Which one among the following statements is incorrect?
A)
Graph of a linear polynomial is a straight line whereas the graph of a quadratic polynomial has one of the two shapes of parabola either open upwards \[\cap \] or open downwards \[\cup \].
doneclear
B)
The shape of the parabola depends on the value of 'a' of the quadratic polynomial\[a{{x}^{2}}+2x+c\].
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C)
The zeroes of a quadratic polynomial \[a{{x}^{2}}+bx+c,\] \[a\ne 0\] are y coordinates of the points where the parabola \[y=a{{x}^{2}}+bx+c\] intersects the y-axis.
doneclear
D)
A real number m is a zero of the polynomial p(x) if p (m) = 0.
Find the values of p and q for which the pair of linear equations \[\underset{4x}{\mathop{(3p+2q)\,x}}\,\underset{+7y}{\mathop{+(q+2p)\,y}}\,\underset{=29}{\mathop{=3p-q+1}}\,\] have infinitely many solutions.
A crow is sitting on the top of a house. The house is 40 m high. The angle of elevation of the crow as seen from a point on the ground is \[45{}^\circ \]. The crow flies away horizontally and remains at a constant height. After 3 seconds, the angle of elevation of the crow from the point of observation becomes\[30{}^\circ \]. Find the speed of the crow. \[[Take\sqrt{3}=1.732]\]
A 28 metres high tower casts a shadow 44 metres long at a certain time and at the same time, a telephone pole casts a shadow 33 metres long. Find the height of the telephone pole.
In the figure given below, if PQR is an equilateral triangle and a square ABCD of side AD = 9 cm is inscribed in it, then by how many \[c{{m}^{2}}\] is the area of the triangle more than that of the square?
If p, q, r, s are positive integers such that p < q < r < s. If mean and median of p, q, r, s are 25 and 26 respectively, then which one of the following statements can be true?
A child's game has 12 triangles of which 5 are blue and rest are green, and 18 squares of which 8 are blue and rest are green. One piece is lost at random. Then, the probability that it is a______.
A die has its six faces marked 2, 3, 3, 3, 5, 5. Two such dice are thrown together and the total score is recorded. What is the probability of getting a total of 8?
In the figure shown below, PQR is a triangle right angled at P. Semicircles are drawn on PQ, PR and QR as diameters. Find the area of the shaded portion.
The trees of a row of a garden are numbered consecutively from 1 to 49. There is a value of p such that the sum of the numbers of trees preceding the tree numbered p is equal to the sum of the numbers of the houses following it, then value of p is:
A vessel in the form of an open inverted cone is filled with water up to the brim. The height and radius of the top of the vessel are 14 cm and 3 cm, respectively. If lead shots of radius 0.5 cm are dropped into the vessel, one-sixth of the water flows out, then find the number of lead shots dropped in the vessel.
Find the difference of the areas of two segments of a circle formed by a chord of length 14 cm subtending an angle of \[90{}^\circ \] at the centre. \[\left[ Take\,\pi =\frac{22}{7} \right]\]
The sum of the length, breadth and height of a cuboid is \[8\,\sqrt{3}\,cm\] and length of its diagonal is\[3\,\sqrt{8}\,cm\]. What will be the total surface area of the cuboid?
The volume of a right prism, whose base is an equilateral triangle, is \[1800\,\sqrt{3}\,c{{m}^{3}}\] and the height of the prism is 120 cm. Find the side of the base of the prism.
Prem walks 10 km towards North. From there he walks 6 km towards South. Then, he walks 3 km towards East. How far and in which direction is he with reference to his starting point?
If the positions of the first and the eighth letters of the word REPRESENTATIVE are interchanged, similarly, the positions of the second and the ninth letters of the word are interchanged and so on, which of the following will be the fourth to the left of the sixth from the left end after the rearrangement?
The integers 1 to 80 are written on a blackboard. The following operation is then repeated 79 times: In each repetition, any two numbers say p and q, currently on the blackboard are erased and a new number \[p+q-3\] is written. What will be the number left on the board at the end?
Let pqr is a three digit number such that \[p\ne 0\] and \[p<q\] and \[r<q\] where p, q and r are hundred's digit, ten's digit and unit's digit, respectively. How many such 3 - digit positive integers are possible?