Tag: maths

Questions Related to maths

A person bought a shirt at a certain price and paid the same price for the trouser. If the trouser had cost rupees twenty less and the shirt $Rs.15$ more, the price of the trouser would have only half that of the shirt. Find the cost of shirt.

maths profit-loss overhead expenses introduction to total cost price of the article profit and loss with overhead expenses

  1. $Rs.60$

  2. $Rs.45$

  3. $Rs.55$

  4. $Rs.50$

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Correct Option: C
Explanation:

Let the price of the shirt and trouser be Rs. $ x $.
As per the statement, " If the trouser had cost rupees twenty less and the shirt Rs. $15$ more, the price of the trouser would have only half that of the shirt " => $ x-20 = \frac {x+15}{2} $
$ => 2x-40 = x  +15 $
$ x = 55 $
Cost of the shirt $ = Rs  55 $.

The instrument in the geometry box having the shape of a triangle is called a 

maths plane geometry line and angle set squares constructing a perpendicular bisector construction of a perpendicular bisector

  1. Protractor

  2. Compasses

  3. Divider

  4. Set-square

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Correct Option: D
Explanation:

The instrument in the geometry box having the shape of a triangle are called set-squares

Two parallel lines have _____ slopes.

maths plane geometry line and angle set squares constructing a perpendicular bisector construction of a perpendicular bisector

  1. opposite

  2. equal

  3. negative

  4. different

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Correct Option: B
Explanation:

Two parallel lines have equal slopes as they are at the same inclination with the positive direction of X-axis. Also, the coefficients of $x$ and $y$ of two parallel lines are in proportion.

Option $B$ is correct.

In the sides a,b,c of a triangle ABC are in A.P then $\dfrac{b}{c}$ belong to

maths plane geometry line and angle set squares constructing a perpendicular bisector construction of a perpendicular bisector

  1. $(0, \dfrac{2}{3})$

  2. $(1,2)$

  3. $(\dfrac{2}{3}, 2)$

  4. $(\dfrac{2}{3}, \dfrac{7}{3})$

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Correct Option: A

With compasses and ruler, construct with each of the following angles:

maths when lines join set squares constructing a perpendicular bisector construction of a perpendicular bisector

  1. 60 $ ^{\circ} $

  2. 30 $ ^{\circ} $

  3. 90 $ ^{\circ} $

  4. 45 $ ^{\circ} $

  5. 22 $\frac{1}{2} ^{\circ} $

  6. 75 $ ^{\circ} $

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Correct Option: A
State True or False:
An angle of $52.5$ can be constructed using the compass.
maths when lines join set squares constructing a perpendicular bisector construction of a perpendicular bisector

  1. True

  2. False

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Correct Option: A
Explanation:

 As $52.5 =\frac{210^{\circ}}{4} \ and \   210 =180 + 30 $  and we can bisect the angle, so given angle can be constructed.

So True.

A trader buys some goods for Rs $150$. If the overhead expenses be $12\%$ of cost price, then at what price should it be sold to earn $10\%$ profit?

maths profit - loss overhead expenses introduction to total cost price of the article profit and loss with overhead expenses

  1. Rs $184.80$

  2. Rs $185.80$

  3. Rs $187.80$

  4. Rs $188.80$

Show answer
Correct Option: A
Explanation:
Total CP = (CP + Overhead expenses) 
Total CP $= 150 + 12\%\, of\, 150 $
Total CP $=150 + \dfrac{12}{100}\times 150= Rs.168$
Given that, gain $= 10\%$
Therefore, $SP = \dfrac{110}{100}\times 168 = Rs.184.80$

$Assertion$ (A) By the early 20th century, America became the biggest supplier of wheat to Europe.

$Reason$ (R) The expansion of the railways during the period greatly facilitated the transport of grain.

maths profit - loss overhead expenses introduction to total cost price of the article profit and loss with overhead expenses

  1. A is true, R is false.

  2. A is false, R is true.

  3. Both A and R are true, but R is not the correct explanation of A.

  4. Both A and R are true and R is the correct explanation of A.

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Correct Option: C
Explanation:

By the early 20th century, America became the biggest supplier of wheat to Europe. This is because wheat production is highest in America at that time due to adoption of various new technology, climate change, etc. Hence, option (c) is correct as reason is incorrect explanation of assertion.

The line of intersection of the planes $\overrightarrow { r } .\left( 3\hat { i } -\hat { j } +\hat { k }  \right) =1$ and $\overrightarrow { r } .\left( \hat { i } +4\hat { j } -2\hat { k }  \right) =2$ is parallel to vector

line of intersection of two planes line and a plane vectors, lines and planes three dimensional geometry maths

  1. $-2\hat { i } +7\hat { j } +13\hat { k } $

  2. $2\hat { i } +7\hat { j } -13\hat { k } $

  3. $-2\hat { i } -7\hat { j } +13\hat { k } $

  4. $2\hat { i } +7\hat { j } +13\hat { k } $

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Correct Option: A

There are two different planes, one passing though the x-axis and the other passing through y-axis. The angle between the planes is $\cfrac{\pi}{4}$. Then locus of a point on the line of intersection of the planes in.

line of intersection of two planes line and a plane vectors, lines and planes three dimensional geometry maths

  1. $(x^2+y^2+z^2)x^2=y^2z^2$

  2. $(x^2+y^2+z^2)z^2=x^2y^2$

  3. $(x^2+y^2+z^2)y^2=x^2z^2$

  4. None of these

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Correct Option: A