2023-03-26 12:01

## Class 12: Inverse Trigonometric Functions – Exercise 4.8

2023-03-26 06:00
Question 1: Evaluate each of the following: Answer: Question 2: Prove the following results: Answer: Answer… Read More

## Class 12: Inverse Trigonometric Functions – Exercise 4.7

2023-03-25 08:02
Question 1: Evaluate each of the following:  Answer: Question 2: Evaluate each of the following: Answer: Question 3: Evaluate each of the following: A… Read More

## Class 12: Inverse Trigonometric Functions – Exercise 4.6

2023-03-24 12:24
Question 1: Find the principal values of each of the following: Answer: Question 2: Find the domain of Answer: Question 3: Evaluate each of the following: Answer: Read More

## Class 12: Inverse Trigonometric Functions – Exercise 4.5

2023-03-21 12:09
Question 1: Find the principal values of each of the following: Answer: Answer: Question 3: For the principal values, evaluate the following: Answer: Read More

## Class 12: Inverse Trigonometric Functions – Exercise 4.4

2023-03-20 11:37
Question 1: Find the principal values for each one of the following: Answer: Question 2: Find the principal values, evaluate the following: Answer: Question 3: Find the domain… Read More

## Class 12: Inverse Trigonometric Functions – Exercise 4.3

2023-03-20 10:42
Question 1: Find the principal value of each of the following: Answer: Question 2: Find the principal values, evaluate each of the following: Answer: Question 3: Evaluate each… Read More

## Class 12: Inverse Trigonometric Functions – Exercise 4.2

2023-03-20 06:32
Question 1: Find the domain of definition Answer: Question 2: Find the domain of Answer:   Question 3: Find the domain of Answer: Question 4: Find the principal value… Read More

## Class 12: Inverse Trigonometric Functions – Exercise 4.1

2023-03-11 05:55
Question 1: Find the principal values of: Answer: Question 2:  Answer: Question 3: Find the domain of each of the following functions: Answer: Answer:… Read More

## Class 12: Binary Operations – CBSE Board Problems

2023-03-10 15:10
Question 1: Let be a binary operation on the set of integers, defined by . Find the value of [CBSE 2011] Answer: Given that is a binary operation on the set I of integers. The operation i… Read More

## Class 12: Binary Operations – Exercise 3.5

2023-03-09 12:36
Answer:  Hence, the composition table is as follows: Answer: Hence, the composition table is as follows: Answer: Hence, the composition table is as follows: Answer:… Read More

## Class 12: Binary Operations – Exercise 3.4

2023-03-08 13:34
Question 1: Let be a binary operation on defined by for all   (i) Show that is both commutative and associative. (ii) Find the identity element in (iii) Find the invertible element… Read More

## Class 12: Binary Operations – Exercise 3.3

2023-03-07 15:16
Question 1: Find the identity element in the set of all positive integers defined by for all, Answer: Given that binary operation is valid for set of all positive integers defined by &n&hell…Read More

## Class 12: Binary Operations – Exercise 3.2

2023-03-07 14:43
Question 1: Let be a binary operation on defined by     Answer: Given that is an operation that is valid on all natural numbers and is defined by According to the problem, b… Read More

## Class 12: Binary Operations – Exercise 3.1

2022-12-27 13:00
Question 1: Determine whether each of the following operations define binary operation on the given set or not:   (i) (ii) (iii) (vi) Answer: (i) Given that is an operatio… Read More

## Class 12: Functions – Exercise 2.4

2022-12-19 15:29
Question 1: State with reasons whether following functions have inverse:  Answer: Therefore, does not have an inverse. Therefore, does not have an inverse. Here, different… Read More

## Class 12: Functions – Exercise 2.3

2022-12-10 04:23
Answer: Let us calculate , Clearly, the range of is not a subset of the domain of Let us calculate Clearly, the range of is a subset of the domain of… Read More

## Class 12: Functions – Exercise 2.2

2022-12-10 04:23
Question 1: Find are defined by:    Answer: Question 2: Let Show that are both defined. Also, find Answer: Question 3: Let Show t… Read More

## Class 12: Functions – Exercise 2.1

2022-12-10 04:22
Question 1: Give an example  of a function (i) which is one-one but not onto (ii) which is not one-one but onto (iii) which is neither one-one nor onto Answer: (i)      C… Read More

## Class 12: Functions – Miscellaneous Problems (2)

2022-08-07 02:18
Question 31: Let be a finite set. If is a one-one function, show that is onto also.  Answer: In order to prove that f is onto function, we will have to show that every element in A… Read More

## Class 12: Functions – Miscellaneous Problems (1)

2022-08-07 02:17
Question 1: Find whether the following functions are one-one or not:  Answer: Hence, is a one-one function from to itself. Here, does not provide the unique solution but it pr… Read More

## Class 12: Relations – Exercise 1.1

2022-07-09 15:54
Question 1: Let A be the set of all human beings in a town at a particular time. Determine whether each of the following relations are reflexive, symmetric and transitive:    &n&hell…Read More

## Class 12: Relations – Exercise 1.2

2022-07-09 15:54
Question 1: Show that the relation defined by    is an equivalence relation.   Answer: To prove that relation is equivalence, we need to prove that it is reflexive, symm… Read More

## Class 12: Relations – Miscellaneous Problems

2022-07-09 15:53
Question 1: Three relations are defined on set as follows:     (i)   (ii) (iii)  Find whether each one of is reflexive, symmetric and transitive. Answer: (i)&nb&hell…Read More

## Class 10: Distance And Section Formulae – Miscellaneous Problems – Set 1

2022-03-17 14:39
Question 1: Find the the distance between the points (3, 6) and (0,2).   Answer: Therefore the distance between the given points Question 2: Find the distance between the orig… Read More

## Class 10: Matrices – Miscellaneous Problems – Set 1

2022-03-08 15:56
Answer: If two matrices are equal, their corresponding elements are also equal. In each case, write the conclusion (if any) that you can draw. Answer: (iii) Yes;… Read More

## Class 10: Remainder And Factor Theorems – Misc. Problems – Set 1

2022-03-08 15:53
Question 1: Find the remainder when is divided by   Answer: Question 2: Find the value of if the division of by leaves a remainder of 5. Answer: The value of at is Quest… Read More

## Class 10: Ratio And Proportion – Miscellaneous Problems – Set 1

2022-03-05 07:06
Question 1: (i) lf find (ii) If find the value of Answer: (i)      [ICSE Board 2002] Answer: Question 3: Two numbers are in the ratio 3 : 5. If 8 is added t… Read More

## Class 10: Coordinate Geometry (Reflections) – Miscellaneous Problems – Set 1

2022-03-02 17:10
Question 1: The triangle and is first reflected in the line onto triangle and then is reflected in the origin onto Write down the co-ordinates of :   (i)      … Read More

## Class 10: Solving Problems (Quadratic Equations) – Miscellaneous Problems – Set 2

2022-03-01 15:50
Question 1: Find two natural numbers which differ by 3 and the sum of whose squares is 117.   Answer:   Let the natural numbers be and Since is not a natural nu… Read More

## Class 10: Quadratic Equations – Miscellaneous Problems – Set 1

2022-02-28 14:30
Question 1: Solve:  (i)      (ii)       (iii) Answer: (i)      (ii)    (iii)    Answer: Que… Read More

## Class 10: Linear Inequations -Miscellaneous Problems -Set 1

2022-02-27 10:38
Question 1: If the replacement set is the set of natural numbers (N), find the solution set of: (i)       (ii)   Answer: Since, the replacement set = N (set of natural… Read More

## Class 10: Shares And Dividend – Miscellaneous Problems – Set 1

2022-02-26 11:22
Question 1: Calculate the money required to buy : (i) 350, Rs. 20 shares at a premium of Rs. 7 (i) 275, Rs. 60 shares at a discount of Rs. 10 (iii) 50, Rs. 75 shares quoted at Rs. 71.50 Answ… Read More

## Class 10: Banking – Miscellaneous Problems-Set 1

2022-02-25 13:27
Question 1: Ronit opened a savings bank account with a bank on l6th May, 1997 and deposited Rs. 850. He withdrew Rs.300 on 3rd June, 1997 and after that he neither deposited nor withdrew any… Read More

## Class 10: Sales Tax And Value Added Tax – Miscellaneous Problems-Set 1

2022-02-23 15:24
Question 1: A person purchased a pair of shoes costing Rs. 850. Calculate the total amount to be paid by him, if the rate of Sales Tax is 6%.  Answer: Question 2: Mr. Gupta purchase… Read More

## Class 10: Compound Interest (Using Formula) – Miscellaneous Problems – Set 2

2022-02-22 15:40
Question 1: Calculate the amount and the compound interest on Rs. 7500 in 2 years and at 6% compounded annually.      Answer:       Question 2: Calculate the a… Read More

## Class 10: Compound Interest (Without Using Formula) – Miscellaneous Problems -Set 1

2022-02-21 16:39
Question 1: Find the amount and the compound interest on Rs. 10,000 at 8 per cent per annum and in 2 years.   Answer:              Question 2:… Read More

## Class 10: ICSE SEMESTER 2 EXAMINATION SQP – MATHEMATICS

2022-02-20 10:23
Maximum Marks: 40Time allowed: One and a half hoursAnswers to this Paper must be written on the paper provided separately.You will not be allowed to write during the first 10 minutes.This ti… Read More

## ICSE SEMESTER 1 EXAMINATION SQP – MATHEMATICS

2022-02-19 16:44
Maximum Marks: 40Time allowed: One and a half hoursAnswers to this Paper must be written on the paper provided separately.You will not be allowed to write during the first 10 minutes.This ti… Read More

## Class 11: Statistics – Exercise 32.7

2022-02-15 16:51
Question 1: Two plants A and B  of a factory show following results about the number of workers and the wages paid to them.     In which plant A or B is there greater va… Read More

## Class 11: Statistics – Exercise 32.6

2022-02-14 17:01
Question 1: Calculate the Mean and Standard Deviation for the following data:  Answer: Calculation of Mean, Variance and Standard Deviation Question 2: Calculate the Standar… Read More

## Class 11: Statistics – Exercise 32.5

2022-02-13 01:43
Question 1: Find the standard deviation for the following distribution:   Answer: Median value of is 34.5 Calculation of Variance and Standard Deviation Question 2: Table b… Read More

## Class 11: Statistics – Exercise 32.4

2022-02-12 05:05
Question 1: Find the mean, variance and standard deviation for the following data:   (i) 2, 4, 5, 6, 8, 17     (ii) 6, 7, 10, 12, 13, 4, 8, 12 (iii) 227, 235, 255, 2… Read More

## Class 11: Statistics – Exercise 32.3

2022-02-09 13:21
Question 1: Compute the mean deviation from the median of the following distribution:  Class 0-10 10-20 20-30 30-40 40-50 Frequency 5 10 20 5 10 Answer:   Calculation of Mean… Read More

## Class 11: Statistics – Exercise 32.2

2022-02-07 01:02
Question 1: Calculate the mean deviation from the median of the following frequency distribution:    Heights in inches 58 59 60 61 62 63 64 65 66 No of students 15 20 32 35 53 22 2… Read More

## Class 11: Statistics – Exercise 32.1

2022-02-06 11:42
Question 1: Calculate the mean deviation about the median of the following observations: (i) 3011, 2780, 3020, 2354, 3541, 4150, 5000 (ii) 38, 70, 48, 34, 42, 55, 63, 46, 54, 44 (iii) 34, 66… Read More

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2022-02-02 13:20

## Class 11: Derivatives – Exercise 30.2

2022-02-01 12:57
Question 1: Differentiate each of the following from first principle:                                  … Read More

## Class 11: Derivatives – Exercise 30.1

2022-01-28 13:27
Answer: We have: Answer: We have: Answer: We have: Answer: We have: Answer: We have: Answer: We have: Question 7: Find the derivation of the foll… Read More

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2021-12-26 11:45

## Class 11: Limits – Exercise 29.6

2021-12-21 12:34
Evaluate the following limits:  Answer:   Answer: Answer: Answer: This is of the form Rationalizing the numerator:   Answer: This is of the form Rat… Read More

## Class 11: Limits – Exercise 29.4

2021-12-12 13:17
Evaluate the following limits:     Answer: Rationalizing the numerator, we get Answer: Rationalizing the numerator, we get Answer: Rationalizing the numera… Read More

2021-12-09 00:46

## Class 11: Limits – Exercise 29.3

2021-12-06 14:49
Evaluate the following limits: Answer: So, is a common factor in numerator and denominator. Factorizing the numerator and denominator, we get     Answer: So, is a… Read More

2021-12-05 15:31

2021-12-05 13:22

## Class 11: Mathematical Reasoning – Exercise 31.6

2021-12-03 16:54
Question 1: Check the validity of the following statements: Answer: (i)  p :100  is a multiple of 4 and 5. \$ Since, 100 is a multiple of 4 and 5, the statement is true. Hence, it i… Read More

## Class 11: Mathematical Reasoning – Exercise 31.5

2021-12-03 02:00
Question 1: Write each of the following statements in the form “if p, then q”. Answer: (i) You can access the website only if you pay a subscription fee. If you pay a subscriptio… Read More

## Class 11: Mathematical Reasoning – Exercise 31.4

2021-12-02 02:33
Question 1: Write the negation of each of the following statements: (i) For every (ii) There exists Answer: (i) For every Negation of the given statement: There exists a number such that… Read More

## Class 11: Mathematical Reasoning – Exercise 31.3

2021-12-01 01:23
Question 1: Find the component statements of the following compound statements: Answer: (i) The sky is blue and the grass is green. The component statements of the given compound statement a… Read More

## Class 11: Mathematical Reasoning – Exercise 31.2

2021-11-30 03:26
Question 1: Write the negation of the following statements: Answer: (i) Bangalore is the capital of Karnataka It is not true that Bangalore is the capital of Karnataka. OR Bangalore is not t… Read More

## Class 11: Mathematical Reasoning – Exercise 31.1

2021-11-29 01:41
Question 1: Find out which of the following sentences are statements and which are not. Justify your answer. (i) Listen to me, Ravi!           (ii) Every set is… Read More

## Class 11: Probability – Exercise 33.4

2021-11-28 11:56
Question 1: (a) If A and B be mutually exclusive events associated with a random experiment such that then find: (i)           (ii)         (ii… Read More

## Class 11: Probability – Exercise 33.3

2021-11-27 00:40
Question 1: Which of the following cannot be valid assignment of probability for elementary events oroutcomes of sample space Elementary Events (i) (ii) (iii) (i… Read More

## Class 11: Probability – Exercise 33.2

2021-11-20 02:00
Question 1: A coin is tossed. Find the total number of elementary events and also the total number events associated with the random experiment. Answer: Note: If there an elements in a set… Read More

## Class 11: Probability – Exercise 33.1

2021-11-19 15:23
Question 1: A coin is tossed once. Write its sample space. Answer: When a coin is tossed, there are two possibilities. It could either turn up Head (H) or Tail (T). Hence the sample space wi… Read More

## Class 11: Three Dimensional Coordinate Geometry – Exercise 28.3

2021-11-19 15:21
Question 1: The vertices of the triangle are The internal bisector of angle meets at Find the coordinates of and the length Answer: is the internal bisector of Therefore divides… Read More

## Class 11: Three Dimensional Coordinate Geometry – Exercise 28.2

2021-10-13 01:14
Question 1: Find the distance between the following pairs of points: (i)            (ii) Answer: (i)      (ii)     … Read More

## Class 11: Three Dimensional Coordinate Geometry – Exercise 28.1

2021-10-09 13:54
Question 1: Name the octants in which the following points lie: (i)       (ii)       (iii)        (iv)        (v)  … Read More

## Class 11: Hyperbola – Exercise 27.1

2021-10-09 03:20
Question 1: The equation of the directrix of a hyperbola is Its focus is and eccentricity . Find the equation of the hyperbola. Answer: Let be the focus and be a point on the Hyperbola… Read More

## Class 11: Ellipse – Exercise 26.1

2021-09-28 13:18
Note: Also plotted the ellipse equations. Students should have a feel of what the equation looks like. Question 1: Find the equation of the ellipse whose focus is the directrix and eccentr… Read More

## Class 11: Parabola – Exercise 25.1

2021-09-08 01:00
Question 1: Find the equation of the parabola whose: (i) focus is and the directrix is       (ii) focus is and the directrix is (iii) focus is and the directrix   &n&hell…Read More

## Class 11: The Circle – Exercise 24.3

2021-02-20 01:20
Note: If the end points of the diameter is and , then the equation of the circle is given by: Question 1: Find the equation of the circle, the end points of whose diameter are and ; Find… Read More

## Class 11: The Circle – Exercise 24.2

2021-02-18 00:49
Note: The general equation of circle is where the center is and radius Question 1: Find the coordinates of the center and radius of each of the following circles : i)      … Read More

## Class 11: The Circle – Exercise 24.1

2021-02-15 00:34
Note: The general equation of a circle is where is the center of the circle and is the radius of the circle. Question 1: Find the equation of the circle with: (i) Centre and radius &nbsp&hell…Read More

## Class 11: The Straight Line – Exercise 23.19

2021-02-11 01:08
Question 1: Find the equation of a straight line through the point of intersection of the lines and and parallel to . Answer: The equation of a straight line passing through the point of i… Read More

## Class 11: The Straight Line – Exercise 23.18

2021-02-06 05:24
Note: We know that the equations of two lines passing through   and making and angle   with the given line   are Question 1: Find the equation of the straight lines passing t… Read More

## Class 11: The Straight Line – Exercise 23.17

2021-02-04 02:20
Question 1: Prove that the area of the parallelogram formed by the lines: is sq. units. Deduce the condition for these lines to form a rhombus. Answer: Let be a parallelogram  the eq… Read More

## Class 11: The Straight Line – Exercise 23.16

2021-02-03 01:03
Question 1: Determine the distance between the following pair of parallel lines : (i) and      (ii) and (iii) and      (iv) and Answer: (i)   … Read More

## Class 11: The Straight Line – Exercise 23.15

2021-02-02 01:04
Question 1: Find the distance of the point from the straight line . Answer: Given equation: Comparing with   we get Therefore perpendicular distance from point   from Thus the… Read More

## Class 11: The Straight Line – Exercise 23.14

2021-02-01 01:27
Question 1: Find the values of so that the point lies inside or on the triangle formed by the lines and . Answer: Let the triangle be . Let,    … … … i) &nb&hell…Read More

## Class 11: The Straight Line – Exercise 23.13

2021-01-31 00:07
Question 1: Find the angles between each of the following pairs of straight lines: (i) and (ii) and (iii) and (iv) and v) and Answer: (i)     Let and be the s… Read More

## Class 11: The Straight Line – Exercise 23.12

2021-01-30 00:47
Note: If is a line, then the equation perpendicular to this line is given by where . If is a line, then the equation parallel to this line is given by where . Question 1: Find the… Read More

## Class 11: The Straight Line – Exercise 23.11

2021-01-24 01:11
Question 1: Prove that the following sets of three lines are concurrent: i) and ii) and iii) and Answer: i)       Given lines are ,   and  We have:… Read More

## Class 11: The Straight Line – Exercise 23.10

2021-01-23 01:21
Note: If and intersect at a point , then and Question 1: Find the point of intersection of the following pairs of lines : i)   and        ii)   and  i… Read More

## Class 11: The Straight Line – Exercise 23.9

2021-01-18 01:10
Question 1: Reduce the equation   to: (i) slope-intercept form and find slope and y-intercept     (ii) intercept form and find intercept on the axes;     (… Read More

## Class 11: The Straight Line – Exercise 23.8

2021-01-17 01:28
Note: The equation of a straight line passing through   and making an angle with the positive x-axis is given by , where is the distance of the point on the line from the point . The… Read More

## Class 11: The Straight Line – Exercise 23.7

2021-01-13 01:20
Note: The equation of the line whose length of the perpendicular from the origin is and the angle made by the perpendicular with the positive x-axis is given by is given by Question 1: Fi… Read More

## Class 11: The Straight Line – Exercise 23.6

2021-01-12 01:03
Note: We know that the equation of the line is where is the x-intercept and is the y-intercept. Question 1: Find the equation to the straight line: (i) cutting off intercepts and from t… Read More

## Class 11: The Straight Line – Exercise 23.5

2021-01-11 01:09
Note: Equation of a like is also defined as Question 1: Find the equation of the straight through the following pair of points: i) and           ii) and iii) an… Read More

## Class 11: The Straight Line – Exercise 23.4

2021-01-10 01:04
Note: When slope and a point is given, the equation of the line is Question 1: Find the equation of the straight line passing through the point and having slope . Answer: Here   and… Read More

## Class 11: The Straight Line – Exercise 23.3

2021-01-09 00:35
Note: The equation of a line having slope of and as is given by Question 1: Find the equation of a line making an angle of  with the x-axis and cutting off an intercept from y-axi… Read More

## Class 11: The Straight Line – Exercise 23.2

2021-01-08 00:58
Question 1: Find the equation of the line parallel to x-axis and passing through . Answer: Equation of a line parallel to x-axis is The line passes through Hence the equation of the line… Read More

## Class 11: The Straight Line – Exercise 23.1

2021-01-07 01:00
Question 1: Find the slopes of the lines which make the following angles with the positive direction of x-axis:  i)           ii)         &n&hell…Read More

## Class 11: Cartesian System Of Rectangular Co-ordinates – Exercise 22.3

2020-12-25 00:44
Question 1:What does the equation become when the axes are transferred to parallel axes through the point ? Answer: Substituting in the equation we get Hence the equation gets transfo… Read More

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