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Find GCD of 18(4x2 - 25) and 12(2x2 + 11x + 15).
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The ages of 2 men are in the ratio 4 : 5. Five years ago their ages were in the ratio 7 : 9.
Find their present ages.
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Prove that cot2A - tan2A = cosec2A - sec2A.
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If tanA = 4/3. Find sinA + cosA
sinA - cosA
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Without using trignometric tables show that :
cot 20 * cot 25 * cot 65 * cot 70 = 1.
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Snehal purchased a T.V. for Rs. 22,680/- which included sales tax @ 8% of list price.
Find the list price.
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Figure.
In the given figure O is the centre of the circle and ÐAOB = 1200.
Find ÐASB and ÐADB.
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Figure.
In the figure AB = 5 cm, BD = 4 cm, CD = 9 cm. Find DE.
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Find the median of the following data.
12 , 17 , 3 , 14 , 5 , 8 , 7 , 15.
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Figure.
In the figure PB and AQ are perpendicular to the segment AB. If PO = 5 cm and OQ = 7 cm
and area (DPOB ) = 150 cm2. Find the area of (DQOA).
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Find the length of the largest rod that can be placed in the room of 12 m * 8 m * 9 m.
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The area of a rhombus is 72 cm2. If one of the diagonals is 18 cm long.
Find the length of the other diagonal.
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The sides of two triangles are given below, select right angled triangle out of these.
a) 6, 8, 10 b) 12, 13, 15.
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Find the value of K if x2 - x = K(3x - 5) is 0 for distinct roots.
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If a = c Prove that (2a + 3b)(2c - 3d) = (2a - 3b) (2c + 3d).
b d
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If A and B are the roots of equation ax2 + bx + c = 0, Find the value of the following :
I ) A3 + B3 ii) A2 + B2
B A
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Factorise 2b2c2 + 2c2a2 + 2a2b2 - a4 - b4 - c4.
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Solve graphically.
3x + 4y = 12
8x + 5y = 40
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If x = a cosA + b sinA and y = a sinA - b cosA. Prove that x2 + y2 = a2 + b2.
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Four equal circles are described about the four corners of a square so that each touches two
of the other.
Find the area of the shaded region as shown in the figure each side of the square measuring 28 cm.
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The area of an isosceles triangle is 60 cm2 and the length of its equal sides is 13 cm.
Find its base.
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Reena goes to a shop to buy a radio, costing Rs. 2568. The rate of sales tax is 7%.
She tells the shopkeeper to reduce the price of the radio to such an extent that she has to pay
Rs. 2568 inclusive of sales tax. Find the reduction in the price of radio.
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How many bricks each of dimension 25 cm * 16 cm * 10 cm will be needed to build a wall 24 m long,
6 m tall and 4cm thick. What will be the cost of bricks at the rate of Rs. 3.5 per 1000 bricks,
10% of the wall is filled with mortar.
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If tangents be drawn from any point on the common chord of two intersecting circles,
prove that they are equal.
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( x + 2 )( x - 5 )( x - 6 ) ( x + 1 ) = 144. Solve.
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If q is the mean proportional between p and r,
Show that pqr( p + q + r )3 = (pq + qr + pr)3.
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ABC is a right angled triangle, right angle at c . If p is the length of the perpendicular side
from c to AB and AB = c , BC = a , CA = b, Prove that :
i) pc = ab ii ) 1 = 1 + 1
p2 a2 b2
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From the top of a tower 50 m high, the angles of depression of the top and bottom of a pole are
observed to be 450 and 600 respectively. Find the height of the pole.
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An inquiry into the budget of the middle class families in a certain city in India gave the
following information :
| Expenses |
Price in 1975 |
Price in 1980 |
| Food (40%) |
140 |
165 |
| Fuel (10%) |
20 |
23 |
| Clothing (20%) |
60 |
70 |
| Rent (20%) |
50 |
80 |
| Misc.(10%) |
30 |
35 |
Complete the cost of living index number of 1980 taking 1975 as base year.
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AB is a line segment and M is its middle point. On one side of AB, semi-circles have been drawn
by taking AM, MB and AB as diameters. A circle has been drawn which touches each of the three
semi-circles. Prove that the radius of the circle = 1/6 AB.
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