If (x + 2)(x – 3) is the HCF of the polynomials
p(x) = (x2 + x – 2)(3x2 – 8x + c) and q(x) = (x2 + x – 12)(2x2 + x + b)
Find the values of c and b.
Using the quadratic formula, solve the equation: a2b2x2 – (4b4 – 3a4)x – 12a2b2 = 0
The 5th term of an Arithmetic Progression (A.P.) is 26 and the 10th term is 51. Determine the 15th term of the A.P.
Find the sum of all the natural numbers less than 100 which are divisible by 6.
A household article is available for Rs. 970 cash or Rs. 210 cash down payment followed by three equal monthly instalments. If the rate of interest charged under the instalment plan is 16% per annum, find the amount of instalment.
A man borrows Rs. 25,200 from a finance company and has to repay it in two equal annual instalments. If the interest is charged at the rate of 10% per annum compounded annually, calculate the amount of instalment.
In the below figure, <BAC=90, AD perpendicular to BC
In Figure 2, PT = 6 cm, AB = 5 cm. Find the length of PA.
Draw the graphs of the equations
The speed of a boat in still water is 11 km/hr. It can go 12 km upstream and return downstream to the original point in 2 hours 45 minutes. Find the speed of the stream.
A solid is in the form of a right circular cylinder with hemispherical ends. The total height of the solid is 58 cm and the diameter of the cylinder is 28 cm. Find the total surface area of the sold.
Construct a triangle ABC in which BC = 7cm,
and median AD = 5 cm. Write the steps of construction also.
Find the co-ordinates of the point equidistant from these points A(5,3), B(5, -5) and C(1, -5).
Find the value of p for which the points (-5,1), (1,p) and (4,-2) are collinear.
The Arithmetic Mean of the following frequency distribution is 47. Determine the value of p.
The following table shows the monthly expenditure of a company. Draw a pie-chart for the data.
|Item||Amount (in Rs.)|
A card is drawn at random from a well shuffled deck of playing cards. Find the probability that the card drawn is
(a) a card of spades or an ace
(b) a red king
(c)neither a king nor a queen
(d) either a king or queen
Prove that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the remaining two sides.
Making use of the above, prove the following:
In the figure below, ABCD is a rhombus. Prove that
Prove that if a chord drawn through the point of contact of a tangent to a circle, then the angles which this chord makes with the given tangent are equal respectively to the angles formed in the corresponding alternate segments.
Using the above, do the following:
AB is a diameter and AC is the chord of the circle such that The tangent at C intersects AB produced in D. Prove that BC = BD
A bucket made up of a metal sheet is in the form of a frustum of a cone. Its depth is 24 cm and the diameters of the top and bottom are 30 cm and 10 cm respectively. Find the cost of milk which can completely fill the bucket at the rate of Rs. 20 per litre and the cost of the metal sheet used, if it costs Rs. 10 per 100 cm2.
A man standing on the deck of a ship, which is 10 m above the water level, observes the angle of elevation of the top of a hill as 60° and the angle of depression of the base of the hill as 300. Calculate the distance of the hill from the ship and the height of the hill.
Mrs. Ruchi’s salary is Rs. 32,250 per month exclusive of HRA. She donates Rs. 12,000 to Prime Minister’s Relief Fund (100% exemption). She also donates Rs. 6,000 to a school and gets a relief of 50% on this donation. She contributes Rs. 5,000 per month towards her Provident Fund. She pays a quarterly premium of Rs. 2,500 towards her LIC policy and invests Rs. 25,000 in NSCs. If Rs. 2,700 is the tax deducted each month from her salary for 11 months, find the tax deducted from her salary in the last month of the year.