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Prove that: `(1)/("log"_8 36) + (1)/("log"_9 36) + (1)/("log"_18 36)` = 2
Concept: undefined >> undefined
If `"a" = "log""p"^2/"qr", "b" = "log""q"^2/"rp", "c" = "log""r"^2/"pq"`, find the value of a + b + c.
Concept: undefined >> undefined
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If a = log 20 b = log 25 and 2 log (p - 4) = 2a - b, find the value of 'p'.
Concept: undefined >> undefined
PQRS is a square whose diagonals PR and QS intersect at O.M is a point on QR such that OQ = MQ. Find the measures of ∠MOR and ∠QSR.
Concept: undefined >> undefined
Prove that the quadrilateral formed by joining the mid-points of a square is also a square.
Concept: undefined >> undefined
In the given figure, ΔPQR is right-angled at P. PABQ and QRST are squares on the side PQ and hypotenuse QR. If PN ⊥ TS, show that:
(a) ΔQRB ≅ ΔPQT
(b) Area of square PABQ = area of rectangle QTNM.
Concept: undefined >> undefined
In the given figure AF = BF and DCBF is a parallelogram. If the area of ΔABC is 30 square units, find the area of the parallelogram DCBF.
Concept: undefined >> undefined
In a parallelogram PQRS, M and N are the midpoints of the sides PQ and PS respectively. If area of ΔPMN is 20 square units, find the area of the parallelogram PQRS.
Concept: undefined >> undefined
In a parallelogram PQRS, T is any point on the diagonal PR. If the area of ΔPTQ is 18 square units find the area of ΔPTS.
Concept: undefined >> undefined
Fadil, a class IX student, scored marks in different subjects (each out of total 100) during his annual examination as given below:
| Subject | Maths | English | Science | Social studies | Hindi | Physical education |
| Mark (out of 100) | 75 | 80 | 77 | 78 | 67 | 89 |
Draw horizontal bar graph for the above data.
Concept: undefined >> undefined
The number of students in different sections of class IX of a certain school is given in the following table.
| Section | IX-A | IX-B | IX-C | IX-D | IX-E |
| Number of students | 48 | 40 | 50 | 45 | 38 |
Draw horizontal bar graph for the above data.
Concept: undefined >> undefined
Draw a histogram for the following frequency distribution:
| Train fare | 0 - 50 | 50 - 100 | 100 - 150 | 150 - 200 | 200 - 250 | 250 - 300 |
| No. of travellers | 25 | 40 | 36 | 20 | 17 | 12 |
Concept: undefined >> undefined
The following frequency distribution table shows the cost of living in a city in a period of 2years. Draw histogram for this frequency distribution:
| Cost of living | 2000 - 2500 | 2500 - 3000 | 3000 - 3500 | 3500 - 4000 | 4000 - 4500 | 4500 - 5000 | 5000 - 5500 | 5500 - 6000 |
| No. of months | 3 | 4 | 2 | 5 | 3 | 2 | 4 | 1 |
Concept: undefined >> undefined
Draw a histogram for the following frequency table:
| Class interval | 5 - 9 | 10 - 14 | 15 - 19 | 20 - 24 | 25 - 29 | 30 - 34 |
| Frequency | 5 | 9 | 12 | 10 | 16 | 12 |
Concept: undefined >> undefined
Draw a histogram for the following cumulative frequency table:
| Marks | Less than 10 | Less than 20 | Less than 30 | Less than 40 | Less than 50 | Less than 60 |
| Number of student | 7 | 18 | 30 | 45 | 55 | 60 |
Concept: undefined >> undefined
Draw a histogram for the following cumulative frequency table:
| Class interval | 0 - 10 | 10 - 20 | 20 - 30 | 30 - 40 | 40 - 50 |
| Cumulative frequency | 6 | 10 | 18 | 32 | 40 |
Concept: undefined >> undefined
Draw a histogram and a frequency polygon for the following data:
| Marks | 0 - 20 | 20 - 40 | 40 - 60 | 60 - 80 | 80 - 100 |
| No. of students | 12 | 18 | 30 | 25 | 15 |
Concept: undefined >> undefined
Draw a histogram and a frequency polygon for the following data:
| Wages | 150 - 200 | 200 - 250 | 250 - 300 | 300 - 350 | 350 - 400 | 400 - 450 |
| No. of workers | 25 | 40 | 35 | 28 | 30 | 22 |
Concept: undefined >> undefined
Draw a frequency polygon for the following data:
| Expenses | 100 - 150 | 150 - 200 | 200 - 250 | 250 - 300 | 300 - 350 | 350 - 400 |
| No. of families | 22 | 37 | 26 | 18 | 10 | 5 |
Concept: undefined >> undefined
Draw a frequency polygon for the following data:
| Class | 15 - 20 | 20 - 25 | 25 - 30 | 30 - 35 | 35 - 40 | 40 - 45 |
| Frequency | 5 | 12 | 15 | 26 | 18 | 7 |
Concept: undefined >> undefined
