Which one of the following statements is true for a rational number?
A)
It is in the form of \[\frac{p}{q}\], where p and q are integers and \[p\ne 0\]
done
clear
B)
The decimal representation of a rational number is either terminating or non-terminating and non-repeating decimals
done
clear
C)
There are five rational number between two given rational numbers
done
clear
D)
Rational numbers are either terminating or non-terminating and repeating decimals
done
clear
E)
None of these
done
clear
View Answer play_arrow
Read the following statements.
(i) Rational number may or may not be an integer (ii) Some rational number can be represented on a number line (iii) On a number line only rational numbers can be represented (iv) There are infinite number of rational number between two given rational numbers Which one of the following set of statements is correct?
A)
(i) and (ii)
done
clear
B)
(i) and (iv)
done
clear
C)
(i), (iii) and (iv)
done
clear
D)
(i), (ii) and (iv)
done
clear
E)
None of these
done
clear
View Answer play_arrow
Which one of the following is repeating decimals?
A)
\[\frac{22}{7}\]
done
clear
B)
\[\pi \]
done
clear
C)
\[\frac{224}{135}\]
done
clear
D)
\[\frac{154}{448}\]
done
clear
E)
None of these
done
clear
View Answer play_arrow
The length, breadth and height of a room are 5 m 25 cm, 3 m 25 cm and 1 m 25 cm respectively. The length of the longest rod which can measure the three dimensions of the room exactly will be______.
A)
50 cm
done
clear
B)
75 cm
done
clear
C)
1 m
done
clear
D)
25 cm
done
clear
E)
None of these
done
clear
View Answer play_arrow
If the unit digit in the product \[(129\,\,\times \,\,256\,\,\times \,\,{{47}^{*}}\,\,\times \,\,1484)\] is 2, the digit in place of (*) is
A)
1
done
clear
B)
6
done
clear
C)
7
done
clear
D)
4
done
clear
E)
None of these
done
clear
View Answer play_arrow
Find the remainder when \[p(y)=12{{y}^{3}}-13{{y}^{2}}-\]\[6y+7\] is divided by\[3y+4\].
A)
\[36\,\,\frac{5}{9}\]
done
clear
B)
\[-\,36\,\,\frac{5}{9}\]
done
clear
C)
36
done
clear
D)
\[-\,\,\frac{829}{9}\]
done
clear
E)
None of these
done
clear
View Answer play_arrow
Factorise: \[7\,{{(a+b)}^{2}}-14\,(a+b)\].
A)
\[(a+b)\,\,\left[ 7(a+b)-14 \right]\]
done
clear
B)
\[7\,\left[ {{(a+b)}^{2}}-2\,(a+b) \right]\,\]
done
clear
C)
\[7\,(a+b)\,\,(a+b-2)\]
done
clear
D)
\[7\,(a+b)\,\,(a+b-2a)\]
done
clear
E)
None of these
done
clear
View Answer play_arrow
If \[(3-2x)\] and \[(5x+8)\] are factors of \[(-10{{x}^{2}}+hx-k)\] then the value of h and k are________.
A)
\[(-\,31,\,24)\]
done
clear
B)
(31, 24)
done
clear
C)
\[(-\,31,-\,24)\]
done
clear
D)
\[(31,-\,24)\]
done
clear
E)
None of these
done
clear
View Answer play_arrow
If a and b are two positive integers such that \[a+b+ab+1=77\] then find the possible value of \[a+b.\]
A)
16
done
clear
B)
18
done
clear
C)
22
done
clear
D)
23
done
clear
E)
None of these
done
clear
View Answer play_arrow
Which one of the following equations is not a linear equation in two variable?
A)
\[4x+\frac{7}{2}y=4\]
done
clear
B)
\[\frac{4}{{{x}^{2}}}+\frac{7}{y}=4\]
done
clear
C)
\[\frac{x+3}{y-3}=4\]
done
clear
D)
\[3x+7y+87=0\]
done
clear
E)
None of these
done
clear
View Answer play_arrow
Which one of the following options is correct?
A)
Linear equation in two variables is in the form of \[ax+by+c=0,\] where \[a=0\]
done
clear
B)
Linear equation in two variables is in the form \[px+qx+c=0\]
done
clear
C)
Linear equation in two variables is in the form of \[sx+ty+r=0,\] where s, r and t are constants and \[s,\,\,t\ne 0\]
done
clear
D)
Linear equation in three variables is\[ax+by+c=0,\] where a, b, c are constants and \[a,\,b\ne 0\]
done
clear
E)
None of these
done
clear
View Answer play_arrow
The area bounded by y-axis, \[2x+3y=12\] and \[x-y=1\] is_______.
A)
7.5 square unit
done
clear
B)
13.5 square unit
done
clear
C)
4.5 square unit
done
clear
D)
75 square unit
done
clear
E)
None of these
done
clear
View Answer play_arrow
In the figure given below shows a pentagon in which TU drawn parallel to SP meet QP produced at U and RV parallel to SQ, meet PQ produced at V then:
A)
\[ar(pentagonPQRST)=ar(\square STUP)+ar\]\[(\Delta QRV)\]
done
clear
B)
\[ar(pentagonPQRST)=ar(\square STUQ)\]
done
clear
C)
\[ar(pentagonPQRST)=ar(\square STUQ)+ar\]\[(\Delta TUP)\]
done
clear
D)
\[ar(pentagonPQRST)=ar(\square STUQ)+ar\]\[(\Delta QRV)\]
done
clear
E)
None of these
done
clear
View Answer play_arrow
In a trapezium non parallel sides are equal. When we join the mid-point of diagonals and parallel sides a quadrilateral is formed, the quadrilateral formed is________.
A)
Rhombus
done
clear
B)
Rectangle
done
clear
C)
Trapezium
done
clear
D)
Square
done
clear
E)
None of these
done
clear
View Answer play_arrow
For a trapezium which one of the following statements is correct?
A)
Adjacent sides are parallel
done
clear
B)
One pair of opposite sides are parallel
done
clear
C)
The line joining the mid points of the diagonal is parallel to the parallel side and equal to half their differences
done
clear
D)
The line joining the mid points of the diagonal is parallel to the parallel side and equal to their differences
done
clear
E)
None of these
done
clear
View Answer play_arrow
In the adjoining figures which one have the equal value of angle x?
A)
I and II
done
clear
B)
II and III
done
clear
C)
III and IV
done
clear
D)
I and IV
done
clear
E)
None of these
done
clear
View Answer play_arrow
In an isosceles D PQR in which PQ = QR. A circle which passes through P and R intersect at point L and M to the side PQ and QR respectively as shown in the figure then which one of the following is true?
A)
L and M are the mid points of PQ and QR respectively
done
clear
B)
\[LM=PR\]
done
clear
C)
\[LM\parallel PR\]
done
clear
D)
\[\angle \,PQR=\angle \,QLM\]
done
clear
E)
None of these
done
clear
View Answer play_arrow
In the figure given below which one of the following relations is correct?
A)
\[\angle \,m=\angle \,I+\angle \,n\]
done
clear
B)
\[\angle \,I=\angle \,m-\angle \,n\]
done
clear
C)
\[\angle \,m=\angle \,n-\angle \,I\]
done
clear
D)
\[\angle \,n=\angle \,m-\angle \,I\]
done
clear
E)
None of these
done
clear
View Answer play_arrow
Find the radius of circle if a chord of length is 30 cm which is drawn at a distance of 8 cm from the centre of circle.
A)
17 cm
done
clear
B)
15 cm
done
clear
C)
4 cm
done
clear
D)
12 cm
done
clear
E)
None of these
done
clear
View Answer play_arrow
In the figure given below PQ is the diametre of the circle with centre O. If PT and QS are the perpendicular to the line I, and QS meet the circle at point R then which one of the following is correct?
A)
\[\Delta \,PRT\] is acute angled triangle
done
clear
B)
\[TP=RS\]
done
clear
C)
Quadrilateral RPST is a square
done
clear
D)
\[\angle \,SRP\] is obtuse angle
done
clear
E)
None of these
done
clear
View Answer play_arrow
The circumcentre of a circle whose vertices are\[(-\,1,\,0),\] \[(7,-\,6)\] and \[(-\,2,3)\] is________.
A)
(5, 0)
done
clear
B)
\[(3,\,-3)\]
done
clear
C)
\[(-\,3,\,3)\]
done
clear
D)
(4, 3)
done
clear
E)
None of these
done
clear
View Answer play_arrow
Find the coordinate of point which trisect the line segment joining the points (1, 3) and (3, 9).
A)
\[\left( 5,\text{ }5 \right),\,\,\left( 3,\text{ }3 \right)\]
done
clear
B)
\[\left( 5,\text{ }5 \right),\,\,\left( 7,\text{ }7 \right)\]
done
clear
C)
\[\left( \frac{5}{3},\,\,5 \right),\,\left( \frac{7}{3},\,\,7 \right)\]
done
clear
D)
\[\left( \frac{5}{3},\,\,\frac{7}{3} \right),\,\left( 5,7 \right)\]
done
clear
E)
None of these
done
clear
View Answer play_arrow
The distance of point \[(X\sin \theta ,\,X\cos \theta )\] from the origin is_______.
A)
\[\pm \,x\]
done
clear
B)
x
done
clear
C)
\[\sqrt{x}\]
done
clear
D)
\[{{x}^{\frac{3}{2}}}\]
done
clear
E)
None of these
done
clear
View Answer play_arrow
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
done
clear
B)
4 : 3
done
clear
C)
3 : 2
done
clear
D)
3 : 4
done
clear
E)
None of these
done
clear
View Answer play_arrow
The distance travelled by the tip of minute hand in 10 minutes when the length of it is 20 cm, is ________.
A)
0.2095 m
done
clear
B)
20.95 cm
done
clear
C)
2.095 cm
done
clear
D)
209.5 cm
done
clear
E)
None of these
done
clear
View Answer play_arrow
The diametre of the wheel of a bicycle is 40 cm. The speed of bicycle if it makes 1/2 revolution in 10 second is _____.
A)
\[4\,\pi \,\,cm/\min \]
done
clear
B)
\[0.4\,\pi \,\,cm/\sec \]
done
clear
C)
\[4\,\pi \,\,m/\sec \]
done
clear
D)
\[4\,\pi \,cm/\sec \]
done
clear
E)
None of these
done
clear
View Answer play_arrow
Find the mean of the following data:
Class Interval Frequency 0 ? 10 7 10 ? 20 8 20 ? 30 12 30 - 40 13 40 ? 50 10
A)
25.6
done
clear
B)
27.2
done
clear
C)
23.3
done
clear
D)
24.5
done
clear
E)
None of these
done
clear
View Answer play_arrow
If the mean of the following frequency distribution is 54, then find the value of P.
Class Interval Frequency 0 ? 20 7 20 ? 40 P 40 ? 60 10 60 ? 80 9 80 ? 100 13
A)
P = 8
done
clear
B)
P = 9
done
clear
C)
P = 10
done
clear
D)
P = 11
done
clear
E)
None of these
done
clear
View Answer play_arrow
Find the arithmetic mean of the following frequency distribution:
Class Interval 25 - 29 30 - 34 35 - 39 40 - 44 45 - 49 50 - 54 55 - 59 Frequency 14 22 16 6 5 3 4
A)
36.46
done
clear
B)
36.36
done
clear
C)
48.56
done
clear
D)
99.95
done
clear
E)
None of these
done
clear
View Answer play_arrow
Find the area of the triangle whose base = 25 cm and height =10.8 cm.
A)
\[125\,\,c{{m}^{2}}\]
done
clear
B)
\[135\,\,c{{m}^{2}}\]
done
clear
C)
\[124\,\,c{{m}^{2}}\]
done
clear
D)
\[199\,\,c{{m}^{2}}\]
done
clear
E)
None of these
done
clear
View Answer play_arrow
A chord of a circle of radius 14 cm makes a right angle of the centre. Find the area of the major segments of the circle.
A)
\[590\,\,c{{m}^{2}}\]
done
clear
B)
\[560\,\,c{{m}^{2}}\]
done
clear
C)
\[595\,\,c{{m}^{2}}\]
done
clear
D)
\[995\,\,c{{m}^{2}}\]
done
clear
E)
None of these
done
clear
View Answer play_arrow
The base of a triangular field is twice its altitude. If the cost of ploughing the field at Rs. 3.75 per \[100\,\,{{m}^{2}}\] is Rs. 13500. Find the altitude and the base of the field
A)
1240 m, 400 m
done
clear
B)
1200 m, 600 m
done
clear
C)
1350 m, 200 m
done
clear
D)
9050 m, 100 m
done
clear
E)
None of these
done
clear
View Answer play_arrow
The length of a rectangular plot of land is twice its breadth. If the perimetre of the plot is 20 m then find its area.
A)
\[2450\,\,{{m}^{2}}\]
done
clear
B)
\[2251\,\,{{m}^{2}}\]
done
clear
C)
\[5560\,\,{{m}^{2}}\]
done
clear
D)
\[9060\,\,{{m}^{2}}\]
done
clear
E)
None of these
done
clear
View Answer play_arrow
The inner diametre of a glass is 7 cm and it has a raised portion at the bottom in the shape of a hemisphere as shown in the figure. If the height of the glass is 16 cm then find the apparent capacity and the actual capacity of the glass.
A)
\[616\,\,c{{m}^{3}},\,\,526.17\,\,c{{m}^{3}}\]
done
clear
B)
\[616\,\,c{{m}^{3}},\,\,1527.95\,\,c{{m}^{3}}\]
done
clear
C)
\[616\,\,c{{m}^{3}},\,\,886.16\,\,c{{m}^{3}}\]
done
clear
D)
\[616\,\,c{{m}^{3}},\,\,9.58\,\,c{{m}^{3}}\]
done
clear
E)
None of these
done
clear
View Answer play_arrow
Find the probability of getting head, if the coin is two headed.
A)
1
done
clear
B)
\[\frac{1}{2}\]
done
clear
C)
\[\frac{1}{3}\]
done
clear
D)
\[\frac{1}{4}\]
done
clear
E)
None of these
done
clear
View Answer play_arrow
What is the probability that an ordinary year has 53 Sunday?
A)
\[\frac{1}{2}\]
done
clear
B)
\[\frac{1}{3}\]
done
clear
C)
\[\frac{1}{4}\]
done
clear
D)
\[\frac{1}{7}\]
done
clear
E)
None of these
done
clear
View Answer play_arrow
One card is drawn from a well shuffled deck of 52 cards. What is the probability of getting a black face card?
A)
\[\frac{1}{26}\]
done
clear
B)
\[\frac{3}{14}\]
done
clear
C)
\[\frac{3}{26}\]
done
clear
D)
\[\frac{3}{13}\]
done
clear
E)
None of these
done
clear
View Answer play_arrow
If \[q(x)=3{{x}^{4}}-5{{x}^{3}}+{{x}^{2}}+8\] then find the value of \[q\,(-\,1).\]
A)
17
done
clear
B)
11
done
clear
C)
13
done
clear
D)
16
done
clear
E)
None of these
done
clear
View Answer play_arrow
Find the factor of \[{{(a-b)}^{3}}+{{(b-c)}^{3}}+{{(c-a)}^{3}}.\]
A)
\[3\,\,(a+b)\,\,(b+c)\,\,(c\,-a)\]
done
clear
B)
\[3\,\,(a-b)\,\,(b-c)\,\,(c+a)\]
done
clear
C)
\[3\,\,(a-b)\,\,(b+c)\,\,(c\,+a)\]
done
clear
D)
\[3\,\,(a-b)\,\,(b-c)\,\,(c-a)\]
done
clear
E)
None of these
done
clear
View Answer play_arrow
The point (3, 0) lies on _______.
A)
\[x-axis\]
done
clear
B)
\[y-axis\]
done
clear
C)
I quadrant
done
clear
D)
II quadrant
done
clear
E)
None of these
done
clear
View Answer play_arrow