Start learning →

Karnataka SSLC (Class 10) Logarithms — practice questions

Explore 29 free Logarithms questions in Karnataka SSLC (Class 10) Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

Practise Logarithms with Quill →

Logarithms questions and exercises with answers

Showing questions 1–29 of 29.

The distance between two points $P(x_1,y_1)$ and $Q(x_2,y_2)$ isRead the answer and worked solution →The distance of a point $P(x,y)$ from the origin isRead the answer and worked solution →The mid-point of the line segment joining $(x_1,y_1)$ and $(x_2,y_2)$ isRead the answer and worked solution →The distance between the points $(0,0)$ and $(3,4)$ isRead the answer and worked solution →The distance between the points $(1,2)$ and $(4,6)$ isRead the answer and worked solution →The mid-point of the segment joining $(2,3)$ and $(4,7)$ isRead the answer and worked solution →The distance of the point $(5,12)$ from the origin isRead the answer and worked solution →The point that divides the segment joining $(1,2)$ and $(3,4)$ in the ratio $1:1$ isRead the answer and worked solution →The area of the triangle with vertices $(0,0)$, $(4,0)$ and $(0,3)$ isRead the answer and worked solution →Three points are collinear if the area of the triangle formed by them isRead the answer and worked solution →The distance between the points $(2,3)$ and $(2,8)$ isRead the answer and worked solution →A point that lies on the x-axis has itsRead the answer and worked solution →Complete the definition of slopeRead the answer and worked solution →True or false: slopeRead the answer and worked solution →Zero slope, undefined slope, or neither?Read the answer and worked solution →Match each condition to what it tells youRead the answer and worked solution →Parallel, perpendicular, or neither?Read the answer and worked solution →True or false: parallel and perpendicularRead the answer and worked solution →Order the steps: test three points for collinearityRead the answer and worked solution →Assertion and reasonRead the answer and worked solution →Two are true, one is notRead the answer and worked solution →Three of these are wrong. Find the one that holds.Read the answer and worked solution →Which test applies?Read the answer and worked solution →Flip and pair: condition with conclusionRead the answer and worked solution →Tap every statement true of slopeRead the answer and worked solution →Reading the definitions backRead the answer and worked solution →Spot the one that does not belongRead the answer and worked solution →Complete the angle between two linesRead the answer and worked solution →True or false: using coordinatesRead the answer and worked solution →

Worked practice questions

The distance between two points $P(x_1,y_1)$ and $Q(x_2,y_2)$ is

  1. $(x_2-x_1)^2+(y_2-y_1)^2$
  2. $\sqrt{(x_2-x_1)+(y_2-y_1)}$
  3. $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
  4. $|x_2-x_1|+|y_2-y_1|$
Show answer and solution

Correct answer: C. $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

1. The distance formula comes from the Pythagoras theorem. 2. $PQ=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$. 3. The square root is essential; without it the value would be the square of the distance. _Source: Karnataka SSLC (KSEEB) Class 10 Mathematics, Ch7 'Coordinate Geometry', §7.2_

Open this question →

The distance of a point $P(x,y)$ from the origin is

  1. $x+y$
  2. $x^2+y^2$
  3. $\sqrt{x+y}$
  4. $\sqrt{x^2+y^2}$
Show answer and solution

Correct answer: D. $\sqrt{x^2+y^2}$

1. The origin is $O(0,0)$. 2. Using the distance formula: $OP=\sqrt{(x-0)^2+(y-0)^2}=\sqrt{x^2+y^2}$. 3. So the distance from the origin is $\sqrt{x^2+y^2}$. _Source: Karnataka SSLC (KSEEB) Class 10 Mathematics, Ch7 'Coordinate Geometry', §7.2_

Open this question →

The mid-point of the line segment joining $(x_1,y_1)$ and $(x_2,y_2)$ is

  1. $\left(\dfrac{x_1+x_2}{2},\ \dfrac{y_1+y_2}{2}\right)$
  2. $\left(x_1+x_2,\ y_1+y_2\right)$
  3. $\left(\dfrac{x_1-x_2}{2},\ \dfrac{y_1-y_2}{2}\right)$
  4. $\left(x_1 x_2,\ y_1 y_2\right)$
Show answer and solution

Correct answer: A. $\left(\dfrac{x_1+x_2}{2},\ \dfrac{y_1+y_2}{2}\right)$

1. The mid-point divides the segment in the ratio 1:1. 2. Its coordinates are the averages: $\left(\dfrac{x_1+x_2}{2},\ \dfrac{y_1+y_2}{2}\right)$. 3. This is a special case of the section formula. _Source: Karnataka SSLC (KSEEB) Class 10 Mathematics, Ch7 'Coordinate Geometry', §7.3_

Open this question →

How to practise

  1. Choose a Logarithms question and try to work out your answer.
  2. Open the question to check the correct answer and read its worked solution.
  3. Continue in the app for bite-sized lessons, explanations and review with Quill. You can start without creating an account.

More Mathematics topics

Binomial TheoremGeometryProbability & StatisticsSequencesSequences and SeriesVectors & 3D GeometryCorrelation and RegressionLinear Programming