Tag: maths

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Questions Related to maths

Multiple choice construction : division of a line segment dividing a line segment into three or five equal parts divsion of line segmet in given ratio constructions maths

Find the points $A(a, b), B(-a, -b)$ and $P(a^2, ab)$ are collinear then the ratio in which p divides $\overline{AB}$ is 

  1. 1 + a : 1 - a

  2. 1 : a

  3. a : 1

  4. 1 - a : 1 + a
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

If P(a^2, ab) lies on AB, then (a^2 - a) / (-a - a^2) = ratio. (a(a-1)) / (-a(1+a)) = -(a-1)/(1+a) = (1-a)/(1+a).

Multiple choice construction : division of a line segment dividing a line segment into three or five equal parts divsion of line segmet in given ratio constructions maths

In $\triangle ABC$ $PQR$ $\overline { BC } .\overline { CA } .\overline { AB } $ respectively dividing them in the ratio $1:4,3:2$ and $3:7$. The point $S$ divides $AB$ in the ratio $1:3$ Then $\dfrac { \left| \overline { AP } +\overline { BQ } +\overline { CR }  \right|  }{ \left| CS \right|  } =$

  1. $\dfrac {1}{5}$
  2. $\dfrac {2}{5}$
  3. $\dfrac {5}{2}$
  4. $\dfrac {7}{10}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice construction : division of a line segment dividing a line segment into three or five equal parts divsion of line segmet in given ratio constructions maths

A straight line through the origin O meets the parallel lines 4x+2y=9 and 2x+y+6=0 at point P and Q respectively. Then the point O divides the segment PQ in the ratio

  1. 1:2

  2. 3:4

  3. 2:1

  4. 4:3
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The parallel lines are 4x + 2y - 9 = 0 (or normalized as 2x + y - 4.5 = 0) and 2x + y + 6 = 0. A line through the origin has the form y = mx. It intersects the first line at P and the second line at Q. The distances from the origin to the lines along any ray are proportional to the constant terms of the parallel lines. Specifically, the ratio OP/OQ equals the ratio of the constant distances from the origin, which is 4.5 / 6 = 9/12 = 3/4.

Multiple choice construction : division of a line segment dividing a line segment into three or five equal parts divsion of line segmet in given ratio constructions maths

The ratio in which the line segment joining the points $\left(3,-4\right)$ and $\left(-5,6\right)$ is divided by the $x-$ axis, is

  1. $2:3$
  2. $3:2$
  3. $6:4$
  4. $none\ of\ these$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The x-axis divides a line segment at a point where the y-coordinate is 0. Using the section formula, if the ratio is k:1, the y-coordinate is (k*6 + 1*(-4)) / (k+1) = 0, which gives 6k = 4, or k = 2/3.

Multiple choice construction : division of a line segment dividing a line segment into three or five equal parts divsion of line segmet in given ratio constructions maths

The ratio in which the point $(x _{1} \sin^{2} \theta, y _{1} \cos^{2} \theta)$ divides the line joining $(x _{1}, 0)$ and $(0, y _{1})$ is -

  1. $\tan^{2} \theta : \cot^{2} \theta$
  2. $\cos \theta : \sin \theta $
  3. $\cos^{2} \theta : \sin^{2} \theta$
  4. $(1-\cos \theta) : (1-\sin \theta)$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using the section formula for a point (x, y) dividing (x1, 0) and (0, y1) in ratio m:n, we get x = n*x1 / (m+n) and y = m*y1 / (m+n). Setting x = x1*sin^2(theta) and y = y1*cos^2(theta) leads to the ratio m:n = tan^2(theta):cot^2(theta).

Multiple choice construction : division of a line segment dividing a line segment into three or five equal parts divsion of line segmet in given ratio constructions maths

A point which divides the joint of $(1,2)$ and $(3,4)$ externally in the ratio $1:1$

  1. Lies in the first quadrant

  2. Lies in the second quadrant

  3. Lies in third quadrat

  4. Cannot be found
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The section formula for external division in the ratio m:n uses the formula ((mx2 - nx1)/(m - n), (my2 - ny1)/(m - n)). When the ratio is 1:1, the denominator becomes m - n = 1 - 1 = 0, which results in division by zero. Therefore, a point dividing a line segment externally in the ratio 1:1 cannot be found mathematically.

Multiple choice construction : division of a line segment dividing a line segment into three or five equal parts divsion of line segmet in given ratio constructions maths

If the ratio in which the line segment joining the points (6,4) and (x,-7) divided internally by y-axis is 6: 1, then x equals

  1. 2

  2. 3

  3. -1

  4. -2
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The y-axis divides a line segment in the ratio -x1:x2 or by setting the x-coordinate of the section formula to zero. Using the given coordinates (6, 4) and (x, -7) with a ratio of 6:1, the x-coordinate formula gives (6*x + 1*6)/(6 + 1) = 0, which yields 6x + 6 = 0, so x = -1.

Multiple choice maths ways to multiply and divide division trick division multiply and divide

238 $\div$ 238 is ________

  1. $0$
  2. $238$
  3. $28$
  4. $1$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The number divided by itself and we get $1$ as quotient except $0$


This is not valid for $0$

Now as per the question 
the number $238$ is divided by itself

$238 \div 238 = \dfrac{238}{238} =1$

So , option $D$ is correct