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Q) A survey regarding the heights (in cm) of 50 girls of class X of a school was conducted and the following data was obtained : Find the mean and mode of the above data. Ans: 1. Mean value of the data: Let’s re-arrange the data with midpoint of each class, frequency, and multiply midpoint with frequency: […]
Q) As observed from the top of a lighthouse, 100 m above sea level, the angle of depression of a ship, sailing directly towards it, changes from 30° to 45°. Determine the distance travelled by the ship during the period of observation. (Use √3 = 1.732) Ans: Let’s start with the diagram for this question:
Q) Evaluate: Ans: We need to find the value of: We know that cos 45 = , sec 30 = , cosec 30 = 2 by substituting these values in the given expression, we get: = = = = …. Answer or to further simplify, we can multiply and divide the expression by (√3 –
Q) Prove that Ans: Method 1: We need to prove that Let’s start with squaring in both sides: We know that:  and ∴ ∴ Since LHS = RHS Hence Proved ! Method 2: Let’s start from LHS: Since, and ∴ LHS = = = Since, ∴ LHS = = =   = = =
Prove that Root ( sec^2 θ + csc^2 θ) = tan θ + cot θ Read More »
Q) If x sin3 θ + y cos3 θ = sin θ cos θ and x sin θ = y cos θ, prove that x2 + y2 = 1 Ans: Given that x sin3 θ + y cos3 θ = sin θ cos θ ∴ x sin θ sin2 θ + y cos θ cos2 θ = sin θ
Q) In a park, four poles are standing at positions A, B, C and D around the circular fountain such that the cloth joining the poles AB, BC, CD and DA touches the circular fountain at P, Q, R and S respectively as shown in the figure. Based on the above information, answer the following
Q)Â While playing in a garden, Samaira saw a honeycomb and asked her mother what is that. Her mother replied that it’s a honeycomb made by honey bees to store honey. Also, she told her that the shape of the honeycomb formed is a mathematical structure. The mathematical representation of the honeycomb is shown in the
While playing in a garden, Samaira saw a honeycomb and asked her mother what is that. Read More »
Q) Calculate the mean of the following data : Ans: Let’s re-arrange the data with midpoint of each class, frequency, and multiply midpoint with frequency: We know that, mean of grouped data is given by: Mean of grouped data = Therefore, Mean value = = 24 Hence, the mean value of the given data is
In a test, the marks obtained by 100 students (out of 50) are given below : Read More »
Q) In a 2-digit number, the digit at the unit’s place is 5 less than the digit at the ten’s place. The product of the digits is 36. Find the number. Ans: Let’s consider X is the digit at unit’s place and Y is the digit at ten’s place. The number will be 10 Y +
In a 2-digit number, the digit at the unit’s place is 5 less than the digit Read More »
Q) Using graphical method, solve the following system of equations : 3x + y + 4 = 0 and 3 x – y + 2 = 0 Ans: Step 1: Let’s try to find the intersection points on X – axis and Y – axis for each of the lines: A. For linear equation 3