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question_answer1)
For \[P\in N,\] \[{{\mathbf{3}}^{\mathbf{4P}}}\text{ }-\text{ }{{\mathbf{2}}^{\mathbf{4P}}}\]is always divisible by ____
A)
15 done
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B)
5 done
clear
C)
13 done
clear
D)
Both B and C done
clear
E)
None of these done
clear
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question_answer2)
The greatest number of 5 digits exactly divisible by 15, 24 and 36 is ____
A)
99620 done
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B)
99720 done
clear
C)
99968 done
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D)
99960 done
clear
E)
None of these done
clear
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question_answer3)
The greatest number of 6 digits exactly divisible by all the numbers between 1 and 10 (both inclusive) is ________
A)
997920 done
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B)
999768 done
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C)
999660 done
clear
D)
999760 done
clear
E)
None of these done
clear
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question_answer4)
The smallest three digit number which leaves remainders 8 and 12 when divided by 28 and 32 respectively, is _________
A)
102 done
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B)
222 done
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C)
202 done
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D)
204 done
clear
E)
None of these done
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question_answer5)
If \[\mathbf{P=}\sqrt{\mathbf{n-1}}\mathbf{+}\sqrt{\mathbf{n+1}}\] where n is a positive integer then the value of P is
A)
a rational number done
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B)
not a rational number done
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C)
an integer done
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D)
a natural number done
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E)
None of these done
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question_answer6)
The largest number that will divide 398, 606 and 474 leaving remainders 7, 11 and 15 respectively is ________
A)
52 done
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B)
26 done
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C)
17 done
clear
D)
18 done
clear
E)
None of these done
clear
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question_answer7)
Which one among the following statements is true?
A)
The remainder when the square of any number is divided by 4 is 1 or 0. done
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B)
There is no natural number for which 4 ends with digit zero. done
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C)
A positive integer n is prime, if no prime p less than or equal to \[\sqrt{n}\] divides n. done
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D)
All the above done
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E)
None of these done
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question_answer8)
The unit value of \[{{\mathbf{6}}^{\mathbf{100}}}\mathbf{- }{{\mathbf{5}}^{\mathbf{100}}}\] is ______
A)
0 done
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B)
1 done
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C)
2 done
clear
D)
3 done
clear
E)
None of these done
clear
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question_answer9)
For any odd natural number n,\[\mathbf{(}{{\sqrt{\mathbf{3)}}}^{\mathbf{4n}}}\mathbf{+(}{{\sqrt{\mathbf{2)}}}^{\mathbf{4n}}}\] is always divisible by ______
A)
5 done
clear
B)
7 done
clear
C)
17 done
clear
D)
13 done
clear
E)
None of these done
clear
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question_answer10)
If I is a positive integer then \[{{(I)}^{2}}\] will be in the form of ????
A)
4m for some integer m done
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B)
8m for some integer m done
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C)
4m+1 for some integer m done
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D)
Both A and C done
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E)
None of these done
clear
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question_answer11)
Which among the following statements is not true?
A)
The square of any odd integer is of the form 4q + 1, for some integer q. done
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B)
For any odd integer p, \[{{p}^{2}}\]- 1 is divisible by 8. done
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C)
If p and q are both odd positive integers/ then \[{{p}^{2}}+\text{ }{{q}^{2}}\]is even and divisible by 4. done
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D)
For any natural number n, \[{{12}^{n}}\]cannot end with the digit 0 or 5. done
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E)
None of these done
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question_answer12)
For any natural number n, \[{{(2n+1)}^{2}}-1\] is always divisible by ______
A)
2 done
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B)
4 done
clear
C)
8 done
clear
D)
All the above done
clear
E)
None of these done
clear
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question_answer13)
Which of the following statements is always true?
A)
The sum or difference of a rational and an irrational number is rational. done
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B)
Every irrational number is a surd. done
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C)
The product or quotient of a non-zero rational number and an irrational number is irrational. done
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D)
All the above done
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E)
None of these done
clear
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question_answer14)
The value of \[{{\mathbf{(27)}}^{\mathbf{3p}}}\mathbf{-(13}{{\mathbf{)}}^{\mathbf{3p}}}\]ends in ______ (where p is a natural number)
A)
0 done
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B)
4 done
clear
C)
6 done
clear
D)
Either B or C done
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E)
None of these done
clear
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question_answer15)
If \[P=1\cdot 3\cdot 5\cdot 7.............\,21\] and\[Q=2\cdot 4\cdot 6\cdot 8\cdot 10\,............\,22\] then HCF of P and Q is ________
A)
12375 done
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B)
14175 done
clear
C)
825 done
clear
D)
925 done
clear
E)
None of these done
clear
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question_answer16)
In a seminar, the numbers of participants in science, English and Mathematics are 144, 180 and 192 respectively. Find the minimum number of rooms required if in each room the same number of participants are to be seated and all of them being in the same subject.
A)
38 done
clear
B)
40 done
clear
C)
43 done
clear
D)
45 done
clear
E)
None of these done
clear
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question_answer17)
Without actually performing the Song division, choose which among the following rational numbers will not have a terminating decimal expansion.
A)
\[\frac{123}{16}\] done
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B)
\[\frac{351}{{{2}^{7}}\times {{5}^{8}}\times {{7}^{18}}}\] done
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C)
\[\frac{32}{{{2}^{8}}\times {{5}^{9}}}\] done
clear
D)
\[\frac{833}{49\times {{2}^{7}}}\] done
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E)
None of these done
clear
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question_answer18)
The largest number that divides 588, 1999 and 1650 leaving 3, 10 and 12 respectively is _____
A)
117 done
clear
B)
109 done
clear
C)
27 done
clear
D)
43 done
clear
E)
None of these done
clear
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question_answer19)
The decimal expansion of the rational number \[\frac{\mathbf{12879}}{\mathbf{1250}}\] will terminate after:
A)
One decimal places done
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B)
Two decimal places done
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C)
Three decimal places done
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D)
Four decimal places done
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E)
None of these done
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question_answer20)
Find the greatest prime factor in 527527.
A)
17 done
clear
B)
11 done
clear
C)
13 done
clear
D)
31 done
clear
E)
None of these done
clear
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question_answer21)
If p is a single digit natural number and the unit digits of \[{{\mathbf{p}}^{\mathbf{4}}}\]and p are same, then how many possibilities p can assume?
A)
2 done
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B)
3 done
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C)
4 done
clear
D)
5 done
clear
E)
None of these done
clear
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question_answer22)
The sum of LCM and HCF of two numbers is 29610. If their LCM is 140 times v the HCF of the numbers then which among the following can be one of the numbers?
A)
330 done
clear
B)
1470 done
clear
C)
525 done
clear
D)
462 done
clear
E)
None of these done
clear
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question_answer23)
The value of \[{{\left( 22 \right)}^{{{3}^{\,m}}}}+\text{ }{{\left( 28 \right)}^{3{{\,}^{m}}}}\] ends in ______\[\{M\in N\}\].
A)
8 done
clear
B)
2 done
clear
C)
6 done
clear
D)
0 done
clear
E)
None of these done
clear
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question_answer24)
If LCM and HCF of two numbers are 324 and 18 respectively, then how many such pairs of numbers are possible?
A)
0 done
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B)
1 done
clear
C)
2 done
clear
D)
3 done
clear
E)
None of these done
clear
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question_answer25)
If \[\mathbf{p=}\sqrt{\mathbf{11}}\mathbf{+}\sqrt{\mathbf{5}}\mathbf{,}\,\,\mathbf{q=}\sqrt{\mathbf{14}}\mathbf{+}\sqrt{\mathbf{2}}\] and\[\mathbf{r=}\sqrt{\mathbf{13}}\mathbf{+}\sqrt{\mathbf{3}}\] then which one of the following holds true?
A)
p > q > r done
clear
B)
p < q < r done
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C)
p > r > q done
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D)
p < r < q done
clear
E)
None of these done
clear
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question_answer26)
The number of ways, in which 360 can be resolved in two factors, is ______
A)
24 done
clear
B)
18 done
clear
C)
12 done
clear
D)
15 done
clear
E)
None of these done
clear
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question_answer27)
If \[u=\sqrt[16]{7}+\sqrt[16]{5},\] \[v=\sqrt{7}+\sqrt{5},\] \[w=\sqrt[8]{7}+\sqrt[8]{5},\]\[x=\sqrt[16]{7}-\sqrt[16]{5},\] and \[y=\sqrt[4]{7}+\sqrt[4]{5},\] then which one of the following is a rational number?
A)
uvxy done
clear
B)
uvwxy done
clear
C)
uxwy done
clear
D)
vwxy done
clear
E)
None of these done
clear
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question_answer28)
A mason has to fit two bathrooms with square marble tiles of the largest possible size. The dimensions of each such bathroom are 12 fts and 10 fts. If the size of the tiles in inches has to be taken then number of such tiles required is ____
A)
15 done
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B)
30 done
clear
C)
60 done
clear
D)
80 done
clear
E)
None of these done
clear
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question_answer29)
If HCF of 374 and 255 is H and H = 255m + 374n then the value of m - n is equal to _____
A)
3 done
clear
B)
4 done
clear
C)
5 done
clear
D)
1 done
clear
E)
None of these done
clear
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question_answer30)
Choose which one among the following statement is incorrect?
A)
HCF of two co-primes a and b is 1. done
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B)
LCM of two co-primes m and n is mn. done
clear
C)
By using Euclid's division lemma for two numbers 155 and 345, we get 345 = 155 \[\mathbf{\times }\] 2 + 35. done
clear
D)
The remainder, when the square of any prime number greater than 3 is divided by 6, is 1. done
clear
E)
None of these done
clear
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question_answer31)
If LCM and HCF of two numbers are 3003 and 21 respectively, then how many such numbers are possible?
A)
0 done
clear
B)
1 done
clear
C)
2 done
clear
D)
3 done
clear
E)
None of these done
clear
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question_answer32)
The largest number which divides 1288 and 2915 and leaves the remainders 1 and 8 respectively, is H and it satisfies the expression, H = 45m + 288n. Find the value of m + n.
A)
11 done
clear
B)
15 done
clear
C)
13 done
clear
D)
10 done
clear
E)
None of these done
clear
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question_answer33)
The smallest number, which when increased by 19 is exactly divisible by both 2079 and 1404, is _______
A)
6200 done
clear
B)
625 done
clear
C)
6218 done
clear
D)
3208 done
clear
E)
None of these done
clear
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question_answer34)
\[\sqrt{\frac{\mathbf{7+4}\sqrt{\mathbf{3}}}{\mathbf{2}}}\]equals to ________
A)
\[\sqrt{2}+\sqrt{6}\] done
clear
B)
\[\frac{2\sqrt{2}+\sqrt{6}}{2}\] done
clear
C)
\[\frac{\sqrt{2}+\sqrt{6}}{2}\] done
clear
D)
\[\frac{\sqrt{3}+2}{4}\] done
clear
E)
None of these done
clear
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question_answer35)
If HCF of the numbers (3600, x) = 20 then how many values are possible for x? (where it is assumed that x is a product of a power of 2 and a power of 5 only)
A)
One done
clear
B)
Two done
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C)
Three done
clear
D)
Four done
clear
E)
None of these done
clear
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question_answer36)
The number of ways, in which 576 can be resolved into two factors, is ________
A)
8 done
clear
B)
9 done
clear
C)
10 done
clear
D)
11 done
clear
E)
None of these done
clear
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question_answer37)
Four runners P, Q, R and S start running around a circular track simultaneously. If they complete one round in 16, 12, 24, 18 minutes respectively, after how much time they will meet next?
A)
2 hours 20 minutes done
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B)
2 hours done
clear
C)
3 hours 18 minutes done
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D)
2 hours 24 minutes done
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E)
None of these done
clear
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question_answer38)
If LCM and HCF of two numbers are equal, then the numbers will be _________
A)
Composite done
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B)
Prime done
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C)
Equal done
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D)
Co-prime done
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E)
None of these done
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question_answer39)
If the product of two numbers is 149058 and HCF of these numbers is 21 then how many pairs of these numbers are possible?
A)
1 done
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B)
2 done
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C)
3 done
clear
D)
4 done
clear
E)
None of these done
clear
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question_answer40)
If \[A=14+(1\times 2\times 3\times 4\times 5\times \,\,................\,10\times 14)\]and \[B=19+(1\times 2\times 3\times 4\times 5\,\,................\,10\times 19)\] then which one of the following is/are correct? |
(i) \[B-A\] is a prime number. |
(ii) \[B+A\] is a composite number. |
(iii) A is a composite number. |
(iv) B is a prime number. |
A)
Both (i) and (ii) done
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B)
Both (ii) and (iii) done
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C)
Both (iii) and (iv) done
clear
D)
All (i), (ii), (iii) and (iv) done
clear
E)
None of these done
clear
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