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If the graph of quadratic polynomial $ax^2 + bx + c$ cuts negative direction of $y$-axis, then what is the sign of $c$?
A bag contains 4 white balls, 5 red balls, 2 black balls and 4 green balls. A ball is drawn at random from the bag. Find the probability that it is:
  1. Black.
  2. Not green.
  3. red or white.
  4. neither red nor green.
In the following figure, from a rectangular region $A B C D$ with $A B=20 cm$, a right triangle $A E D$ with $A E=9 cm$ and $D E$ $=12 cm$, is cut off.
On the other end, taking BC as diameter, a semicircle is added on outside' the region. Find the area of the shaded region. [Use $\pi=\frac{22}{7}$ ]
In the given figure, CP and CQ are tangents to a circle with centre O. ARB is another tangent touching the circle at R. If CP = 11cm and BC = 7cm, then find the length of BR.

 
One of the roots of quadratic equation 2x2 + kx – 2 = 0 is -2, find k.
Find $a_{30} - a_{20}$_ for the A.P.
$a, a + d, a + 2d, a + 3d$, .....
A card is drawn at random from a pack of well shuffled 52 playing cards. Find the probability that the card drawn is -
a spade.
Solve the following quadratic equations by factorization:
(x - 4)(x + 2) = 0
A card is drawn at random from a well shuffled pack of 52 cards. Find the probability that the card drawn is neither a red card nor a queen.
In figure 3.91, line PR touches the circle at point Q. Answer the following questions with the help of the figure.
(1) What is the sum of ∠ TAQ and∠ TSQ?
(2) Find the angles which are congruent to ∠ AQP.
(3) Which angles are congruent to ∠QTS ?
(4) ∠ TAS = 65°, find the measure of ∠TQS and arc TS.
(5) If ∠AQP = 42°and ∠SQR = 58° find measure of ∠ATS.