Mathematics - Rational Numbers
Exam Duration: 45 Mins Total Questions : 25
Divide the sum of \({65\over 12}\) and \({12\over 7}\) by their difference.
- (a)
\({599\over 311}\)
- (b)
\({680\over 216}\)
- (c)
\({642\over 133}\)
- (d)
\({501\over 301}\)
The sum of the additive inverse and multiplicative inverse of \({1\over 5}\) is ________.
- (a)
\({24\over 5}\)
- (b)
\(-{24\over 5}\)
- (c)
25
- (d)
-25
The product of two rational numbers is \({-28\over 81}\) If one of the numbers is \({14\over 27}\) then find the other number.
- (a)
\({2\over 5}\)
- (b)
\({8\over 17}\)
- (c)
\(-{2\over 3}\)
- (d)
\(-{4\over 3}\)
If a = 7, then the value of \(-({1-2a\over a-5})\) is _________.
- (a)
\(-{13\over 2}\)
- (b)
\(-{15\over 2}\)
- (c)
\({13\over 2}\)
- (d)
\({15\over 2}\)
Which of the following statements is TRUE?
- (a)
Every point on the number line represents a rational number.
- (b)
The product of a rational number and its reciprocal is 0.
- (c)
(17 x 12)-1 = 17-1 x 12
- (d)
Reciprocal of \({1\over a},a\ne0\) is a.
The multiplicative inverse of \(-{a\over b}\) is __________.
- (a)
\({a\over b}\)
- (b)
\({b\over a}\)
- (c)
\(-{b\over a}\)
- (d)
None of these
Which of the following properties of rational numbers is given below?
\({7\over 4}\times ({-8\over 3}+{-13\over 12})={7\over 4}\times {-8\over 3}+{7\over 4}\times {-13\over 12}\)
- (a)
Commutativity of addition
- (b)
Associativity of multiplication
- (c)
Distributivity of multiplication over addition
- (d)
Distributivity of addition over multiplication
If \(x={2+3\times 2\over -5}\) then |-x| is equal to _______.
- (a)
\({8\over 5}\)
- (b)
\(-{8\over 5}\)
- (c)
0
- (d)
1
Which of the following options is true?
- (a)
\({5\over 7}<{7\over 9}<{9\over 11}<{11\over 13}\)
- (b)
\({11\over 13}<{9\over 11}<{7\over 9}<{5\over 7}\)
- (c)
\({5\over 7}<{11\over 13}<{7\over 9}<{9\over 11}\)
- (d)
\({5\over 7}<{9\over 11}<{11\over 13}<{7\over 9}\)
The rational number which is not lying between \({5\over 16}\) and \({1\over 2}\) is _______.
- (a)
\({3\over 8}\)
- (b)
\({7\over 16}\)
- (c)
\({1\over 4}\)
- (d)
\({13\over 32}\)
Simplify: \(({3\over 11}\times {5\over 6})-({9\over 12}\times {4\over 3})+({5\over 13}\times {6\over 15})\)
- (a)
\(-{177\over 286}\)
- (b)
\(-{303\over 40}\)
- (c)
\({286\over 492}\)
- (d)
\({17\over 24}\)
What should be subtracted from \(({3\over 4}-{2\over 3})\) to get \({-1\over 6}?\)
- (a)
\(-{6\over 13}\)
- (b)
\({1\over 4}\)
- (c)
\({2\over 7}\)
- (d)
\(-{1\over 8}\)
Simplify: \({3\over 8}+{7\over 2}+({-3\over 5})+{9\over 8}+({-3\over 2})+{6\over 5}\)
- (a)
\({-2\over 3}\)
- (b)
\({-41\over 10}\)
- (c)
\({39\over 5}\)
- (d)
\({41\over 10}\)
If \(x={2\over 3}\) and \(y={3\over 2}\) then find the value of (x + y) + (x - y).
- (a)
\({15\over 2}\)
- (b)
\(-{13\over 5}\)
- (c)
\(17\over 6\)
- (d)
\(-{11\over 6}\)
If \(x=-{4\over 11}\) then which of the following rational number lies between x and |x|?
- (a)
\({7\over 13}\)
- (b)
\(-{11\over 15}\)
- (c)
\(-{2\over 11}\)
- (d)
\({5\over 8}\)
There are 42 students in a class. Out of these \({3\over 4}\) of the boys and \({2\over 3}\) of the girls come to school by bus. The total number of boys and girls of the same class who come to school by bus is 30. How many boys are there in the class?
- (a)
20
- (b)
24
- (c)
26
- (d)
16
Mrs Priya earns Rs 18000 per month. She spends \({7\over 12}\) on household Items and \({1\over 8}\) on rest of the things. The amount she saves is ________.
- (a)
Rs 7120
- (b)
Rs 5250
- (c)
Rs 5520
- (d)
Rs 6562.50
One fruit salad recipe requires \({1\over 2}\) cup of sugar. Another recipe for the same fruit salad requires 2 tablespoons of sugar. If 1 tablespoon is equivalent to \({1\over 16}\) cup, then how much more sugar does the first recipe require?
- (a)
\({4\over 5}\) cup
- (b)
\({6\over 5}\) cup
- (c)
\({3\over 8}\) cup
- (d)
\({5\over 8}\) cup
The wingspans of different species of birds is given below.
Species of birds | Blue jay | Golden eagle | Seagull | Albatross |
---|---|---|---|---|
Length of wingspans |
\({41\over 100}\)m | \(2{1\over 2}\)m | \(1{7\over 10}\)m | \(3{3\over 5}\)m |
How much longer is the wingspan of a Golden eagle than the wingspan of a Blue jay?
- (a)
\({209\over 100}cm\)
- (b)
\({209\over 100}m\)
- (c)
\({9\over 100}m\)
- (d)
\({215\over 100}cm\)
There are few adults and children in a restaurant. If \({3\over 8}\) of the people in the restaurant are adults and there are 90 more children than adults, then how many children are there in the restaurant?
- (a)
180
- (b)
200
- (c)
225
- (d)
230
Which of the following options is INCORRECT?
- (a)
The rational number 0 is the additive identity for rational numbers
- (b)
The additive inverse of the rational number a/b is -a/b and vice-versa
- (c)
Rational numbers are closed under the operations of subtraction, multiplication and division
- (d)
There are infinite rational numbers between any two rational numbers
Match the following.
Column-I | Column-II |
---|---|
(P) Product of a rational number and its reciprocal is | -1 |
(Q) If \({12\over 30}\) and \({x\over 5}\) are equivalent, then x = | 0 |
(R) \([{8\over 21}-({-32\over 39}\div {16\over 13})]\times {7\over 4}=\) | 2 |
(S) Sum of a rational number and its additive inverse is | 1 |
- (a)
(P) \(\rightarrow\) (iv); (Q) \(\rightarrow\) (iii); (R) \(\rightarrow\) (i); (S) \(\rightarrow\) (ii)
- (b)
(P) \(\rightarrow\) (i); (Q) \(\rightarrow\) (iii); (R) \(\rightarrow\) (iv); (S) \(\rightarrow\) (ii)
- (c)
(P) \(\rightarrow\) (iv); (Q) \(\rightarrow\) (iii); (R) \(\rightarrow\) (ii); (S) \(\rightarrow\) (i)
- (d)
(P) \(\rightarrow\) (i); (Q) \(\rightarrow\) (iv); (R) \(\rightarrow\) (iii); (S) \(\rightarrow\) (ii)
Fill in the blanks.
(i) 0 is neither ___P___ nor __Q____.
(ii) ___R____ has/have no reciprocal.
(iii) The rational numbers ____S____ and ____T____ are equal to their reciprocal.
- (a)
P Q R S T Positive negative 1 1/2 -1/2 - (b)
P Q R S T Integer rational 0 -1 0 - (c)
P Q R S T Positive negative 0 1 -1 - (d)
P Q R S T Natural integer -1 1 -1
Which of the following options holds?
Statement - 1: Rational numbers are closed under division.
Statement - 2: The value of \(({-7\over 18}\times {15\over -7})-(1\times {1\over 4})+({1\over 2}\times {1\over 4})\) is \({17\over 24}\)
- (a)
Both Statement - 1 and Statement - 2 are true
- (b)
Statement - 1 is true and Statement - 2 is false
- (c)
Statement - 1 is false but Statement - 2 is true
- (d)
Both Statement - 1 and Statement - 2 are false
State 'T' for true and 'F' for false.
(i) The rational number \({-8\over -3}\) lies neither to the right nor to the left of zero on the number line
(ii) The rational numbers \({1\over 2}\) and \(-{5\over 2}\) are on the opposite sides of 0 on the number line.
(iii) 0 is the smallest rational number.
(iv) For every rational number x, x + 1 = x.
- (a)
(i) (ii) (iii) (iv) F T T F - (b)
(i) (ii) (iii) (iv) T T F F - (c)
(i) (ii) (iii) (iv) F T F F - (d)
(i) (ii) (iii) (iv) T T F F