Find a rational number lying between\[\frac{1}{3}\]and\[\frac{1}{2}\].
A)
\[\frac{5}{12}\]
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B)
\[\frac{7}{12}\]
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C)
\[\frac{1}{2}\]
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D)
\[\frac{6}{2}\]
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E)
None of these
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Express \[\frac{2}{11}\] in decimal form.
A)
\[0.2\overline{1}\]
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B)
\[0.1\overline{5}\]
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C)
\[0.\overline{18}\]
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D)
\[0.\overline{99}\]
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E)
None of these
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If a and b are rational numbers and \[\frac{4+3\sqrt{5}}{4-3\sqrt{5}}=a+b\sqrt{5},\] Find the values of a and b.
A)
\[+\,\,\frac{61}{29}\And +\,\,\frac{24}{29}\]
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B)
\[-\,\,\frac{29}{61}\And -\,\,\frac{29}{24}\]
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C)
\[-\,\,\frac{24}{29}\And +\,\,\frac{61}{29}\]
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D)
\[-\,\,\frac{61}{29}\And -\,\,\frac{24}{29}\]
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E)
None of these
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If \[x=3+\sqrt{8},\] find the value of \[({{x}^{2}}+\frac{1}{{{x}^{2}}})\]
A)
32
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B)
34
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C)
39
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D)
49
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E)
None of these
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Simplify: \[\left( \frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}}+\frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}+\sqrt{2}} \right)\]
A)
10
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B)
30
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C)
60
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D)
90
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E)
None of these
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Find the value of a for which \[(x-1)\] is factor of \[2{{x}^{3}}+9{{x}^{2}}+x+a\]
A)
11
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B)
\[-11\]
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C)
12
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D)
\[-12\]
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E)
None of these
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Find the remainder when polynomial \[f\,(x)=4{{x}^{3}}-12{{x}^{2}}+16x-3\] is divided by \[(2x-1)\]
A)
\[\frac{5}{2}\]
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B)
\[\frac{6}{5}\]
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C)
\[\frac{9}{8}\]
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D)
\[\frac{8}{5}\]
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E)
None of these
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Factorize: \[{{(p-q)}^{3}}+{{(q-r)}^{3}}+{{(r-p)}^{3}}\]
A)
\[3\,(p-q)\,\,(q-r)\,\,(r-p)\]
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B)
\[3\,(p+q)\,\,(q+r)\,\,(r+p)\]
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C)
\[4\,(p+q)\,\,(4q+9r)\,\,(r+p)\]
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D)
\[3\,\,(-\,2p+z)\,\,(z+r)\,\,(r+2p)\]
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E)
None of these
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\[x+2y=3\] and \[4x+3y=2,\] The system of equation has:
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 the above
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E)
None of these
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For the given system of equation \[4x-15y=65,\]\[3x+2y=9,\] Find the value of x and y
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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The sum of the numerator and the denominator of a fraction is 12. If the denominator is increased by 3, the fraction becomes \[\frac{5}{10}\]. Find the fraction.
A)
\[\frac{1}{2}\]
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B)
\[\frac{5}{7}\]
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C)
\[\frac{7}{5}\]
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D)
\[\frac{3}{2}\]
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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.
A)
A = 15 years, B = 45 years
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B)
A = 10 years, B = 40 years
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C)
A = 20 years, B = 50 years
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D)
A = 50 years, B = 20 years
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E)
None of these
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Find the distance between two points \[A\,(0,-2)\]and\[B\,(-\,4,2)\].
A)
\[4\,\sqrt{2}\,units\]
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B)
\[3\,\sqrt{2}\,units\]
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C)
\[2\,\sqrt{2}\,units\]
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D)
\[\sqrt{2}\,units\]
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E)
None of these
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Find the co-ordinates of the point which divides the line segment joining the points (4, 3) and (6, 3) externally in the ratio 1 : 2 is
A)
(4, 5)
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B)
(2, 3)
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C)
(4, 6)
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D)
(5, 6)
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E)
None of these
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In which quadrant does the point \[(-\,4,-\,3)\] lies?
A)
First Quadrant
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B)
Second Quadrant
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C)
Third Quadrant
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D)
Fourth Quadrant
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E)
None of these
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In the adjoining figure, AOB is a straight line. Find \[\angle AOC\].
A)
\[60{}^\circ \]
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B)
\[65{}^\circ \]
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C)
\[45{}^\circ \]
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D)
\[75{}^\circ \]
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E)
None of these
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In the adjoining figure, what value of x will make AOB a straight line?
A)
\[x=35{}^\circ \]
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B)
\[x=38{}^\circ \]
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C)
\[x=40{}^\circ \]
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D)
\[x=45{}^\circ \]
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E)
None of these
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In the adjoining figure, OD and OE are angle bisectors. Find the measure of\[\angle DOE\].
A)
\[45{}^\circ \]
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B)
\[90{}^\circ \]
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C)
\[40{}^\circ \]
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D)
\[60{}^\circ \]
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E)
None of these
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From figure. Find the value of x.
A)
\[30{}^\circ \]
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B)
\[45{}^\circ \]
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C)
\[75{}^\circ \]
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D)
\[35{}^\circ \]
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E)
None of these
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The angles of the quadrilateral are in ratio 2 : 3 : 5 : 8. Find the smallest angle of the quadrilateral.
A)
\[30{}^\circ \]
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B)
\[45{}^\circ \]
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C)
\[40{}^\circ \]
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D)
\[35{}^\circ \]
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E)
None of these
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The angles of a triangle are in the ratio 2 : 3 : 7. Find the measure of the smallest angle of the triangle.
A)
\[15{}^\circ \]
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B)
\[30{}^\circ \]
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C)
\[45{}^\circ \]
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D)
\[105{}^\circ \]
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E)
None of these
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In the triangle given below find the shortest side of the triangle.
A)
AB
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B)
AC
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C)
BC
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D)
inadequate data
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E)
None of these
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If the angles of the quadrilateral are in ratio 2 : 3 : 4 : 3 then find the measure of smallest angle of the quadrilateral.
A)
\[60{}^\circ \]
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B)
\[80{}^\circ \]
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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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In the figure given below if AM, BM, CN, DN are angle bisectors of respective angles then the quadrilateral MPNQ is:
A)
Square
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B)
Rectangle
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C)
Rhombus
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D)
Parallelogram
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E)
None of these
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In a circle of radius 13 cm, a chord of length 24 cm is drawn. Find the distance of the chord from the centre of the circle.
A)
10 cm
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B)
12 cm
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C)
5 cm
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D)
15 cm
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E)
None of these
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Find the value of x from the given figure below.
A)
\[60{}^\circ \]
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B)
\[80{}^\circ \]
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C)
\[90{}^\circ \]
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D)
\[40{}^\circ \]
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E)
None of these
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Find the length of a chord which is at a distance of 8 cm from the centre of a circle of radius 17 cm.
A)
11 cm
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B)
12 cm
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C)
15 cm
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D)
30 cm
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E)
None of these
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Find the area of an isosceles triangle, each of whose equal sides is 13 cm and whose base is 24 cm.
A)
\[50\,\,c{{m}^{2}}\]
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B)
\[60\,\,c{{m}^{2}}\]
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C)
\[70\,\,c{{m}^{2}}\]
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D)
\[10\,\,c{{m}^{2}}\]
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E)
None of these
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The difference between the sides of a right angle triangle is 14 cm. The area of the triangle is\[120\,c{{m}^{2}}\]. Calculate the perimeter of the triangle.
A)
60 cm
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B)
40 cm
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C)
30 cm
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D)
20 cm
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E)
None of these
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A cylindrical metallic pipe is 14 cm long. The difference between the outside and inside curve surface area is \[44\,c{{m}^{2}}.\]If the sum of outer and inner radius is 1.5 cm. Find the outer and inner radius of the pipe.
A)
\[1\,\,cm\,\,\And \,\,\frac{1}{2}\,\,cm\]
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B)
\[\frac{3}{2}\,\,cm\,\,\And \,\,2\,\,cm\]
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C)
\[\frac{1}{2}\,\,cm\,\,\And \,\,2\,\,cm\]
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D)
\[\frac{5}{2}\,\,cm\,\,\And \,\,\frac{1}{2}\,\,cm\]
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E)
None of these
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The external diameter of an iron pipe is 25 cm and its length is 20 cm. If the thickness of the pipe is 1 cm, find the total surface area of the pipe.
A)
\[3092\,\,c{{m}^{2}}\]
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B)
\[3263\,c{{m}^{2}}\]
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C)
\[3162\,c{{m}^{2}}\]
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D)
\[3363\,c{{m}^{2}}\]
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E)
None of these
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The radii of two spheres are in the ratio 1 : 2. Find the ratio of their surface area.
A)
1 : 4
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B)
2 : 3
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C)
5 : 4
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D)
6 : 1
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E)
None of these
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Three sphere whose radii is 3 cm, 4 cm and 5 cm are melted to form a big sphere. Then what is the radius of big sphere.
A)
6 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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A cone of height 8 m has a curved surface area 188.4 square meters find its volume. \[(Take\,\pi =\]\[3.14)\]
A)
\[301.44\,\,{{m}^{3}}\]
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B)
\[302.45\,\,{{m}^{3}}\]
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C)
\[303.46\,\,{{m}^{3}}\]
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D)
\[304.47\,\,{{m}^{3}}\]
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E)
None of these
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The different mode of transport used by 70 employee of a company from their respective home to their office has been shown in the bar graph below. Which mode of transport is used by maximum number of employee?
A)
Car
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B)
Bus
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C)
Bike
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D)
Cycle
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E)
None of these
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Find the mean marks obtained by 10 students in a class in a unit test conducted in the class. The marks are 25, 36, 42, 43, 48, 15, 10, 17, 28 and 30
A)
24.85
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B)
25.6
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C)
29.4
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D)
28.23
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E)
None of these
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The mean of 12 data is 22. If 5 is subtracted from each data then what will be the mean?
A)
22
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B)
17
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C)
20
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D)
15
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E)
None of these
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Find the median of the data given below. 2, 10, 8, 8, 4, 1, 2, 6, 10, 5
A)
2
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B)
4
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C)
5
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D)
6
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E)
None of these
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In a group of 15 students in a class there are 8 girls and 7 boys. Class monitor is to be chosen from the group. Find the probability that it is a girl.
A)
\[\frac{8}{15}\]
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B)
\[\frac{7}{15}\]
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C)
\[\frac{1}{15}\]
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D)
\[\frac{4}{15}\]
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E)
None of these
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A card is drawn from the deck of 52 cards. Find the probability that it is a jack of red suit.
A)
\[\frac{1}{52}\]
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B)
\[\frac{1}{26}\]
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C)
\[\frac{1}{13}\]
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D)
\[\frac{2}{13}\]
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E)
None of these
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