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John and javanti together have $45$ marbles. Both of them lost $5$ marbles each, and the product of the number of marber of marbles they now have is $128$. From the quadratic equation to find how many marbles had to start with, if john and x marbles.
→Find the sum of the following arithmetic progressions:
$1, 3, 5, 7, .....$ to $12$ terms.
→$1, 3, 5, 7, .....$ to $12$ terms.
A piece of equipment cost a certain factory Rs. 60,000. If it depreciates in value, 15% the first, 13.5% the next year, 12% the third year, and so on. What will be its value at the end of 10 years, all percentages applying to the original cost?
In △ ABC point △ on side BC is such that △C = 6, BC = 15. Find A(△ ABD) : A(△ ABC) and A(△ ABD) : A(△ ADC) .
Write the value of k for which the system of equations has infinitely many solutions.
→$2x - y = 5$
$6x + ky = 15$
In the given figure, the side of square is $28\ cm$ and radius of each circle is half of the length of the side of the square where O and O' are centres of the circles. Find the area of shaded region.
→Find the roots of the following equations, if they exist, by applying the quadratic formula:
$36x^2 - 12ax + (a^2 - b^2) = 0$
→$36x^2 - 12ax + (a^2 - b^2) = 0$
Find the coordinates of the midpoint of the line segment joining P(0,6)and Q(12,20).
If $\sin A=\frac{3}{5}$ then show that $4 \tan A+3 \sin A=6 \cos A$
→Following are the lives in hours of 15 pieces of the components of aircraft engine. Find the median:
715, 724, 725, 710, 729, 745, 694, 699, 696, 712, 734, 728, 716, 705, 719
715, 724, 725, 710, 729, 745, 694, 699, 696, 712, 734, 728, 716, 705, 719