Q) If in Δ ABC, AD is median and AE ⊥ BC, then prove that AB2 + AC2 = 2 AD2 + BC2 Ans: Step 1: Let’s make a diagram for the question: Step 2: In Δ ABE, ∠ AEB is 900, ∴ by Pythagoras theorem: AB2 = AE2 + BE2 …….. (i) Similarly, In Δ […]
If in Δ ABC, AD is median and AE ⊥ BC, then prove that AB2 + AC2= 2 AD2 +1/2 BC2 Read More »
Q) If in a triangle ABC right angled at B, AB = 6 units and BC = 8 units, then find the value of sin A cos C + cos A sin C. Ans: Step 1: Let’s make a diagram to better understand the question: Here Δ ABC is a right angle triangle and
Q) Write the smallest number which is divisible by both 306 and 657. Ans: (Note: Here, it is important to understand that since we need to find a number which is divisible by given 2 numbers, then it has to be a multiple of these given numbers, not a factor. Why? Because, factor will always
Write the smallest number which is divisible by both 306 and 657. Read More »
Q) A cylindrical tub, whose diameter is 12 cm and height 15 cm is full of ice-cream. The whole ice-cream is to be divided into 10 children in equal ice-cream cones, with conical base surmounted by hemispherical top. If the height of conical portion is twice the diameter of base, find the diameter of conical
Q) A metallic solid sphere of radius 10.5 cm melted and recasted into smaller solid cones each of radius 3.5 cm and height 3 cm. How may cones will be made? Ans: Step 1: Let’s draw a diagram to better understand the question: Here, according to question, we have sphere of radius 10.5 cm. This
Q) Write all the values of p for which the quadratic equation x2 + px +16 = 0 has equal roots. Find the roots of the equation so obtained. Ans: We know that in a standard quadratic equation, a x2 + b x + c = 0 will have equal
Q) Find X in terms of a b, and c: , X ≠ a, b, c Ans: Given equation is: ∴ ∴ [a (X – b) + b (X – a)] (X – c) = 2 c (X – a) (X – b) ∴ (a X – a b +
Find x in terms of a b, and c: a/(x – a) + b/(x – b) = 2 c/(x – c), x ≠ a, b, c Read More »
Q) In figure, a circle is inscribed in a Δ ABC having sides BC = 8 cm, AB = 10 cm and AC = 12 cm. Find the length BL, CM, and AN. Ans: Step 1: Let’s consider BL = X CL = BC – BL ∴ CL = 8 – X ………(i) Step 2: Since,
Q) Literacy rates of 40 cities are given in the following table. It is given that mean literacy rate is 63.5, then find the missing frequencies x and y. Ans: Step 1: Let’s re-organize the data in the frequency table to find out each part: Step 2: Given that the total of frequencies = 40
Q) If the median of the following frequency distribution is 32.5. Find the values of f1 and f2 . Ans: Step 1: Let’s re-organize the data in the frequency table to find out each part: Step 2: Given that the total of frequencies = 40 ∴ 31 + f1 + f2 = 40 ∴ f1