The distance of a point (2, 5) from Xaxis is
5 units.
If the distance between points (p, –7),(9, –7) is 15 units, then p is
– 6 or 24.
If 7 is the mean of 5, 3, .5, 4.5, b, 8.5, 9.5, then the value of b is
18
Which of the following is the HCF of two consecutive natural numbers?
1
sec+ tan.
The value of sin 15° =
The greatest number which divides 258 and 323 leaving remainders 2 and 3 respectively is
64
The coordinates of the centre of a circle Which is passing through (1, 2),(3, –4) and (5, –6) is
(11, 2)
The lines y = 4x – 10 and y = 7x + 11 intersect at
(7, 38).
If the roots of quadratic equation 3x^{2} – 2x – k = 0, are real and equal, then value of k is _____.
If x^{2 }– 3x – 18 = 0, then the roots of quadratic equation are 6 and ____.
If the first term of an AP is ‘x’ and the common difference is ‘y’, then the n^{th} term of the series is _________.
If the first term and common difference of an AP be ‘a’ and ‘d’ respectively, then n^{th} term of AP is:
T_{n} = a + (n – 1)d
Here, a = x and d = y
Then, for the given series, the n^{th} term is:
T_{n} = x + (n – 1)y
Therefore, if the first term of an AP is ‘x’ and the common difference is ‘y’,
then the n^{th} term of the series is x + (n – 1)y.
A sphere of diameter 7 cm is dropped in a right circular cylinder vessel completely filled with water. Find the volume of water which will fall out of the vessel.
A number is chosen at random from the numbers –8, –7, –6, –5, –4, –3, –2, –1, 0, 1, 2, 3, 4, 5, 6, 7, and 8. If the selected number is a positive multiple of 3, then the probability of the selected number is ________.
Let three numbers in an AP are a –d, a, a + d.
Therefore, a – d + a + a + d = 15
3a=15
a = 5
So, the required point is (0, 9).
(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)
(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)
(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)
(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)
(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)
Total events = 6 x 6 = 36
Favourable event is when the sum is 8.
(2, 6), (3, 5), (4, 4), (5, 3), (6, 2)
Favourable events = 5
Hence, probability of getting 8 as a sum = 5/36
So, we have 32760 = 2 2 2 3 3 5 7 13
So quotient = x  2, remainder = 3
Divisor Quotient + Remainder
= (x^{2} + x  1) (x  2) + 3
= x^{3} + 3x^{2}  3x + 5 = Dividend
(i) Let CD AB. Then, CD = p
Area of ABC = (AB CD)/2 = cp/2 ...(1)
Also,
Area of ABC = (BC AC)/2 = ab/2 ...(ii)
From (i) and (ii) we have,
cp = ab.
(ii) Since ABC is a right triangle right–angled at C
Step 3: Taking M as centre and MO as radius, draw a circle.
Step 4: Let this circle intersect the previous circle at point Q and R.
Step 5: Join PQ and PR. PQ and PR are the required tangents.


Some students arranged a picnic. The budget for food was Rs.240. Because four students of the group failed to go, the cost of food to each student got increased by Rs 5. How many students went for the picnic?
Let ABCD be the given rectangle and let O be a point within it. Join OA, OB, OC and OD.
Through O, draw EOF  AB. Then, ABFE is a rectangle
In right triangles OEA and OFC, we have
Now, in right triangles OFB and ODE, we have
Let AB be a mountain of height h metres and angle of elevation of its top is 30° from a point at x km away from mountain and that of 15° from (x+10)km away from the base of the mountain.
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