,ABC\] the angle bisector of \[\angle \,B\] and \[\angle C\]meet at O. If \[\angle \,A=90{}^\circ ,\] then find\[\angle \,BOC\].
A)
\[125{}^\circ \]
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B)
\[135{}^\circ \]
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C)
\[45{}^\circ \]
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D)
\[145{}^\circ \]
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E)
None of these
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The length of the chord which is at a distance of 12 cm from the centre of a circle of radius 13 cm is:
A)
5 cm
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B)
12 cm
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C)
10 cm
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D)
13 cm
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E)
None of these
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Which one of the following equations is not a linear equation in two variable?
A)
\[4x+\frac{7}{2}y=4\]
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B)
\[\frac{4}{x}+\frac{7}{y}=4\]
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C)
\[\frac{x+3}{x-3}=4\]
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D)
\[3x+7y+87=0\]
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E)
None of these
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Solve for x and y:
\[4x-15y=65\] \[3x+2y=9\].
A)
\[(5,\,-3)\]
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B)
\[(-\,5,\,3)\]
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C)
(2, 3)
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D)
\[(-\,2,\,3)\]
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E)
None of these
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In \[\Delta \,PQR,\] \[PS=2\sqrt{2}\,cm,\] \[SQ=3\sqrt{2}\,cm\] and \[PR=10\,cm,\]\[ST\parallel QR\]. Find the length of TR.
A)
\[6\,\sqrt{2}\]
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B)
\[5\,\sqrt{2}\]
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C)
6 cm
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D)
\[10\,\sqrt{2}\,cm\]
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E)
None of these
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The length of a side of a rhombus is 10 m and one of its diagonal is 12 m. The length of the other diagonal is:
A)
12 m
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B)
15 m
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C)
16 m
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D)
24 m
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E)
None of these
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A solid metal ball of diameter 16 cm is melted and cast into smaller balls, each of radius 1 cm. The number of such balls is:
A)
256
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B)
512
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C)
2048
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D)
4096
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E)
None of these
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Which one of the coordinate is incorrectly represented in the figure given below?
A)
P
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B)
Q
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C)
R
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D)
S
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E)
None of these
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A bag contain 5 red balls, 6 white balls, 9 green balls and 10 yellow balls. Radha draws one ball from it randomly and found to be white. Find the probability of drawing white ball from the bag.
A)
\[\frac{1}{5}\]
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B)
\[\frac{7}{30}\]
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C)
\[\frac{1}{15}\]
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D)
\[\frac{1}{30}\]
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E)
None of these
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If the angle of triangle are in the ratio 1 : 4 : 7, then the value of the largest angle is:
A)
\[135{}^\circ \]
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B)
\[84{}^\circ \]
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C)
\[105{}^\circ \]
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D)
\[75{}^\circ \]
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E)
None of these
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The factors of \[x\,({{y}^{2}}-{{z}^{2}})+y\,({{z}^{2}}-{{x}^{2}})+z\,({{x}^{2}}-{{y}^{2}})\] are:
A)
\[(x-y)\,\,(y-z)\,\,(z-x)\]
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B)
\[(x+y)\,(y+z)\,(z+x)\]
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C)
\[(y-x)\,(z-y)\,\,(x-z)\]
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D)
\[(x+y)\,(z-y)\,(x-z)\]
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E)
None of these
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If \[\left( 3x-\frac{2}{x} \right)=5,\] then the value of \[\left( 9{{x}^{2}}+\frac{4}{{{x}^{2}}} \right)\]is:
A)
37
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B)
27
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C)
36
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D)
63
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E)
None of these
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Find the value of 'a' for which \[(x-1)\] is factor of\[{{x}^{3}}-3{{x}^{2}}+4x+a\].
A)
12
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B)
10
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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 \[5\sqrt{5}\times {{5}^{3}}\div {{5}^{\frac{-3}{2}}}={{5}^{a+2}}\] then the value of a is:
A)
3
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B)
7
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C)
4
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D)
9
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E)
None of these
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The value of \[\frac{\sqrt{5}-2}{\sqrt{5}+2}\] is:
A)
\[4-9\,\sqrt{5}\]
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B)
\[9+4\,\sqrt{5}\]
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C)
\[9-4\,\sqrt{5}\]
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D)
\[7-4\,\sqrt{5}\]
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E)
None of these
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In the figure given below, O is the centre of the circle. The value of y is________.
A)
\[135{}^\circ \]
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B)
\[45{}^\circ \]
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C)
\[130{}^\circ \]
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D)
\[115{}^\circ \]
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E)
None of these
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The radii of two cylinders are in the ratio of 3 : 5 and their heights are in the ratio 4 : 3. The ratio of their volumes is:
A)
4 : 5
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B)
5 : 4
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C)
13 : 25
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D)
12 : 25
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E)
None of these
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Which one of the following statements is false for the following pair of linear equation?
\[{{a}_{1}}x+{{b}_{1}}y+{{c}_{1}}=0\] \[{{a}_{2}}x+{{b}_{2}}y+{{c}_{2}}=0\]
A)
If \[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{b}_{1}}}{{{b}_{2}}}=\frac{{{c}_{1}}}{{{c}_{2}}},\] then the line will be coincident
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B)
If \[\frac{{{a}_{1}}}{{{a}_{2}}}\]and \[\frac{{{b}_{1}}}{{{b}_{2}}}\] are not equal, then the line will be intersecting
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C)
If \[\frac{{{a}_{1}}}{{{a}_{2}}}\]and \[\frac{{{b}_{1}}}{{{b}_{2}}}\] are equal, then the line will be intersecting
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D)
If \[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{b}_{1}}}{{{b}_{2}}}\ne \frac{{{c}_{1}}}{{{c}_{2}}},\] then the lines will be parallel
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E)
None of these
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If \[\sqrt{15-x\sqrt{14}}=\sqrt{8}-\sqrt{7},\] then find the value of "x".
A)
4
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B)
6
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C)
5
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D)
3
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E)
None of these
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The slope of the line \[4x+3y-4=0\] is_______.
A)
\[\frac{3}{4}\]
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B)
\[\frac{-\,4}{3}\]
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C)
\[\frac{4}{3}\]
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D)
\[\frac{-\,3}{4}\]
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E)
None of these
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If the sides of a triangle are produced, then the sum of the exterior angles i.e., \[\angle DAB+\angle EBC+\angle FCA\] is equal to:
A)
\[180{}^\circ \]
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B)
\[270{}^\circ \]
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C)
\[360{}^\circ \]
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D)
\[240{}^\circ \]
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E)
None of these
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The edge of a cube is doubled. What will be the new volume?
A)
2 times
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B)
3 times
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C)
4 times
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D)
8 times
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E)
None of these
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Find the ratio of radii of two circles, if arc of equal length subtend angles \[30{}^\circ \] and \[45{}^\circ \] at their centre.
A)
2 : 3
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B)
4 : 3
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C)
3 : 2
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D)
3 : 4
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E)
None of these
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The diameter of a wheel is 1.26 m. How far will it travel in 500 revolutions?
A)
1492 m
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B)
1980 m
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C)
2530 m
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D)
2880 m
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E)
None of these
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In a cricket match, Dhoni hits the boundary 15 times out of 20 balls played by him. Find the probability that the boundary is not hit by the Dhoni.
A)
\[\frac{3}{4}\]
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B)
\[\frac{1}{4}\]
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C)
\[\frac{1}{2}\]
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D)
\[\frac{4}{3}\]
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E)
None of these
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How many metres of cloth 5 m wide will be required to make a conical tent having the radius of the base 7 m and the height 24 m.
A)
55 m
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B)
110 m
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C)
75 m
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D)
150 m
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E)
None of these
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In the given figure, O is the centre of the circle and\[\angle \,ABO=60{}^\circ \]. Find the value of\[\angle \,ACB\].
A)
\[40{}^\circ \]
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B)
\[90{}^\circ \]
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C)
\[30{}^\circ \]
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D)
\[45{}^\circ \]
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E)
None of these
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The radius and the height of a closed cylindrical water tank are 1 m and 7 m. Find the total cost for painting the lateral surface area of this tank, if the cost per \[{{m}^{2}}\] is Rs. 15.
A)
Rs. 1000
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B)
Rs. 1200
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C)
Rs. 1100
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D)
Rs. 1125
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E)
None of these
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How many cubic metres of earth must be dug to a make a well 14 m deep and 4 m in diameter?
A)
\[230\,c{{m}^{3}}\]
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B)
\[225\,c{{m}^{3}}\]
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C)
\[176\,c{{m}^{3}}\]
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D)
\[220\,c{{m}^{3}}\]
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E)
None of these
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If \[x=\sqrt{3+\sqrt{3+\sqrt{3+......}}},\] then the value of x is:
A)
\[\frac{2\pm \sqrt{13}}{2}\]
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B)
\[\frac{3\pm \sqrt{13}}{2}\]
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C)
\[\frac{4\pm \sqrt{13}}{2}\]
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D)
\[\frac{1\pm \sqrt{13}}{2}\]
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E)
None of these
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If P denotes \[\div ,\] Q denotes x, R denotes + and S denotes \[-,\] then 18 Q 12 P 4 R 5 S 6 = ?
A)
35
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B)
53
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C)
59
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D)
36
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E)
None of these
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The area of a trapezium is \[441\,c{{m}^{2}}\] and the ratio of parallel side is 5 : 9. Also the perpendicular distance between them is 21 cm. Find the longest parallel side.
A)
36 cm
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B)
28 cm
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C)
18 cm
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D)
27 cm
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E)
None of these
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