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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The sum of first five prime numbers is:
A)
11
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B)
18
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C)
26
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D)
28
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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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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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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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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)
\[\left( 2,\text{ }3 \right)\]
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D)
\[(-\,2,\,3)\]
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E)
None of these
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Find the length of the diagonal of a rectangle whose sides are 12 cm and 9 cm.
A)
\[4\sqrt{13}\,cm\]
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B)
13 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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In the figure given below, ABCD is a parallelogram in which \[\angle \,DAB=40{}^\circ \] and \[\angle \,DBC=60{}^\circ \]. Find the measure of\[\angle \,CDB\].
A)
\[40{}^\circ \]
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B)
\[80{}^\circ \]
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C)
\[60{}^\circ \]
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D)
\[70{}^\circ \]
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E)
None of these
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The angles of a quadrilateral are respectively\[100{}^\circ ,\] \[98{}^\circ \] and \[92{}^\circ \].The fourth angle of the quadrilateral is:
A)
\[36{}^\circ \]
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B)
\[48{}^\circ \]
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C)
\[60{}^\circ \]
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D)
\[70{}^\circ \]
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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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Find the value of x, if the distance between the points \[(x,-\,1)\] and (3, 2) is 5.
A)
8
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B)
\[-1\]
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C)
7
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D)
Both (B) and (C)
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E)
None of these
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Distance between points \[(a\,\cos 25{}^\circ ,0)\] and \[(0,a\cos 65{}^\circ )\]is:
A)
a
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B)
2 a
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C)
3 a
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D)
4 a
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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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The volumes of two spheres are in the ratio of 64 : 27. Find the ratio of their surface areas.
A)
3 : 4
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B)
4 : 9
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C)
9 : 4
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D)
16 : 9
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E)
None of these
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The marks obtained by the 12 students in Mathematics in the first term of the school examination are given as 13, 17, 16, 14, 11, 13, 10, 16, 11, 18, 12, 17. Find the mean.
A)
12
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B)
14
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C)
16
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D)
18
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E)
None of these
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In a lottery there are 8 prizes and 16 blanks. What is the probability of getting a prize?
A)
\[\frac{1}{2}\]
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B)
\[\frac{1}{3}\]
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C)
\[\frac{2}{3}\]
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D)
\[\frac{4}{5}\]
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E)
None of these
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A bag contains 8 red, 2 black and 5 white balls. One ball is drawn at random. What is the probability that the ball drawn is not black?
A)
\[\frac{2}{15}\]
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B)
\[\frac{13}{15}\]
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C)
\[\frac{8}{15}\]
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D)
\[\frac{1}{3}\]
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E)
None of these
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If \[\sin \theta :\cos \theta =4:7\]. Then the value of \[\frac{7\,\sin \theta -3\,\cos \theta }{7\,\sin \theta +2\,\cos \theta }\] is______.
A)
\[\frac{3}{7}\]
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B)
\[\frac{1}{6}\]
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C)
\[\frac{4}{7}\]
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D)
\[\frac{7}{4}\]
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E)
None of these
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In the given figure \[\angle \,A=50{}^\circ \] and\[\angle \,ABC=75{}^\circ \]. Find the value of \[\angle \,DPC\] and \[\angle \,BQC\].
A)
\[40{}^\circ ,50{}^\circ \]
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B)
\[50{}^\circ ,60{}^\circ \]
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C)
\[55{}^\circ ,25{}^\circ \]
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D)
\[55{}^\circ ,35{}^\circ \]
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E)
None of these
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The sales of different articles are shown in the histogram given below. What is the maximum sales of the articles?
A)
50
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B)
41
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C)
45
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D)
30
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E)
None of these
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Which one of the following is the correct option
A)
\[Mode=3\,\,median-2\,\,mean\]
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B)
\[Mode\,=3\,\,median+2\,\,mean\]
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C)
\[2\,Mode=Median\,\,-\,\,2\,mean\]
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D)
\[2\,Mode=3\,\,median\,\,+\,\,4\,mean\]
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E)
None of these
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In the given figure ABCD is a cyclic quadrilateral in which AE is drawn parallel to CD, and BA is produced to F. If \[\angle \,ABC=80{}^\circ \] and \[\angle \,FAE=30{}^\circ \]Find the value of\[\angle \,BCD\].
A)
\[130{}^\circ \]
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B)
\[120{}^\circ \]
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C)
\[110{}^\circ \]
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D)
\[108{}^\circ \]
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E)
None of these
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If \[x=3+\sqrt{8},\] find the value of \[\left( {{x}^{2}}+\frac{1}{{{x}^{2}}} \right)\].
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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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)
\[\frac{9}{8}\]
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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.
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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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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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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The volume of the following figure is:
A)
\[10\pi \,\,{{m}^{3}}\]
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B)
\[20\pi \,\,{{m}^{3}}\]
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C)
\[30\pi \,\,{{m}^{3}}\]
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D)
\[40\pi \,\,{{m}^{3}}\]
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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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The length of a rectangular plot of land is twice its breadth. If the perimetre of the plot be 210 m then find its area.
A)
\[2450\,\,{{m}^{2}}\]
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B)
\[2251\,\,{{m}^{2}}\]
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C)
\[5560\,\,{{m}^{3}}\]
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D)
\[9060\,\,{{m}^{3}}\]
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E)
None of these
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The sides of a triangle are 3 cm, 3 cm and 4 cm, find the area of triangle.
A)
\[20\,c{{m}^{2}}\]
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B)
\[4\sqrt{5}\,c{{m}^{2}}\]
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C)
\[10\,c{{m}^{2}}\]
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D)
\[2\sqrt{5}\,c{{m}^{2}}\]
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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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In \[\Delta \,ABC,\] \[\angle \,A+\angle \,B=70{}^\circ \] and \[\angle \,B+\angle \,C=135{}^\circ \]. Find the value of\[\angle \,A\].
A)
\[25{}^\circ \]
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B)
\[55{}^\circ \]
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C)
\[40{}^\circ \]
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D)
\[115{}^\circ \]
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E)
None of these
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The perimetre of a right triangle is 60 cm and its hypotenuse is 26 cm. The other two sides of the triangle are
A)
24 cm, 10 cm
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B)
25 cm, 9 cm
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C)
20 cm, 14 cm
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D)
26 cm, 8 cm
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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)
\[\left( \frac{61}{29},\frac{24}{29} \right)\]
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B)
\[\left( -\frac{29}{61},-\frac{29}{24} \right)\]
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C)
\[\left( -\frac{24}{29},\frac{61}{29} \right)\]
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D)
\[\left( -\frac{61}{29},-\frac{24}{29} \right)\]
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E)
None of these
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Express \[\frac{2}{11}\] in decimal form.
A)
\[0.\overline{21}\]
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B)
\[0.\overline{15}\]
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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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\[x+2y=3\] 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 solutions
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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 is the condition for infinitely many solutions?
A)
\[{{a}_{1}}\,{{a}_{2}}={{b}_{1}}\,{{b}_{2}}\]
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B)
\[\frac{{{a}_{1}}}{{{a}_{2}}}\ne \frac{{{b}_{1}}}{{{b}_{2}}}\]
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C)
\[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{b}_{1}}}{{{b}_{2}}}\ne \frac{{{c}_{1}}}{{{c}_{2}}}\]
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D)
\[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{b}_{1}}}{{{b}_{2}}}=\frac{{{c}_{1}}}{{{c}_{2}}}\]
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E)
None of these
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If code for 'TAMILNADU' = 'UDANLIMAT', then code for 'KARNATAKA'= '?'
A)
AAKTANRAK
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B)
AKTAANRAK
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C)
AKATANRAK
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D)
ATKAANRAK
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E)
None of these
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If code for 'BIEF' = '2956', then code for 'FADH'=______.
A)
6814
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B)
6418
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C)
6841
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D)
6148
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E)
None of these
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