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If the quadratic equation px2 − 2√5px + 15 = 0 has two equal roots then find the value of p.
Concept: Nature of Roots of a Quadratic Equation
Find the 19th term of the following A.P.:
7, 13, 19, 25, ...
Concept: General Term of an Arithmetic Progression
Solve the following quadratic equation by using formula method: 5m2 + 5m – 1 = 0
Concept: Nature of Roots of a Quadratic Equation
Solve the equation by using the formula method. 3y2 +7y + 4 = 0
Concept: Nature of Roots of a Quadratic Equation
Find the sum of all numbers from 50 to 350 which are divisible by 6. Hence find the 15th term of that A.P.
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
Find the term t15 of an A.P. : 4, 9, 14, …………..
Concept: General Term of an Arithmetic Progression
If the 9th term of an A.P. is zero, then prove that 29th term is double of 19th term.
Concept: General Term of an Arithmetic Progression
Decide whether the following sequence is an A.P., if so find the 20th term of the progression:
–12, –5, 2, 9, 16, 23, 30, ..............
Concept: General Term of an Arithmetic Progression
The sequence −10, −6, −2, 2, ... is ______.
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
Choose the correct alternative answer for the following question.
For an given A.P. a = 3.5, d = 0, n = 101, then tn = ....
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
The Sum of first five multiples of 3 is ______.
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
In an A.P. the first term is – 5 and the last term is 45. If the sum of all numbers in the A.P. is 120, then how many terms are there? What is the common difference?
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
If the sum of first p terms of an A.P. is equal to the sum of first q terms then show that the sum of its first (p + q) terms is zero. (p ≠ q)
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
The first term of an A. P. is 5 and the common difference is 4. Complete the following activity and find the sum of the first 12 terms of the A. P.
a = 5, d = 4, s12 = ?
`s_n = n/2 [ square ]`
`s_12 = 12/2 [10 +square]`
`= 6 × square `
` =square`
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
Market value of a share is Rs 200. If the brokerage rate is 0.3% then find the purchase value of the share.
Concept: Shares
The market value of a mutual fund is 400 crore rupees. Which is divided into 8 crore units.
(a) Suppose you invest Rs. 10,000 in the units, how many units will you get ?
(b) While selling the units if their market value is increased by 10%, how much amount will you get by selling them ?
Concept: Mutual Funds and Systematic Investment Plan
The marks scored by students in Mathematics in a certain Examination are given below:
| Marks Scored | Number of Students |
| 0 — 20 | 3 |
| 20 — 40 | 8 |
| 40 — 60 | 19 |
| 60 — 80 | 18 |
| 80 — 100 | 6 |
Draw histogram for the above data.
Concept: Histograms
Draw the frequency polygon for the following frequency distribution
| Rainfall (in cm) | No. of Years |
| 20 — 25 | 2 |
| 25 — 30 | 5 |
| 30 — 35 | 8 |
| 35 — 40 | 12 |
| 40 — 45 | 10 |
| 45 — 50 | 7 |
Concept: Histograms
Given below is the frequency distribution of driving speeds (in km/hour) of the vehicles of 400 college students:
| Speed (in km/hr) | No. of Students |
| 20-30 | 6 |
| 30-40 | 80 |
| 40-50 | 156 |
| 50-60 | 98 |
60-70 |
60 |
Draw Histogram and hence the frequency polygon for the above data.
Concept: Histograms
Represent the following data by Histogram:
|
Price of Sugar per kg (in Rs.) |
Number of Weeks |
| 18-20 | 4 |
| 20-22 | 8 |
| 22-24 | 22 |
| 24-26 | 12 |
| 26-28 | 8 |
| 28-30 | 6 |
Concept: Histograms
