If \[x=\sqrt{15}-\sqrt{13}\] and \[y=\sqrt{15}+\sqrt{13},\] then find the value of\[\left( {{x}^{3}}+80\sqrt{13} \right)-\left( {{y}^{2}}-37\sqrt{13} \right)\].
A)
0
done
clear
B)
1
done
clear
C)
\[2\,\sqrt{13}\]
done
clear
D)
\[\sqrt{3}\]
done
clear
E)
None of these
done
clear
View Answer play_arrow
If \[\frac{{{2}^{3n}}}{8}+1+3\times \frac{{{2}^{n}}}{2}+3\times \frac{{{2}^{2n}}}{4}=729,\] then find the value of n.
A)
3
done
clear
B)
4
done
clear
C)
5
done
clear
D)
6
done
clear
E)
None of these
done
clear
View Answer play_arrow
If \[{{x}^{4}}-{{x}^{3}}+a{{x}^{2}}+x+b\] is exactly divisible by \[(x+\]\[2)\] as well as \[(x-3)\] then _______.
A)
\[a+b=1\]
done
clear
B)
\[a+2b=5\]
done
clear
C)
\[a=b+1\]
done
clear
D)
All the above
done
clear
E)
None of these
done
clear
View Answer play_arrow
\[{{I}^{3}}\,{{(m-n)}^{3}}+{{m}^{3}}\,{{(n-I)}^{3}}+{{n}^{3}}\,{{(I-m)}^{3}}\] equals to ___.
A)
\[{{(lmn)}^{3}}\,(l-m)\,\,(m-n)\,\,(n-l)\]
done
clear
B)
\[(lm+mn+nl)\,\,(3{{l}^{2}}{{m}^{2}}{{n}^{2}})\]
done
clear
C)
\[3\,lmn\,\,(m-n)\,\,(n-l)\,\,(l-m)\]
done
clear
D)
0
done
clear
E)
None of these
done
clear
View Answer play_arrow
In the shown figure, if \[PQ\parallel BC\]and AP = 5.4 cm, AQ = (x + 1) cm, AB = 8.1 cm and \[QC=(x-\]\[1)\]cm, then AC equals to ______.
A)
12 cm
done
clear
B)
6 cm
done
clear
C)
3 cm
done
clear
D)
4 cm
done
clear
E)
None of these
done
clear
View Answer play_arrow
The area of the figure obtained by joining the mid-points of the adjacent sides of a rhombus with diagonals 16 cm and 20 cm is _______.
A)
\[48\,\,c{{m}^{2}}\]
done
clear
B)
\[64\,\,c{{m}^{2}}\]
done
clear
C)
\[80\,\,c{{m}^{2}}\]
done
clear
D)
\[96\,\,c{{m}^{2}}\]
done
clear
E)
None of these
done
clear
View Answer play_arrow
In an event, laddoos of same size were distributed among 400 students in which each student got 1 laddoo. If the size of each laddoos was decreased by 50% then to how many students it could be distributed?
A)
400
done
clear
B)
800
done
clear
C)
1600
done
clear
D)
3200
done
clear
E)
None of these
done
clear
View Answer play_arrow
In a triangle, the average of any two sides is 36 cm more than half of the third side. The area of the triangle (in sq cm) is ___.
A)
\[1028\,\sqrt{3}\]
done
clear
B)
\[1296\,\sqrt{3}\]
done
clear
C)
\[1018\,\sqrt{3}\]
done
clear
D)
\[1024\,\sqrt{3}\]
done
clear
E)
None of these
done
clear
View Answer play_arrow
One card is selected from a well shuffled deck of cards. The probability that it is a black jack is ________.
A)
\[\frac{2}{13}\]
done
clear
B)
\[\frac{1}{52}\]
done
clear
C)
\[\frac{1}{26}\]
done
clear
D)
\[\frac{1}{13}\]
done
clear
E)
None of these
done
clear
View Answer play_arrow
The following observations are arranged in ascending order: 36, 39, 45, 48, x, x + 4, 57, 62, 65, 68. If the median is 52, then the mean of the observations is _______.
A)
52.4
done
clear
B)
50.6
done
clear
C)
51.8
done
clear
D)
51.2
done
clear
E)
None of these
done
clear
View Answer play_arrow
\[\text{cosec}\theta (\sec \theta -1)-\cot \theta (1-\cos \theta )\] equals to _______.
A)
\[\tan \theta +\sin \theta \]
done
clear
B)
\[\tan \theta +\cot \theta \]
done
clear
C)
\[\tan \theta +\cos \theta \]
done
clear
D)
\[\tan \theta -\sin \theta \]
done
clear
E)
None of these
done
clear
View Answer play_arrow
If \[\cot \theta \,(1+\sin \theta )=2\,m\] and \[\cot \theta \,(1-\sin \theta )=2\,n\] then \[{{({{m}^{2}}-{{n}^{2}})}^{2}}\] equals to ____.
A)
2 mn
done
clear
B)
8 mn
done
clear
C)
4 mn
done
clear
D)
3 mn
done
clear
E)
None of these
done
clear
View Answer play_arrow
If \[{{\log }_{3}}4+{{\log }_{3}}7=x-1,\] then find the value of\[\frac{{{\log }_{10}}84}{{{\log }_{10}}28}\].
A)
\[\frac{x}{x+1}\]
done
clear
B)
\[\frac{x+1}{x}\]
done
clear
C)
\[\frac{x-1}{x}\]
done
clear
D)
\[\frac{x}{x-1}\]
done
clear
E)
None of these
done
clear
View Answer play_arrow
\[{{3}^{\frac{2}{^{{{\log }_{{{32}^{9}}}}}}}}+{{8}^{\frac{1}{^{{{\log }_{{{25}^{4}}}}}}}}+{{4}^{\frac{1}{^{{{\log }_{{{27}^{2}}}}}}\,=\_\_\_\_\_\_.}}\]
A)
729
done
clear
B)
150
done
clear
C)
886
done
clear
D)
782
done
clear
E)
None of these
done
clear
View Answer play_arrow
A person purchased an article and sold it at a loss of 20%. If he had brought it for 40% less and sold it for Rs. 30 more, he would have made a profit of 50%. The cost price of the article is _______.
A)
Rs. 300
done
clear
B)
Rs. 240
done
clear
C)
Rs. 225
done
clear
D)
Rs. 250
done
clear
E)
None of these
done
clear
View Answer play_arrow
A boat in the direction of flow covers a distance of 48 km in 4 hours. If the speed of the boat is twice the speed of flow, then how much distance will it cover in 2 hours opposite to the flow?
A)
8 km
done
clear
B)
10 km
done
clear
C)
12 km
done
clear
D)
9 km
done
clear
E)
None of these
done
clear
View Answer play_arrow
Find the remainder where \[2{{x}^{2}}-6{{x}^{3}}+3{{x}^{2}}+\]\[3x-2\] is divided by\[{{x}^{2}}-3x+2\].
A)
\[-\,3\]
done
clear
B)
0
done
clear
C)
1
done
clear
D)
3
done
clear
E)
None of these
done
clear
View Answer play_arrow
In a \[\Delta \,ABC\] if \[\angle A-\angle C=36{}^\circ \] and \[\angle B-\angle C=30{}^\circ ,\] then _____.
A)
\[\angle \,A+2\,\angle \,B=200{}^\circ \]
done
clear
B)
\[\angle B\,+\,2\angle C\,=\,144{}^\circ \]
done
clear
C)
\[\angle \,A+\angle \,B=96{}^\circ \]
done
clear
D)
\[\angle \,A+\angle C=130{}^\circ \]
done
clear
E)
None of these
done
clear
View Answer play_arrow
In the shown figure, for which value of m is \[{{I}_{1}}||{{I}_{2}}\,?\]
A)
\[48{}^\circ \]
done
clear
B)
\[51{}^\circ \]
done
clear
C)
\[49{}^\circ \]
done
clear
D)
\[34{}^\circ \]
done
clear
E)
None of these
done
clear
View Answer play_arrow
In a \[\Delta \,PQR,\] M and N are points on PQ and QR, respectively such that \[MN||PR\] and MN divides the triangular region PQR into two parts equal in area, then \[\frac{PM}{PQ}\] is equal to _______.
A)
\[\frac{2-\sqrt{2}}{2}\]
done
clear
B)
\[\frac{2+\sqrt{2}}{2}\]
done
clear
C)
\[\frac{3-\sqrt{2}}{2}\]
done
clear
D)
\[\frac{3+\sqrt{2}}{2}\]
done
clear
E)
None of these
done
clear
View Answer play_arrow
Which of the following is not a rational number between \[0.1\overline{43}\] and\[0.1\overline{69}\] ?
A)
\[\frac{148}{990}\]
done
clear
B)
\[\frac{85}{495}\]
done
clear
C)
\[\frac{167}{990}\]
done
clear
D)
\[\frac{79}{495}\]
done
clear
E)
None of these
done
clear
View Answer play_arrow
If \[x=233+88\sqrt{7}\] then what will be the value of\[{{x}^{1/4}}-3{{x}^{-1/4}}\] ?
A)
4
done
clear
B)
3
done
clear
C)
2
done
clear
D)
1
done
clear
E)
None of these
done
clear
View Answer play_arrow
A line passes through the points A (2, 8), B (4, 11) and \[C\,(-\,8,\,-\,7)\]. The equation of this line will be ______.
A)
\[3x-y=1\]
done
clear
B)
\[3x-2y=-\,10\]
done
clear
C)
\[2x-y=10\]
done
clear
D)
\[y=3x+2\]
done
clear
E)
None of these
done
clear
View Answer play_arrow
If \[\sin \theta \] and \[\cos \theta \]are the roots of the equation \[a{{x}^{2}}+x+c=0\] where \[a\ne 0\], then which one of the following is true?
A)
\[{{a}^{2}}-2ac=a\]
done
clear
B)
\[{{a}^{2}}+2c=1\]
done
clear
C)
\[{{a}^{2}}+2ac=1\]
done
clear
D)
\[{{a}^{2}}-2ac=1\]
done
clear
E)
None of these
done
clear
View Answer play_arrow
If \[\operatorname{cosec}\theta -\sin \theta =\frac{1}{p}\] and \[\sec \theta -\cos \theta =\frac{1}{q}\], then _______.
A)
\[{{({{p}^{2}}q)}^{\frac{2}{3}}}+{{(p{{q}^{2}})}^{\frac{2}{3}}}=1\]
done
clear
B)
\[{{({{p}^{2}}q)}^{\frac{1}{3}}}+{{(p{{q}^{2}})}^{\frac{1}{3}}}=1\]
done
clear
C)
\[{{\left( \frac{1}{{{p}^{2}}q} \right)}^{\frac{2}{3}}}+{{\left( \frac{1}{p{{q}^{2}}} \right)}^{\frac{2}{3}}}=1\]
done
clear
D)
\[{{\left( \frac{1}{{{p}^{2}}q} \right)}^{\frac{1}{3}}}+{{\left( \frac{1}{p{{q}^{2}}} \right)}^{\frac{1}{3}}}=1\]
done
clear
E)
None of these
done
clear
View Answer play_arrow
If \[\cos ec\theta +\cot \theta =2+\sqrt{5},\] then find the value of\[3\cos \theta -2\sin \theta \].
A)
\[\frac{4}{5}\,\,\sqrt{5}\]
done
clear
B)
\[\frac{2}{5}\,\,\sqrt{5}\]
done
clear
C)
\[\frac{3}{5}\,\,\sqrt{5}\]
done
clear
D)
\[\frac{1}{5}\,\,\sqrt{5}\]
done
clear
E)
None of these
done
clear
View Answer play_arrow
Two coins are tossed 1000 times and the outcomes are recorded as given below:
Number of Tails 0 1 2 Frequency 320 352 328
Based on this information, the probability of getting at least 1 head is ________.
A)
\[\frac{84}{125}\]
done
clear
B)
\[\frac{17}{25}\]
done
clear
C)
\[\frac{81}{125}\]
done
clear
D)
\[\frac{44}{125}\]
done
clear
E)
None of these
done
clear
View Answer play_arrow
Average of 6 distinct natural numbers is 49. If the average of the three largest numbers is found to be 57, then find the difference of the highest and the lowest possible median of these numbers.
A)
52
done
clear
B)
38
done
clear
C)
13
done
clear
D)
17
done
clear
E)
None of these
done
clear
View Answer play_arrow
Find the mode for the following frequency distribution from the table given below.
Class Interval Frequency 0 - 10 5 10 - 20 8 20 - 30 7 30 - 40 12 40 - 50 28 50 - 60 20 60 - 70 10 70 - 80 10
A)
46.67
done
clear
B)
45.2
done
clear
C)
42.2
done
clear
D)
43.2
done
clear
E)
None of these
done
clear
View Answer play_arrow
The area of an equilateral triangle is \[17320\,\,c{{m}^{2}}\]. With each vertex of the triangle a circle is drawn with radius equal to half the length of the side of the triangle. Find the area of the shaded region. \[\left[ Take,\sqrt{3}=1.732\,\,and\,\,\pi =\frac{22}{7} \right]\]
A)
\[992.57\,\,c{{m}^{2}}\]
done
clear
B)
\[1605.71\,\,c{{m}^{2}}\]
done
clear
C)
\[1238.57\,\,c{{m}^{2}}\]
done
clear
D)
\[1732.28\,\,c{{m}^{2}}\]
done
clear
E)
None of these
done
clear
View Answer play_arrow
How many squares are there in the figure given below?
A)
36
done
clear
B)
60
done
clear
C)
77
done
clear
D)
91
done
clear
E)
None of these
done
clear
View Answer play_arrow
If 'PMQE' is coded as '51', then how will 'NRSZ' be coded?
A)
105
done
clear
B)
85
done
clear
C)
98
done
clear
D)
77
done
clear
E)
None of these
done
clear
View Answer play_arrow
Four of the following five are alike in a certain way and so form a group. Which is the one that does not belong to that group?
A)
RPN
done
clear
B)
WSU
done
clear
C)
HDF
done
clear
D)
LHJ
done
clear
E)
QMO
done
clear
View Answer play_arrow
The missing number in place of the question mark (?) in the following table is:
A)
12
done
clear
B)
16
done
clear
C)
26
done
clear
D)
20
done
clear
E)
None of these
done
clear
View Answer play_arrow
Direction: The following questions are based on the information given below:
(i) \['P\times Q'\] means 'P is the father of Q' ;
(ii) \['P-Q'\] means 'P is the sister of Q' ;
(iii) \['P+Q'\]means 'P is the mother of Q' ;
(iv) \['P\div Q'\] means 'P is the brother of Q' ;
In the expression \[B+D\times M\div N,\] how is M related to B?
A)
Granddaughter
done
clear
B)
Son
done
clear
C)
Grandson
done
clear
D)
Granddaughter or Grandson
done
clear
E)
None of these
done
clear
View Answer play_arrow
Direction: The following questions are based on the information given below:
(i) \['P\times Q'\] means 'P is the father of Q' ;
(ii) \['P-Q'\] means 'P is the sister of Q' ;
(iii) \['P+Q'\]means 'P is the mother of Q' ;
(iv) \['P\div Q'\] means 'P is the brother of Q' ;
Which one of the following represents ?J is son of F??
A)
\[J\div R-T\times F\]
done
clear
B)
\[J+R-T\times F\]
done
clear
C)
\[J\div M-N\times F\]
done
clear
D)
\[J-R-T\times F\]
done
clear
E)
None of these
done
clear
View Answer play_arrow
Daksh is taller than Manick but not as tall as Rohan. Somesh is shorter than Daksh but taller than Farhan. Who among them is the tallest?
A)
Daksh
done
clear
B)
Manick
done
clear
C)
Farhan
done
clear
D)
Rohan
done
clear
E)
None of these
done
clear
View Answer play_arrow
Find out the missing number in place of the question mark (?) from the given responses.
A)
32
done
clear
B)
28
done
clear
C)
38
done
clear
D)
30
done
clear
E)
None of these
done
clear
View Answer play_arrow
Direction: In each of the questions below four statements are given followed by four conclusions numbered I, II, III and IV. You have to take the given statements to be true even if there seem to be some variance from commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follow(s) from the given statements disregarding commonly known facts.
Statements: Some rubbers are toys. Some toys are books. Some books are mirrors. No mirror is a glass. Conclusions: (i) Some toys are mirrors. (ii) Some books are glasses. (iii) Some rubbers are mirrors. (iv) No glass is book.
A)
Only I follows
done
clear
B)
Only II follows
done
clear
C)
Either II or IV follows
done
clear
D)
Only III and IV follow
done
clear
E)
None of these
done
clear
View Answer play_arrow
Direction: In each of the questions below four statements are given followed by four conclusions numbered I, II, III and IV. You have to take the given statements to be true even if there seem to be some variance from commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follow(s) from the given statements disregarding commonly known facts.
Statements: All planets are stars. All stars are suns. All suns are moons. Some moons are rocks. Conclusions: I. All suns are planets. II. All suns are stars. III. All moons are stars. IV. Some rocks are stars.
A)
Only I follows
done
clear
B)
Only II follows
done
clear
C)
Only either I or II follows
done
clear
D)
Only III follows
done
clear
E)
None of these
done
clear
View Answer play_arrow
If \[{{m}^{4}}-4{{m}^{3}}+22{{m}^{2}}-36m+18\] is a perfect square for all positive integers m, then how many values of m are possible?
A)
1
done
clear
B)
2
done
clear
C)
0
done
clear
D)
3
done
clear
E)
None of these
done
clear
View Answer play_arrow
Suppose you have a currency named zen in three denominations 1 zen, 10 zens and 500 zens. Find the number of different ways so that you can pay a bill of 1080 zens.
A)
177
done
clear
B)
180
done
clear
C)
184
done
clear
D)
198
done
clear
E)
None of these
done
clear
View Answer play_arrow
A number when divided by 63 gives remainder 37. If this same number is divided by 126, the remainder will be ________.
A)
Either 37 or 26
done
clear
B)
Either 37 or 100
done
clear
C)
Only 37
done
clear
D)
Only 26
done
clear
E)
None of these
done
clear
View Answer play_arrow
Two mutually perpendicular chords PQ and RS meet at a point M inside the circle such that PM = 12 cm, SM = 3 cm, QM = 4 cm. Find the area of the circle. \[\left( Use\,\pi =\frac{22}{7} \right)\]
A)
\[333\,\,\frac{13}{14}\,\,c{{m}^{2}}\]
done
clear
B)
\[213\,\,\frac{5}{7}\,\,c{{m}^{2}}\]
done
clear
C)
\[228\,\,\frac{19}{20}\,\,c{{m}^{2}}\]
done
clear
D)
\[328\,\,\frac{19}{20}\,\,c{{m}^{2}}\]
done
clear
E)
None of these
done
clear
View Answer play_arrow
The value of \[\frac{3}{1+2\,{{\log }_{{{a}^{2}}{{b}^{2}}}}c}+\frac{3}{1+2\,{{\log }_{{{a}^{2}}{{c}^{2}}}}b}+\]\[\frac{3}{1+2\,{{\log }_{{{b}^{2}}{{c}^{2}}}}a}\] is equal to ______.
A)
2
done
clear
B)
4
done
clear
C)
6
done
clear
D)
\[{{\log }_{{{a}^{2}}{{b}^{2}}{{c}^{2}}}}\]
done
clear
E)
None of these
done
clear
View Answer play_arrow
If \[\frac{\sqrt{\sqrt{\sqrt{\sqrt{{{5}^{x-4}}-{{8.7}^{x-6}}-8}}}}}{{{\left( {{2}^{x+2}}-{{3}^{x-6}}-{{10}^{x-5}} \right)}^{\frac{3}{8}}}{{15}^{\frac{-5}{4}}}}={{(3375)}^{\frac{1}{3}}},\] then find the value of x.
A)
6
done
clear
B)
8
done
clear
C)
9
done
clear
D)
10
done
clear
E)
None of these
done
clear
View Answer play_arrow
The ratio of a two digit natural number to the number obtained on reversing its digit is 3 : 8. Find the sum of all the numbers of all such pairs.
A)
212
done
clear
B)
218
done
clear
C)
316
done
clear
D)
108
done
clear
E)
None of these
done
clear
View Answer play_arrow
Find the number of ways in which 504 can be resolved as the product of two factors.
A)
12
done
clear
B)
14
done
clear
C)
15
done
clear
D)
10
done
clear
E)
None of these
done
clear
View Answer play_arrow
If \[\cos x+\sin x=\sqrt{2}\,\cos x,\] then find the value of\[\tan x-\cot x\].
A)
\[-\,2\]
done
clear
B)
\[-\,1\]
done
clear
C)
0
done
clear
D)
1
done
clear
E)
None of these
done
clear
View Answer play_arrow
How many 5 digit numbers have at least one even digit?
A)
86875
done
clear
B)
88775
done
clear
C)
85625
done
clear
D)
87895
done
clear
E)
None of these
done
clear
View Answer play_arrow
