In a \[\Delta \,ABC,\]\[30\,A=6B=5C\]. Find the value of \[\angle \,A,\] \[\angle \,B\] and \[\angle C\].
A)
\[75{}^\circ ,80{}^\circ ,25{}^\circ \]
done
clear
B)
\[65{}^\circ ,35{}^\circ ,80{}^\circ \]
done
clear
C)
\[25{}^\circ ,70{}^\circ ,85{}^\circ \]
done
clear
D)
\[15{}^\circ ,75{}^\circ ,90{}^\circ \]
done
clear
E)
None of these
done
clear
View Answer play_arrow
The sum and difference of two angles of a triangle are \[128{}^\circ \] and \[22{}^\circ \] respectively. Find all the angles of the triangle.
A)
\[75{}^\circ ,70{}^\circ ,60{}^\circ \]
done
clear
B)
\[70{}^\circ ,60{}^\circ ,50{}^\circ \]
done
clear
C)
\[75{}^\circ ,53{}^\circ ,52{}^\circ \]
done
clear
D)
\[80{}^\circ ,52{}^\circ ,50{}^\circ \]
done
clear
E)
None of these
done
clear
View Answer play_arrow
In \[\Delta \,ABC,\] \[\angle \,A+\angle \,B=84{}^\circ \] and \[\angle B+\angle C=146{}^\circ \]. Find the measure of each of the angles of the triangle.
A)
\[70{}^\circ ,85{}^\circ ,95{}^\circ \]
done
clear
B)
\[34{}^\circ ,50{}^\circ ,96{}^\circ \]
done
clear
C)
\[30{}^\circ ,45{}^\circ ,80{}^\circ \]
done
clear
D)
\[20{}^\circ ,35{}^\circ ,50{}^\circ \]
done
clear
E)
None of these
done
clear
View Answer play_arrow
Find the value of\[x,\]\[\sqrt[3]{3x-2}=4\].
A)
22
done
clear
B)
25
done
clear
C)
20
done
clear
D)
30
done
clear
E)
None of these
done
clear
View Answer play_arrow
Simplify: \[\sqrt[4]{\frac{1008}{63}}\]
A)
1
done
clear
B)
2
done
clear
C)
3
done
clear
D)
4
done
clear
E)
None of these
done
clear
View Answer play_arrow
Simplify: \[4\sqrt{2}-2\sqrt{8}+\frac{3}{\sqrt{2}}\]
A)
\[\frac{2}{3}\sqrt{3}\]
done
clear
B)
\[\frac{3}{4}\sqrt{2}\]
done
clear
C)
\[\frac{4}{3}\sqrt{3}\]
done
clear
D)
\[\frac{3}{2}\sqrt{2}\]
done
clear
E)
None of these
done
clear
View Answer play_arrow
Simplify: \[\sqrt{{{m}^{2}}{{n}^{2}}}\times \sqrt[6]{{{m}^{2}}{{n}^{2}}}\times \sqrt[3]{{{m}^{2}}{{n}^{2}}}\]
A)
\[{{m}^{2}}{{n}^{3}}\]
done
clear
B)
\[{{m}^{3}}{{n}^{2}}\]
done
clear
C)
\[{{m}^{2}}n\]
done
clear
D)
\[m{{n}^{2}}\]
done
clear
E)
None of these
done
clear
View Answer play_arrow
If \[x=2+\sqrt{3},\] find the value\[{{x}^{2}}+\frac{1}{{{x}^{2}}}\].
A)
15
done
clear
B)
14
done
clear
C)
18
done
clear
D)
24
done
clear
E)
None of these
done
clear
View Answer play_arrow
Find the remainder when \[{{x}^{3}}+3{{x}^{2}}+3x+1\] is divided by \[x-\frac{1}{2}\].
A)
\[\frac{8}{27}\]
done
clear
B)
\[\frac{-\,8}{27}\]
done
clear
C)
\[\frac{27}{8}\]
done
clear
D)
\[\frac{-\,27}{8}\]
done
clear
E)
None of these
done
clear
View Answer play_arrow
What must be added to \[({{x}^{3}}-3{{x}^{2}}+4x-13)\] to obtain a polynomial which is exactly divisible by\[(x-3)\]?
A)
1
done
clear
B)
3
done
clear
C)
6
done
clear
D)
5
done
clear
E)
None of these
done
clear
View Answer play_arrow
Factorise: \[\frac{1}{2}{{x}^{2}}+4x+6\]
A)
\[(x+6)\,\,\left( \frac{x}{2}-1 \right)\]
done
clear
B)
\[(x+6)\,\,\left( \frac{x}{3}-1 \right)\]
done
clear
C)
\[(x+6)\,\,\left( \frac{x}{2}+1 \right)\]
done
clear
D)
\[(x-6)\,\,\left( \frac{x}{2}+1 \right)\]
done
clear
E)
None of these
done
clear
View Answer play_arrow
Factorise: \[{{a}^{3}}-\frac{1}{{{a}^{3}}}-2a+\frac{2}{a}\]
A)
\[\left( a-\frac{1}{a} \right)\left( {{a}^{2}}+\frac{1}{{{a}^{2}}}-1 \right)\]
done
clear
B)
\[\left( a+\frac{1}{a} \right)\left( {{a}^{2}}+\frac{1}{{{a}^{2}}}-1 \right)\]
done
clear
C)
\[\left( a+\frac{1}{a} \right)\left( {{a}^{2}}-\frac{1}{{{a}^{2}}}+1 \right)\]
done
clear
D)
\[\left( a-\frac{1}{a} \right)\left( {{a}^{2}}+\frac{1}{{{a}^{2}}}+1 \right)\]
done
clear
E)
None of these
done
clear
View Answer play_arrow
Find the Co-ordinates of point P in the adjoining figure.
A)
\[(b,\,-c)\]
done
clear
B)
\[(-\,b,\,c)\]
done
clear
C)
\[(-\,b,\,-c)\]
done
clear
D)
\[(b,\,c)\]
done
clear
E)
None of these
done
clear
View Answer play_arrow
Find the value of \[x:\sqrt{3}x-2=2\sqrt{3}+4\]
A)
\[x=2+2\sqrt{3}\]
done
clear
B)
\[x=-\,2+2\sqrt{3}\]
done
clear
C)
\[x=2-2\sqrt{3}\]
done
clear
D)
\[x=2+3\sqrt{3}\]
done
clear
E)
None of these
done
clear
View Answer play_arrow
Evaluate:\[25x-19-\{3-(4x-5)\}=3x-(6x-5)\]
A)
x = 1
done
clear
B)
x = 5
done
clear
C)
x = 2
done
clear
D)
x = 4
done
clear
E)
None of these
done
clear
View Answer play_arrow
The sum of three consecutive odd natural numbers is 249. Find the numbers
A)
71, 73, 75
done
clear
B)
81, 83, 85
done
clear
C)
61, 63, 65
done
clear
D)
82, 84, 86
done
clear
E)
None of these
done
clear
View Answer play_arrow
The numerator of a fraction is 3 less than denominator. If numerator is added to the denominator then the fraction becomes \[\frac{2}{7}\]. Find the fraction.
A)
\[\frac{1}{7}\]
done
clear
B)
\[\frac{3}{7}\]
done
clear
C)
\[\frac{2}{5}\]
done
clear
D)
\[\frac{3}{5}\]
done
clear
E)
None of these
done
clear
View Answer play_arrow
There are 36 students in a class. The number of boys is twice of the number of girls. There are 13 boys ahead of Sarita who ranked 19th in the class. How many girls are behind Sarita?
A)
5
done
clear
B)
6
done
clear
C)
11
done
clear
D)
12
done
clear
E)
None of these
done
clear
View Answer play_arrow
Consider the diagram given below:
Five hundred candidates appeared in the examination conducted for the test of English, Hindi and Mathematics. The diagram gives the number of candidates who failed in different tests. What is the percentage of candidates who failed in at least two subjects?
A)
0.078%
done
clear
B)
1.0%
done
clear
C)
6.8%
done
clear
D)
7.8%
done
clear
E)
None of these
done
clear
View Answer play_arrow
In an examination, 42% students failed in Hindi and 52% failed in English. If 17% failed in both the subjects, the percentage of those who passed in both the subjects, is:
A)
23%
done
clear
B)
27%
done
clear
C)
34%
done
clear
D)
40%
done
clear
E)
None of these
done
clear
View Answer play_arrow
ABCD is a parallelogram and M is the mid-point of BC. If AB and DM are produced to meet at N, then:
A)
\[AN=\sqrt{3}AB\]
done
clear
B)
\[AN=2AB\]
done
clear
C)
\[A{{N}^{2}}=\frac{3}{2}A{{B}^{2}}\]
done
clear
D)
\[A{{N}^{2}}=2A{{B}^{2}}\]
done
clear
E)
None of these
done
clear
View Answer play_arrow
Which one of the following statement is correct?
A)
\[(a-3)\] is a factor of the polynomial \[={{a}^{3}}+{{a}^{2}}-17a+15\]
done
clear
B)
\[{{a}^{3}}+{{a}^{2}}-17a+15\] divided by \[(a-3)\] leaves 5 as the remainder
done
clear
C)
\[(a-3)\] is factor of the polynomial \[{{a}^{3}}-6{{a}^{2}}+\]\[6a+3\]
done
clear
D)
\[(a-2)\] is a factor of the polynomial \[3{{a}^{4}}-6{{a}^{2}}\]\[-8a+2\]
done
clear
E)
None of these
done
clear
View Answer play_arrow
If\[{{\log }_{3}}a=4\], then find the value of a.
A)
89
done
clear
B)
81
done
clear
C)
92
done
clear
D)
85
done
clear
E)
None of these
done
clear
View Answer play_arrow
Read the following statements carefully:
Statements 1: The equation of a line parallel to y-axis at a distance "a" from origin is x = a Statements 2: The equation of a line parallel to y - axis at a distance \[''-a''\] from origin is \[x-a=0\] Statements 3: The equation of a line parallel to x-axis at a distance \[''-a''\] from origin is \[y-a=0\] Statements 4: The equation of a line parallel to x - axis at a distance "a" from origin is y + a = 0 Which one of the following options represents the correct statements?
A)
1, 2, 3 and 4
done
clear
B)
1, 3 and 4
done
clear
C)
1, 2 and 3
done
clear
D)
2, 3 and 4
done
clear
E)
None of these
done
clear
View Answer play_arrow
In the figure given below, if \[\Delta ABC\cong \Delta QPR\], then the measure of DQPR is:
A)
\[70{}^\circ \]
done
clear
B)
\[60{}^\circ \]
done
clear
C)
\[80{}^\circ \]
done
clear
D)
\[30{}^\circ \]
done
clear
E)
None of these
done
clear
View Answer play_arrow
In the figure \[BD\parallel CE,\] find the value of x, y, z.
A)
\[50{}^\circ ,70{}^\circ ,60{}^\circ \]
done
clear
B)
\[70{}^\circ ,50{}^\circ ,60{}^\circ \]
done
clear
C)
\[50{}^\circ ,60{}^\circ ,70{}^\circ \]
done
clear
D)
\[70{}^\circ ,70{}^\circ ,40{}^\circ \]
done
clear
E)
None of these
done
clear
View Answer play_arrow
In the figure ABCD is a parallelogram. Find the values of X and Y.
A)
\[X=6{}^\circ ,\,Y=10{}^\circ \]
done
clear
B)
\[X=6{}^\circ ,\,Y=7{}^\circ \]
done
clear
C)
\[X=7{}^\circ ,\,Y=6{}^\circ \]
done
clear
D)
\[X=10{}^\circ ,\,Y=9{}^\circ \]
done
clear
E)
None of these
done
clear
View Answer play_arrow
In the figure given below ABCD is a parallelogram and\[\angle CBE=70{}^\circ \]. Find the measure of all angles.
A)
\[60{}^\circ ,120{}^\circ ,60{}^\circ \,and\,120{}^\circ \]
done
clear
B)
\[70{}^\circ ,110{}^\circ ,70{}^\circ \,and\,120{}^\circ \]
done
clear
C)
\[70{}^\circ ,110{}^\circ ,60{}^\circ \,and\,110{}^\circ \]
done
clear
D)
\[70{}^\circ ,110{}^\circ ,70{}^\circ \,and\,110{}^\circ \]
done
clear
E)
None of these
done
clear
View Answer play_arrow
In the parallelogram PQRS given below \[\angle \,P=(5x+25{}^\circ )\] and \[\angle Q=75{}^\circ \]. Find the measure of all angles.
A)
\[105{}^\circ ,75{}^\circ ,105{}^\circ \,and\,\,75{}^\circ \]
done
clear
B)
\[95{}^\circ ,85{}^\circ ,95{}^\circ \,and\,\,85{}^\circ \]
done
clear
C)
\[115{}^\circ ,65{}^\circ ,115{}^\circ \,and\,\,65{}^\circ \]
done
clear
D)
\[105{}^\circ ,75{}^\circ ,45{}^\circ \,and\,\,75{}^\circ \]
done
clear
E)
None of these
done
clear
View Answer play_arrow
In a parallelogram ABCD diagonals AC and BD intersect at O and AC = 12.8 cm and BD = 7.6 cm. Find the measures of OC and OD.
A)
6 cm, 4 cm
done
clear
B)
6.5 cm, 3.5 cm
done
clear
C)
6.4 cm, 3.8 cm
done
clear
D)
5.4 cm, 3.8 cm
done
clear
E)
None of these
done
clear
View Answer play_arrow
In a figure, ABCD is a parallelogram, \[AE\bot DC\] and \[CF\bot AD\]. If AB = 16 cm, AE = 8 cm and CF = 10 cm. Find the value of AD.
A)
13.5 cm
done
clear
B)
13.2 cm
done
clear
C)
12.8 cm
done
clear
D)
12.5 cm
done
clear
E)
None of these
done
clear
View Answer play_arrow
In the figure, ABCD is a quadrilateral in which diagram BD = 20 cm. If \[AL\bot BD\] and\[CM\bot BD\] such that AL = 10 cm and CM = 5 cm, find the area of quad. ABCD.
A)
\[45\,c{{m}^{2}}\]
done
clear
B)
\[52\,c{{m}^{2}}\]
done
clear
C)
\[54\,c{{m}^{2}}\]
done
clear
D)
\[64\,c{{m}^{2}}\]
done
clear
E)
None of these
done
clear
View Answer play_arrow
Peter moves 20 km toward north, turn left and covers a distance of 10 km. Finally he turns left and covers a distance of 40 km. Which one of the following represents the final position of Peter as a coordinate? (take stating point as origin)
A)
\[(-\,10,\,-20)\]
done
clear
B)
\[(10,\,20)\]
done
clear
C)
\[(-\,10,\,-\,40)\]
done
clear
D)
\[(10,\,40)\]
done
clear
E)
None of these
done
clear
View Answer play_arrow
Which one of the following is the correct option
A)
\[Mode=3\,median-2\,mean\]
done
clear
B)
\[Mode=3\,median+2\,mean\]
done
clear
C)
\[2\,Mode=median-2\,mean\]
done
clear
D)
\[2\,Mode=3\,median+4\,mean\]
done
clear
E)
None of these
done
clear
View Answer play_arrow
In a lottery there are 8 prizes and 16 blanks. What is the probability of getting a prize?
A)
\[\frac{1}{2}\]
done
clear
B)
\[\frac{1}{3}\]
done
clear
C)
\[\frac{2}{3}\]
done
clear
D)
\[\frac{4}{5}\]
done
clear
E)
None of these
done
clear
View Answer play_arrow
A cricketer has a mean of 60 runs in ten innings. Find out how many runs are to be scored in the eleventh inning to raise the mean score to
A)
65
done
clear
B)
78
done
clear
C)
80
done
clear
D)
82
done
clear
E)
None of these
done
clear
View Answer play_arrow
The diameter of a copper sphere is 6 cm. The sphere is melted and is drawn into a long wire of uniform circular cross-section. If the length of the wire is 36 cm, find its radius. \[(Take\,\pi =3.14)\]
A)
4 cm
done
clear
B)
3 cm
done
clear
C)
2 cm
done
clear
D)
1 cm
done
clear
E)
None of these
done
clear
View Answer play_arrow
Two circles with centres, A and B, of radii 5 cm and 3 cm respectively touch each other internally. If the perpendicular bisector of segment AB meets the bigger circle in P and Q, find the length of PQ.
A)
\[2\,\sqrt{6}\,cm\]
done
clear
B)
\[3\,\sqrt{6}\,cm\]
done
clear
C)
\[4\,\sqrt{6}\,cm\]
done
clear
D)
\[5\,\sqrt{6}\,cm\]
done
clear
E)
None of these
done
clear
View Answer play_arrow
O is the center of the circle. If\[\angle BAC=50{}^\circ \]. Find the value of\[\angle OBC\].
A)
\[120{}^\circ \]
done
clear
B)
\[100{}^\circ \]
done
clear
C)
\[80{}^\circ \]
done
clear
D)
\[40{}^\circ \]
done
clear
E)
None of these
done
clear
View Answer play_arrow
A bag contains 5 red balls and some blue balls. If the probability of drawing a blue ball is double that of a red ball, find the number of blue balls in the bag.
A)
15
done
clear
B)
12
done
clear
C)
10
done
clear
D)
8
done
clear
E)
None of these
done
clear
View Answer play_arrow