Polynomials
Find the value of “p” from the polynomial x2 + 3x + p, if one of the zeroes of the polynomial is 2.
-10
The discriminant of the quadratic equation 𝑥 2 − 3 𝑥 − 2 = 0 is
17
The pair of linear equations 2x + 3y = 5 and 4x + 6y = 10 is
CONSISTENT
The ratio of the area of a quadrant of a circle to the area of the same circle is :
1:4
Compute the zeroes of the polynomial 4x2 – 4x – 8. Also, establish a relationship between the zeroes and coefficients.
-1 and 2
-4/4 and -8,4
A faster train takes one hour less than a slower train for a journey of 200 km. If the speed of the slower train is 10 km/hr less than that of the faster train, find the speeds of the two trains.
40 KM/HR
Find the value(s) of k so that the pair of equations x + 2y = 5 and 3x + ky + 15 = 0 has a unique solution
ANY NUMBER EXCEPT 6
Chord AB subtends an angle of 40° at the centre of the circle of radius 9 cm. The length of arc AB is
44/7 CM
α and β are zeroes of the quadratic polynomial x2 – 6x + y. Find the value of ‘y’ if 3α + 2β = 20.
-16
Find the value of k for which the equation x2 + k(2x + k – 1) + 2 = 0 has real and equal roots
2
The sum of the digits of a two digit number is 9. The number obtained by reversing the order of digits of the given number exceeds the given number by 27. Find the given number.
36 AND 63
A chord of a circle of diameter 20 cm subtends an angle of 60° at the centre of the circle. Find the area of the corresponding minor segment of the circle.
RADIUS= 10 CM , ANGLE=60
Find the zeros of the polynomial x2 – 6x – 7 and also verify for the sum and product of zeroes.
7 and -1
he sum of the areas of two squares is 640 m 2 . If the difference in their perimeters is 64 m, find the sides of the two squares.
24 M AND 8 M
Two numbers are in ratio of 4 : 5. If 8 is subtracted from each of the numbers the ratio becomes 3 : 4. Find the numbers.
32 AND 40
In the given figure, chord AB subtends an angle of 120° at the centre of the circle with radius 7 cm. Find (i) perimeter of major sector OACB, and (ii) area of the shaded segment, if area of △ 𝑂 𝐴 𝐵 = 21.2 cm².
43.3 CM
30.1 CM2
Find the zeroes of the polynomial p(x) = 3x2 - 4x - 4. Hence, write a polynomial whose each of the zeroes is 2 more than the zeroes of p(x).
4 and 4/3
3x2- 16x + 16.
Venkat can row a boat in still water at the speed of 12 km/h. He ferries tourists 15 km upstream and 18 km downstream in 3 hours. Find the speed of the stream
4 KM/HR
The monthly incomes of A and B are in ratio of 6 : 4 & their monthly expenses are in ratio 4 : 2. If each saves Rs 20000/per month, find monthly income of each.
60000 - A
40000 - B
The Governing council of a local public development authority of Dehradun decided to build an adventurous playground on the top of a bill, which will have adequate space for parking. After the survey, it was decided to build a rectangular playground with a semi-circular area allotted for parking at one end of the playground. The length and breadth of the rectangular playground are 14 units and 7 units, respectively. There are two quadrants of radius 2 units on one side for special seats. Based on the above information, answer the following questions: (i) What is the total perimeter of the parking area? (ii) What is the total area of parking and the two quadrants?
18 UNITS
25.54 UNITS2