Q) Prove that the tangents drawn at the ends of a diameter of a circle are parallel. Ans: Let AB and CD are the 2 lines. Since, line AB is tangent to the circle at point P, therefore ∠ APO = 90° (angle between radius and tangent) Similarly, line CD is tangent to the circle at […]
Prove that the tangents drawn at the ends of a diameter of a circle are parallel. Read More »
Q) Find the mean of the following frequency distribution: Ans: To calculate Mean value of the distribution, 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 = = 36.857 Hence, the mean value of
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Q) A fraction becomes when 1 is subtracted from the numerator. It becomes when 8 is added to the denominator. Find the fraction. Ans: Let’s consider the fraction is First, when 1 is subtracted from numerator, then: = ∴ 3 (P -1) = Q ∴ 3P – Q = 3 …………… (i) Next, when 8
A fraction becomes 1/3 when 1 is subtracted from the numerator. It becomes 1/4 Read More »
Q) Prove that = 2 cosec A Ans: Let’s start from LHS LHS = = = = = = = 2 cosec A = RHS ……….. Hence, proved !
Prove that tan A / (1+ sec A) – tan A / (1- sec A) = 2 cosec A Read More »
Q) Find the common difference of an A.P. whose first term is 8, the last term is 65 and the sum of all its terms is 730. Ans: In the AP question, we are given, a = 8 Last term Tn = 65, Sum of AP Sn = 730; We need to find value of
Q) Two pillars are standing on either side of a 80 m wide road. Height of one pillar is 20 m more than the height of the other pillar. From a point on the road between the pillars, the angle of elevation of the higher pillar is 60°, whereas that of the other pillar is 30°.
Q) Find the ratio in which line y = x divides the line segment joining the points (6, -3) and (1, 6). Ans: Let’s draw the diagram to solve: Also consider that the line y = x divided the line PQ in the ratio of m : n. By section formula, if a point (x,
Q) In the given figure, PQ is a chord of the circle centered at O. PT is a tangent to the circle at P. If ∠ QPT = 55°, Find the ∠ PRQ. Ans: Since ∠ OPT = 90° (angle between radius and tangent) and ∠ QPT = 55° ∴ ∠ OPQ = ∠ OPT
Q) Find the mean of the following distribution: Ans: To calculate Mean value of the distribution, 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 = = 41.1 Hence, the mean value of the
Find the mean of the following distribution: Read More »
Q) A 2-digit number is seven times the sum of its digits. The number formed by reversing the digits is 18 less than the given number. Find the given number. Ans: Let’s consider X and Y are the digits of the given number. Hence the given number is 10 X + Y Also given that Number