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If 4 is a root of equation x2 + kx – 4 = 0; the value of k is ______.
Concept: undefined >> undefined
The roots of the quadratic equation x2 – 6x – 7 = 0 are ______.
Concept: undefined >> undefined
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The roots of quadratic equation x(x + 8) + 12 = 0 are ______.
Concept: undefined >> undefined
If one root of equation (p – 3) x2 + x + p = 0 is 2, the value of p is ______.
Concept: undefined >> undefined
Equation 2x2 – 3x + 1 = 0 has ______.
Concept: undefined >> undefined
Which of the following equations has two real and distinct roots?
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If the roots of x2 – px + 4 = 0 are equal, the value (values) of p is ______.
Concept: undefined >> undefined
Which of the following equations has imaginary roots?
Concept: undefined >> undefined
One root of equation 3x2 – mx + 4 = 0 is 1, the value of m is ______.
Concept: undefined >> undefined
If the quadratic equation kx2 + kx + 1 = 0 has real and distinct roots, the value of k is ______.
Concept: undefined >> undefined
One factor of x3 – kx2 + 11x – 6 is x – 1. The value of k is ______.
Concept: undefined >> undefined
If (x – a) is a factor of x3 – ax2 + x + 5; the value of a is ______.
Concept: undefined >> undefined
(x – 2) is a factor of ______.
Concept: undefined >> undefined
For the polynomial x5 – x4 + x3 – 8x2 + 6x + 15, the maximum number of linear factors is ______.
Concept: undefined >> undefined
If f(x) = 3x + 8; the value of f(x) + f(– x) is ______.
Concept: undefined >> undefined
If b is the mean proportion between a and c, show that: `(a^4 + a^2b^2 + b^4)/(b^4 + b^2c^2 + c^4) = a^2/c^2`.
Concept: undefined >> undefined
The daily wages of 80 workers in a project are given below.
| Wages (in Rs.) |
400-450 | 450-500 | 500-550 | 550-600 | 600-650 | 650-700 | 700-750 |
| No. of workers |
2 | 6 | 12 | 18 | 24 | 13 | 5 |
Use a graph paper to draw an ogive for the above distribution. (Use a scale of 2 cm = Rs. 50 on x-axis and 2 cm = 10 workers on y-axis). Use your ogive to estimate:
- the median wage of the workers.
- the lower quartile wage of workers.
- the numbers of workers who earn more than Rs. 625 daily.
Concept: undefined >> undefined
Using properties of proportion, solve for x. Given that x is positive:
`(2x + sqrt(4x^2 -1))/(2x - sqrt(4x^2 - 1)) = 4`
Concept: undefined >> undefined
The weight of 50 workers is given below:
| Weight in Kg | 50-60 | 60-70 | 70-80 | 80-90 | 90-100 | 100-110 | 110-120 |
| No. of Workers | 4 | 7 | 11 | 14 | 6 | 5 | 3 |
Draw an ogive of the given distribution using a graph sheet. Take 2 cm = 10 kg on one axis and 2 cm = 5 workers along the other axis. Use a graph to estimate the following:
1) The upper and lower quartiles.
2) If weighing 95 kg and above is considered overweight, find the number of workers who are overweight.
Concept: undefined >> undefined
The marks obtained by 100 students in a Mathematics test are given below:
| Marks | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 | 70-80 | 80-90 | 90-100 |
| No. of students |
3 | 7 | 12 | 17 | 23 | 14 | 9 | 6 | 5 | 4 |
Draw an ogive for the given distribution on a graph sheet.
Use a scale of 2 cm = 10 units on both axes.
Use the ogive to estimate the:
1) Median.
2) Lower quartile.
3) A number of students who obtained more than 85% marks in the test.
4) A number of students who did not pass in the test if the pass percentage was 35.
Concept: undefined >> undefined
