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Numerical Applications Applied Maths - Numerical Applications

CBSE - STD 12 Science - Applied Maths (CBSE - English Medium). 57 questions in this chapter.

Question types

Numerical Applications question types

57 questions across 6 question groups — pick any mix to generate a Applied Maths paper with step-by-step answer keys.

57
Questions
6
Question groups
5
Question types
Sample Questions

Numerical Applications questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1MCQ1 Mark
If $0 < x < 1$ then which of the following is greatest
  • A
    $x$
  • B
    $x^2$
  • C
    $\frac{1}{x}$
  • ✓
    $\frac{1}{x^2}$

Answer: D.

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Q 2MCQ1 Mark
If $\text{B} >\text{A},$ then which expression will have the highest value, given that A and B are positive integers.
  • A
    $A - B$
  • B
    $A\times B$
  • C
    $A + B$
  • ✓
    Can't say

Answer: D.

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Q 3MCQ1 Mark
The solution set of the inequation $|x+2| \leq 5$ is:
  • A
    (-7, 5)
  • ✓
    [-7, 3]
  • C
    [-5, 5]
  • D
    (-7, 3)

Answer: B.

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Q 4MCQ1 Mark
Pipe A can fill a tank 6 times faster than a pipe B. If B can fill a tank in 21 minutes, then the time taken by both the pipes together to fill the tank is:
  • ✓
    3 minutes
  • B
    $4 \frac{1}{2}$ minutes
  • C
    7 minutes
  • D
    9 minutes

Answer: A.

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Q 5MCQ1 Mark
20 litres of a mixture contains milk and water in the ratio $3 : 1.$ The amount of milk, in litres, to be added to the mixture so as to have milk and water in the ratio $4 : 1,$ is:
  • A
    7
  • B
    4
  • ✓
    5
  • D
    6

Answer: C.

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Q 62 Marks Questions2 Marks
Find the ratio of swimming speed of Raj in still water to speed of river, if ratio of time taken to go 10 km upstream to time taken to go 10 km downstream is $11: 5$?
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Q 72 Marks Questions2 Marks
Guddi speed of swimming in still water to that of river water is $7: 1.$ She swims 4.2 km up the river in just 14 min. How much time will Guddi take to swim 18.4 km down the river?
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Q 102 Marks Questions2 Marks
Two pipes A and B can fill a tank in 24 minutes and 32 minutes respectively. If both the pipes are opened simultaneously, after how much time B should be closed so that the tank is full in 18 minute?
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Q 113 Marks Question3 Marks
A cistern has two taps attached to it. Tap B can empty the cistern in 45 minutes. But Tap A can fill the cistern in just 30 minutes. Rohit started both taps unknowingly but realized his mistake after 30 minutes. He immediately closed Tap B. Now, in how many minutes the cistern will be filled?
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Q 133 Marks Question3 Marks
If the boat takes 12 hours to row 48 km upstream and 8 hours to row the same distance downstream, then find the boat's speed in still water and speed of river.
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Q 155 Marks Questions5 Marks
(i) If two pipes function simultaneously, the reservoir will be filled in 12 hours. One pipe fills the reservoir 10 hours faster than the other. How many hours will the second pipe take to fill the reservoir?
(ii) The longest side of a triangle is 3 times the shortest side and the third side is 2 cm shorter than the longest side. If the perimeter of the triangle is at least 61 cm, find the minimum length of the shorter side.
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Q 165 Marks Questions5 Marks
(i) A can contains a mixture of two liquids A and B in the ratio $7:5.$ When $9$ litres of mixture are drawn off and can is filled with B, the ratio of A and B becomes $7: 9.$ How many litres A was contained by the can initially?
(ii) A man can row 40 km upstream and 55 km downstream in 13 hours. Also, he can row 30 km upstream and 44 km downstream in 10 hours. Find the speed of the man in still water and speed of the current.
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Q 17Case study (4 Marks)4 Marks
Read the following text and answer the following questions on the basis of the same:
While making the notes on linear inequalities, Riya note down the following points in her notebook.
Inequality: Two real numbers or two algebraic expressions related by the symbol '$<$', '$>$', '$\leq$' prime , form an inequality.
Linear Inequality: An inequality is said to be linear, if each variable occurs in first degree only and there is no term involving the product of the variables.
e.g., $a x+b \leq 0, a x+b y+c>0, a x \leq 4$.
An inequality in one variable in which degree of variable is 2, is called quadratic inequality in one variable,
e.g., $a x^2+b x+c \geq 0,3 x^2+2 x+4 \leq 0$.
Linear equality In one Variable: A linear inequality which has only one variable, is called linear inequality in one variable.
e.g., $a x+b<0$, where $a \neq 0,4 c+7 \geq 0$.
(i) Rules of solving inequalities:
• If $a \geq b$ then $a \pm k \geq b \pm k$ where $k$ is any number.
• If $a \geq b$ then $k a$ is not always $\geq k b$
If $k>0$ (i.e., positive) then $a \geq b \Rightarrow k a \geq k b$
If $k>0$ (i.e., negative) then $a \geq b \Rightarrow k a \leq k b$
Thus, always reverse the sign of inequality while multiplying or dividing both sides of an inequality by a negative number.
(ii) Procedure to solve a linear inequality in one variable:
• Simplify both sides by collecting like terms.
• Remove fractions (or decimals) by multiplying both sides by appropriate factor (L.C.M. of denominator or a power of 10 in case of decimals.)
• Isolate the variable on one side and all constants on the other side. Collect like terms whenever possible.
• Make the coefficient of the variable equal to 1.
• Choose the solution set from the replacement set.
Solution set: A solution to an inequality is a number which when substituted for the variable, makes the inequality true. The set of all solutions of an inequality is called the solution set of the inequality.
Q. 1. The solution set for the following figure is:

Image
(A) $x \in(-\infty, 5)$ $\quad$ (B) $x \in(-\infty, 5]$ $\quad$ (C) $x \in[5, \infty)$ $\quad$ (D) $x \in(5, \infty)$
Q. 2. If $\frac{-3}{4} x \leq-3$ then x ... 4.
(A) x < 4 $\quad$ (B) $x \geq 4$ $\quad$ (C) x > 4 $\quad$ (D) x = 4
Q. 3. The solution set for the given inequality is:
$4 x+3 \geq 2 x+17,3 x-5<-2$
(A) x < 1 $\quad$ (B) $x \geq 7$ $\quad$ (C) No Solution $\quad$ (D) x > 1
Q. 4. The solution set for the following figure is:
Image
(A) $x \in(-\infty,-2]$ $\quad$ (B) $x \in(\infty, 2)$ $\quad$ (C) $x \in(-2, \infty]$ $\quad$ (D) $x \in[-2, \infty)$
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Q 18Case study (4 Marks)4 Marks
Read the following text and answer the following questions on the basis of the same:
Riya is doing her Mathematics homework given in the class. Her teacher gave a problem related to the topic 'Boats and Streams'. She is very confused in this topic, the question given by the teacher is "A man can row 5 km/h in still water. If in a river running at 2 km an hour, it takes him 40 minutes to row to a place and return back".
Image
Q. 1. What is the downstream speed?
(A) 2 km/h $\quad$ (B) 5 km/h $\quad$ (C) 7 km/h $\quad$ (D) 3 km/h
Q. 2. What is the upstream speed?
(A) 2 km/h $\quad$ (B) 5 km/h $\quad$ (C) 7 km/h $\quad$ (D) 3 km/h
Q. 3. Man starts from A, travels to B and comes back. Let distance between A and B = x.
Image
Total time to travel from A to B and come back to A =
(A) Distance from A to B/downstream speed + Distance from B to A/upstream speed
(B) Distance from B to A/downstream speed + Distance from A to B/upstream speed
(C) Distance from A to B + Distance from B to A
(D) None of these
Q. 4. A man rows downstream 30 km and upstream 12 km. If he takes 4 hours to cover each distance, then the speed of the stream is:
(A) 2.25 km/h $\quad$ (B) 25.5 km/h $\quad$ (C) 22.5 km/h $\quad$ (D) 52.2 km/h
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Q 19Case study (4 Marks)4 Marks
Read the following text and answer the following questions on the basis of the same:
Sohil is good in Mathematics. His friend gave him a question from the topic Pipes and Cisterns i.e., "Pipe R can empty a full tank in 30 hours. But two pipes P and Q can fill a tank in 15 hours and 10 hours respectively. Ram unknowingly opened all three taps. After 2 hours Shyam realized it and closed Pipe R."
Image
Q. 1. In 1 hour tank filled by pipe P is
(A) $\frac{1}{15}$ $\quad$ (B) $\frac{1}{30}$ $\quad$ (C) $\frac{1}{10}$ $\quad$ (D) $\frac{5}{30}$
Q. 2. In 1 hour tank emptied by pipe R is
(A) $\frac{1}{15}$ $\quad$ (B) $\frac{1}{30}$ $\quad$ (C) $\frac{1}{10}$ $\quad$ (D) $\frac{5}{30}$
Q. 3. When P, Q and R all are open, then tank filled in 1 hour is
(A) $\frac{1}{15}$ $\quad$ (B) $\frac{1}{30}$ $\quad$ (C) $\frac{4}{30}$ $\quad$ (D) $\frac{5}{30}$
Q. 4. If R is closed, then entire tank get filled in how much time?
(A) 6 hours $\quad$ (B) 4 hours $\quad$ (C) 8 hours $\quad$ (D) 2 hours
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Q 214 Marks Question4 Marks
(i) A runs $1 \frac{3}{4}$ times as fast as B. If A gives B a start of 84 m, how far must winning post be so that A and B might reach it at the same time?
(ii) 8 litres are drawn from a cask full of wine and is then filled with water. This operation is performed three more times. The ratio of the quantity of wine now left in cask to that of the water is $16: 65.$ How much wine did the cask hold originally ?
(iii) Show that graph of the solution $2x - 3 > x - 5$ on number line.
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Q 224 Marks Question4 Marks
Two pipes can fill a cistern in 14 hours and 16 hours respectively. The pipes are opened simultaneously and it is found that due to leakage in the bottom it took 32 minutes more to fill the cistern. When the cistern is full, in what time will the leak empty it?
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Q 234 Marks Question4 Marks
(i) The milk and water in two vessels A and B are in the ratio $4 : 3$ and $2 : 3$ respectively. In what ratio, the liquids in both the vessels be mixed to obtain a new mixture in vessel C containing half milk and half water?
(ii) A man can row $7 \frac{1}{2}~ \text{km/h}$ in still water. If in a river running at 1.5 km in an hour, it takes him 50 minutes to row to place and back, how far off is the place ?
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