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question_answer1)
Which of the following numbers have terminating decimal expansion?
A)
\[\frac{8}{225}\] done
clear
B)
\[\frac{5}{18}\] done
clear
C)
\[\frac{11}{21}\] done
clear
D)
\[\frac{21}{150}\] done
clear
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question_answer2)
A positive integer n when divided by 9, gives 7 as remainder. What will be the remainder when \[(3n-1)\] is divided by 9?
A)
1 done
clear
B)
2 done
clear
C)
3 done
clear
D)
4 done
clear
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question_answer3)
The fraction \[\frac{2\left( \sqrt{2}+\sqrt{6} \right)}{3\left( \sqrt{2}+\sqrt{3} \right)}\] is equal to___ .
A)
\[\frac{2\sqrt{2}}{3}\] done
clear
B)
1 done
clear
C)
\[\frac{2\sqrt{3}}{3}\] done
clear
D)
\[\frac{4}{3}\] done
clear
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question_answer4)
\[1.22\overline{4}\]can be expressed as a fraction in simplest form as ____.
A)
\[\frac{450}{551}\] done
clear
B)
\[\frac{1224}{1000}\] done
clear
C)
\[\frac{551}{450}\] done
clear
D)
\[\frac{1000}{1224}\] done
clear
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question_answer5)
Given that H.C.F. (306, 954, 1314) = 18, find L.C.M. (306, 954, 1314).
A)
1183234 done
clear
B)
1123238 done
clear
C)
1183914 done
clear
D)
1123328 done
clear
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question_answer6)
If 'a' and 'b' are rational numbers and \[\frac{2+\sqrt{3}}{2-\sqrt{3}}=a+b\sqrt{3},\]then \[{{(a+b)}^{2}}=\_\_\_\_\_\_\_.\]
A)
121 done
clear
B)
171 done
clear
C)
116 done
clear
D)
198 done
clear
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question_answer7)
The descending order of the surds \[\sqrt[3]{2},\sqrt[6]{3},\sqrt[9]{4}\]is,__
A)
\[\sqrt[6]{4},\sqrt[6]{3},\sqrt[3]{2}\] done
clear
B)
\[\sqrt[9]{4},\sqrt[3]{2},\sqrt[6]{3}\] done
clear
C)
\[\sqrt[3]{2},\sqrt[6]{3},\sqrt[9]{4}\] done
clear
D)
\[\sqrt[6]{3},\sqrt[9]{4},\sqrt[3]{2}\] done
clear
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question_answer8)
The product of two consecutive natural numbers is always ____-
A)
An even number done
clear
B)
An odd number done
clear
C)
A prime number done
clear
D)
Divisible by 3 done
clear
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question_answer9)
The value of \[\frac{1}{1+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{4}}+\frac{1}{\sqrt{4}+\sqrt{5}}+\frac{1}{\sqrt{5}+\sqrt{6}}\] \[+\frac{1}{\sqrt{6}+\sqrt{7}}+\frac{1}{\sqrt{7}+\sqrt{8}}+\frac{1}{\sqrt{8}+\sqrt{9}}\] is _____.
A)
0 done
clear
B)
1 done
clear
C)
2 done
clear
D)
4 done
clear
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question_answer10)
The 100th root of \[{{10}^{({{10}^{10}})}}\] is ___.
A)
\[{{10}^{{{8}^{10}}}}\] done
clear
B)
\[{{10}^{{{10}^{8}}}}\] done
clear
C)
\[{{\left( \sqrt{10} \right)}^{{{\left( \sqrt{10} \right)}^{10}}}}\] done
clear
D)
\[{{10}^{{{\left( \sqrt{10} \right)}^{\sqrt{10}}}}}\] done
clear
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question_answer11)
The value of \[\frac{a+\sqrt{{{a}^{2}}-{{b}^{2}}}}{a-\sqrt{{{a}^{2}}-{{b}^{2}}}}+\frac{a-\sqrt{{{a}^{2}}-{{b}^{2}}}}{a+\sqrt{{{a}^{2}}-{{b}^{2}}}}\] is __.
A)
\[\frac{{{a}^{2}}}{{{b}^{2}}}\] done
clear
B)
\[\frac{{{b}^{2}}}{{{a}^{2}}}\] done
clear
C)
\[\frac{a}{b}\] done
clear
D)
\[\frac{2(2{{a}^{2}}-{{b}^{2}})}{{{b}^{2}}}\] done
clear
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question_answer12)
The rationalizing factor of \[\sqrt[7]{{{x}^{3}}{{y}^{5}}{{z}^{2}}}\] is __.
A)
\[\sqrt[7]{{{z}^{5}}{{y}^{2}}{{x}^{4}}}\] done
clear
B)
\[\sqrt[47]{{{x}^{3}}{{y}^{2}}z}\] done
clear
C)
\[\sqrt{{{x}^{4}}{{y}^{2}}{{z}^{5}}}\] done
clear
D)
\[\sqrt[3]{{{y}^{2}}{{x}^{4}}{{z}^{3}}}\] done
clear
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question_answer13)
Which of the following is an irrational number?
A)
\[\pi \] done
clear
B)
\[\frac{22}{7}\] done
clear
C)
Both (a) and (b) done
clear
D)
Neither (a) nor (b) done
clear
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question_answer14)
A real number \[\frac{{{2}^{2}}\times {{3}^{2}}\times {{7}^{3}}}{{{2}^{2}}\times {{5}^{3}}\times {{3}^{5}}\times {{7}^{4}}}\]will have _______.
A)
Terminating decimal expansion done
clear
B)
Non-terminating decimal expansion done
clear
C)
Repeating decimal expansion done
clear
D)
Both (b) and (c) done
clear
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question_answer15)
According to the Fundamental Theorem of Arithmetic, if p (a prime number) divides \[{{b}^{2}}\]and b is positive, then _____.
A)
b divides p done
clear
B)
\[{{b}^{2}}\]divides p done
clear
C)
p divides b done
clear
D)
None of these done
clear
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question_answer16)
In a seminar the number of participants in Mathematics, Physics and Biology are 192 240 and 168. Find the minimum number of rooms required if in each room same number of participants is to be seated and all of them being in the same subject.
A)
20 done
clear
B)
25 done
clear
C)
28 done
clear
D)
30 done
clear
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question_answer17)
Sam, Advik and Trishu go for a morning walk. They step off together and their steps measure 35 cm, 32 cm and 40 cm, respectively. What is the minimum distance each should walk so that each can cover the same distance in complete steps?
A)
1109 done
clear
B)
1102 done
clear
C)
1100 done
clear
D)
1120 done
clear
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question_answer18)
A boy multiplied 987 by a certain number and obtained 559981 as his answer. If in the answer both 9s are wrong and the other digits are correct, then the correct answer would be _____.
A)
553681 done
clear
B)
555181 done
clear
C)
555681 done
clear
D)
556581 done
clear
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question_answer19)
A boy was asked to multiply a given number by (8/17). Instead, he divided the given number by (8/17) and got the result 225 more than what he should have got if he had multiplied the number by (8/17). The given number was _____.
A)
8 done
clear
B)
17 done
clear
C)
64 done
clear
D)
136 done
clear
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question_answer20)
Four different electronic devices make a beep after every 30 minutes, 1 hour, \[1\frac{1}{2}\]hour and 1 hour 45 minutes respectively. All the devices beeped together at 12 noon. They will again beep together at _____.
A)
12 midnight done
clear
B)
3a.m. done
clear
C)
6a.m. done
clear
D)
9a.m. done
clear
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question_answer21)
Which of the following statements is INCORRECT?
A)
For natural numbers a and b, if a divides \[{{b}^{2}}\]then a divides b. done
clear
B)
For any natural number \[n,\,\sqrt{n-1}+\sqrt{n+1}\]is irrational. done
clear
C)
Product of distinct prime numbers is always equal to their L.C.M. done
clear
D)
For any natural number n, \[{{6}^{n}}\] never ends with digit zero. done
clear
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question_answer22)
Fill in the blanks.
(i) Every point on the number line is a P number which may either Q or R. |
(ii) S numbers have either terminating or non-terminating repeating decimal expansion. |
A)
B)
C)
D)
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question_answer23)
Match the following.
Column-l | Column-II |
(P) Rational form of \[0.\overline{32}\]is | (i) \[\frac{14}{55}\] |
(Q) Rational form of \[0.\overline{254}\]is | (ii) \[\frac{11}{45}\] |
(R) Rational form of \[0.\overline{12}\]is | (iii) \[\frac{32}{99}\] |
(S) Rational form of \[0.\overline{24}\]is | (iv) \[\frac{11}{90}\] |
A)
(P)\[\to \](iii);(Q)\[\to \](iv);(R)\[\to \](i);(S)\[\to \](ii) done
clear
B)
(P)\[\to \](iv);(Q)\[\to \](i);(R)\[\to \](ii);(S)\[\to \](iii) done
clear
C)
(P)\[\to \](iii);(Q)\[\to \](i);(R) \[\to \](iv);(S)\[\to \](ii) done
clear
D)
(P)\[\to \](i);(Q)\[\to \](iii);(R)\[\to \](iv);(S)\[\to \](ii) done
clear
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question_answer24)
A charitable trust donates 28 different; books of Maths, 16 different books of Science and 12 different books of Social Science to poor students. Each student. is given maximum number of books of only one subject of their interest and each student got equal number of books. (a) Find the number of books each student got. (b) Find the total number of students who got books.
A)
B)
C)
D)
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question_answer25)
Read the statements carefully and state 'T for true and 'F' for false.
(i) \[\frac{501}{25}\] is a terminating decimal, |
(ii) \[\frac{621}{125}\] is a non-terminating decimal. |
(iii) \[\frac{6805}{27\times {{5}^{2}}}\] is a non-terminatina decimal. |
(iv) \[\frac{7105}{7\times {{5}^{2}}}\] is a terminating decimal, |
A)
B)
C)
D)
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