Question
Show that the line segment joining the points $(5,7),(3,9)$ and $(8,6),(0,10)$ bisect each other.
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The forewheel of a carriage makes 6 revolutions more than the rearwheel in going 120 m . If the diameter of the forewheel be increased by $\frac{1}{4}$ its present diameter and the diameter of the rearwheel be increased by $\frac{1}{5}$ of its present diameter, then the forewheel makes 4 revolutions more than the rearwheel in going the same distance. Find the circumference of each wheel of the carriage.
→In an A.P. the first term is – 5 and last term is 45. If sum of all numbers in the A.P. is 120, then how many terms are there? What is the common difference?
The table below shows the yield of jowar per acre. Show the data by histogram.
Solve for x and y:$\frac{\text{bx}}{\text{a}}+\frac{\text{ay}}{\text{b}}=\text{a}^2+\text{b}^2,$
$\text{x}+\text{y}=\text{2ab}$
→$\text{x}+\text{y}=\text{2ab}$
Prove the following identities:
$\frac{\cot^2\theta(\sec\theta-1)}{(1+\sin\theta)}+\frac{\sec^2\theta(\sin\theta-1)}{(1+\sec\theta)}=0$
→$\frac{\cot^2\theta(\sec\theta-1)}{(1+\sin\theta)}+\frac{\sec^2\theta(\sin\theta-1)}{(1+\sec\theta)}=0$
If tan θ = 2, find the values of other trigonometric ratios.
A two-digit number is such that the product of its digit is 18. When 63 is subtracted from the number, the digits interchange their places. Find the number.
In an A.P. 19th term is 52 and 38th term is 128, find sum of first 56 terms.
Solve the following quadratic equations by factorization:
$\frac{5+\text{x}}{5-\text{x}}-\frac{5-\text{x}}{5+\text{x}}=3\frac{3}{4},$ $\text{x}\neq5,-5$
→$\frac{5+\text{x}}{5-\text{x}}-\frac{5-\text{x}}{5+\text{x}}=3\frac{3}{4},$ $\text{x}\neq5,-5$
Calculate the mean of the following data, using direct method:
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Class
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$25-35$
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$35-45$
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$45-55$
|
$55-65$
|
$65-75$
|
|
Frequency
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$6$
|
$10$
|
$8$
|
$12$
|
$4$
|