Q) Two water taps together can fill a tank in 9 hours. The tap of larger diameter takes 10 hours less than the smaller one to fill the tank separately. Find the time (in hrs) which each tap can separately fill the tank. Ans: VIDEO SOLUTION STEP BY STEP SOLUTION It is given that,Time taken […]
Q) A motor boat whose speed is 18 km/h in still water takes 1 hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream. Ans: VIDEO SOLUTION STEP BY STEP SOLUTION It is given that, Speed of motor boat = 18 km/hrDistance travelled =24
Q) The length of 40 leaves of a plant are measured correct to nearest millimetre, and the data obtained is represented in the following table: Find the mean length of the leaves. Ans: Let’s re-arrange the data with midpoint of each class, frequency, and multiply midpoint with frequency: We know that, mean value of grouped data
Q) If 1 + sin2 θ = 3 sin θ cos θ, then prove that tan θ = 1 or 1/2 Ans: Given that 1 + sin2 θ = 3 sin θ cos θ We know that sin2 θ + cos2 θ = 1 Hence, 1 + sin2 θ = 3 sin θ cos θ will become:
If 1 + sin^2 θ = 3 sin θ cos θ, then prove that tan θ = 1 or 1/2 Read More »
Q) PA and PB are tangents drawn to a circle of centre O from an external point P. Chord AB makes and angle of 30 with the radius at the point of contact. If length of the chord of 6 cm, find the length of the tangent PA and the length of the radius OA. Ans:
Q) Solve :- = 2; = – 1, x, y > o Ans: Let’s consider, = A and = B therefore the given equations will be: Equation = 2 will become: 2 A + 3 B = 2 ………. (i) Similarly, = – 1 will become: 4 A – 9 B = -1
Solve 2 by root x + 3 by root y = 2 ; 4 by root x – 9 by root y = -1, x, y > o Read More »
Q) The sum of a two digit number and the number obtained by reversing the digits is 66. If the digits of the number differ by 2, find the number. How many such numbers are there? Ans: Let’s consider X and Y are the digits of the given number. Hence the given number is 10 X
The sum of a two digit number and the number obtained by reversing the digits is 66. Read More »
Q) If 𝛼, β are zeroes of quadratic polynomial 5×2 + 5x + 1, find the value of1. 𝛼2 + 𝛽22. 𝛼‾1 + 𝛽‾1 Ans: Given polynomial equation 5×2 + 5x + 1 = 0 The roots of the polynomial be α and β. We know that sum of roots (α + β) = α + β
Q) National Art convention got registrations from students from all parts of the country, of which 60 are interested in music, 84 are interested in dance and 108 students are interested in handicrafts. For optimum cultural exchange, organisers wish to keep them in minimum number of groups such that each group consists of students interested
National Art convention got registrations from students from all parts of the country Read More »
Q) Find the area of the unshaded region shown in the given figure. Ans: Let’s redraw the diagram: As we can see in the diagram, in the center area: diameter of semicircle (2R) = side of the inside square (S) or S = 2R ………………. (i) Also we see that Side of larger square = Gap
Find the area of the unshaded region shown in the given figure. Read More »