Every rational number is:
A)
A natural number
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B)
An integer
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C)
A real number
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D)
A whole number
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E)
None of these
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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 \[q\,(x)=3{{x}^{4}}-5{{x}^{3}}+{{x}^{2}}+8,\] 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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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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The factor of \[-10{{a}^{2}}+31a-24\]is_________.
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 \[abc=4,\] \[ab+bc+ca=5,\] \[a+b+c=0,\] then \[{{a}^{3}}+{{b}^{3}}+{{c}^{3}}\] is equal to:
A)
0
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B)
12
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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 \[a\,|\,\,|\,gm\] ABCD, if\[\angle \,A=105{}^\circ ,\] find \[\angle D\]
A)
\[65{}^\circ \]
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B)
\[75{}^\circ \]
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C)
\[115{}^\circ \]
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D)
\[15{}^\circ \]
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E)
None of these
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The distance of point \[(x\,\,\sin \theta ,\,x\,\,\cos \theta )\] from the origin is______.
A)
\[\pm x\]
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B)
x
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C)
\[\sqrt{x}\]
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D)
\[{{x}^{\frac{3}{2}}}\]
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E)
None of these
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Which one of the following statement is false?
A)
The coordinate of mid-point of a line segment with end points \[({{x}_{1}},\,{{y}_{1}})\] and \[({{x}_{2}},\,{{y}_{2}})\] is \[\left( \frac{{{x}_{1}}+{{x}_{2}}}{2},\frac{{{y}_{1}}+{{y}_{2}}}{2} \right)\]
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B)
The coordinate of origin is 0
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C)
The point on \[y-\]axis is written as (0, y)
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D)
The point on \[x-\] axis is written as (x, 0)
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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 the figure given below 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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Calculate the value of x in the given figure:
A)
\[75{}^\circ \]
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B)
\[50{}^\circ \]
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C)
\[55{}^\circ \]
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D)
\[65{}^\circ \]
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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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If the mode of the following data 10, 11, 12, 10, 15, 14, 15, 13, 12, x, 9, 7, 10, 15 is 10 then the value of x is:
A)
15
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B)
10
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C)
12
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D)
9
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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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The longer side of a rectangular hall is 24 m and the length of its diagonal is 26 m. Find the area of the hall.
A)
\[140\,{{m}^{2}}\]
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B)
\[250\,{{m}^{2}}\]
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C)
\[240\,{{m}^{2}}\]
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D)
\[258\,{{m}^{2}}\]
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E)
None of these
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If D is the mid-point of the straight line joining\[A\,(-\,2,\,9),\] and B (4, 3), then the coordinates of D is:
A)
(4, 5)
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B)
\[(10,\,-3)\]
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C)
\[(-10,\,-4)\]
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D)
(1, 6)
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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 \[\frac{{{b}_{1}}}{{{b}_{2}}}\] is not equal then the line will be intersecting
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C)
If \[\frac{{{a}_{1}}}{{{a}_{2}}}\] and \[\frac{{{b}_{1}}}{{{b}_{2}}},\] is 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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In the given figure, ABCD is a cyclic quadrilateral whose diagonals intersect at P. \[\angle \,DBC=70{}^\circ \]and\[\angle \,BAC=50{}^\circ \]. Find the value of \[\angle \,BCD\].
A)
\[80{}^\circ \]
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B)
\[60{}^\circ \]
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C)
\[50{}^\circ \]
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D)
\[110{}^\circ \]
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E)
None of these
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If \[x=1+\sqrt{2},\] then find the value of \[\left( {{x}^{2}}+\frac{1}{{{x}^{2}}} \right)\].
A)
2
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B)
4
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C)
6
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D)
8
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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 \[\sqrt{15-x\sqrt{14}}=\sqrt{8}-\sqrt{7},\] 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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From the given figure, find out the values of x and y.
A)
x = 26, y = 19
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B)
x = 26, y = 29
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C)
x = 25, y = 20
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D)
x = 40, y = 25
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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 black face card?
A)
\[\frac{1}{26}\]
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B)
\[\frac{3}{14}\]
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C)
\[\frac{3}{26}\]
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D)
\[\frac{3}{13}\]
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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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Find the area of triangle, when each side of an equilateral triangle measures 10 cm. \[(Given\,\,\sqrt{3}=1.732\,\,cm)\]
A)
\[46.6\,\,c{{m}^{2}}\]
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B)
\[43.3\,\,c{{m}^{2}}\]
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C)
\[45.8\,\,c{{m}^{2}}\]
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D)
\[46.9\,\,c{{m}^{2}}\]
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E)
None of these
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The diagonals of a rectangle ABCD meet at O. If \[\angle \,BOC=45{}^\circ ,\] then \[\angle \,BCD\] is equal to:
A)
\[17{}^\circ \]
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B)
\[34{}^\circ \]
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C)
\[68{}^\circ \]
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D)
\[98{}^\circ \]
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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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The volume of sphere is numerically equal to twice the surface area of the sphere. Find the length of radius of the sphere.
A)
6 cm
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B)
9 cm
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C)
5 cm
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D)
7 cm
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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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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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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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The surface area of a cube is 726 sq. metres. Find the volume of the cube.
A)
\[1728\,\,{{m}^{3}}\]
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B)
\[1000\,\,{{m}^{3}}\]
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C)
\[1331\,\,{{m}^{3}}\]
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D)
\[2197\,\,{{m}^{3}}\]
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E)
None of these
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In what ratio are the volumes of a cylinder, a cone and a sphere, if each has the same radius and the same height?
A)
1 : 3 : 2
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B)
2 : 3 : 1
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C)
3 : 1 : 2
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D)
3 : 2 : 1
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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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Choose the group of letters which is different from the other.
A)
ABD
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B)
FGI
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C)
LMO
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D)
STU
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E)
None of these
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