Tag: maths

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Questions Related to maths

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

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.

  1. $Rs.60$
  2. $Rs.45$
  3. $Rs.55$
  4. $Rs.50$
Reveal answer Fill a bubble to check yourself
C Correct answer
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 $.

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

Two parallel lines have _____ slopes.

  1. opposite

  2. equal

  3. negative

  4. different
Reveal answer Fill a bubble to check yourself
B Correct answer
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.

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

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

  1. $(0, \dfrac{2}{3})$
  2. $(1,2)$
  3. $(\dfrac{2}{3}, 2)$
  4. $(\dfrac{2}{3}, \dfrac{7}{3})$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

If a, b, c are in A.P., then 2b = a + c. By triangle inequality, a + c > b, so 2b > b (always true). Also, a + b > c and b + c > a. Substituting a = 2b - c into the inequalities leads to the range for b/c.

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

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?

  1. Rs $184.80$
  2. Rs $185.80$
  3. Rs $187.80$
  4. Rs $188.80$
Reveal answer Fill a bubble to check yourself
A Correct answer
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, $SP = \dfrac{110}{100}\times 168 = Rs.184.80$
Multiple choice maths profit - loss overhead expenses introduction to total cost price of the article profit and loss with overhead expenses

$Assertion$ (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.

  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.
Reveal answer Fill a bubble to check yourself
C Correct answer
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.

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

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

  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 } $
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The line of intersection of two planes is parallel to the cross product of their normal vectors. The normals are n1 = (3, -1, 1) and n2 = (1, 4, -2). The cross product is (-1*-2 - 1*4, 1*1 - 3*-2, 3*4 - -1*1) = (2-4, 1+6, 12+1) = (-2, 7, 13).

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

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.

  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
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

This is a classic problem involving the intersection of planes passing through axes. The derivation leads to the relationship between the coordinates and the angle, resulting in the given locus.