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M, D, T and W are sitting around a circle facing at the centre. Who is to the immediate left of D? I. M is between T and W and D is to the immediate left of T. II. D is second to the left of M.

If tan A = cot B, then prove that A + B = 90^@.

A solid cone of height 8 cm and base radius 6 cm is melted and recast into identical cones, each of height 2 cm and diameter 1 cm. Find the number of cones formed.

Suppose you have Rs. 12000 to invest. You have to invest some amount at 10% and the rest at 15%. How much should be invested at each rate to yield 12%on the total amount invested?

Which of the following sequence are Arithmetice progression ? If it is an A.P. then write common difference. 1^3,2^3,3^3,4^3,….

A lady holds 1800 , 100rs shares of a company that pays 15% dividend annually. Calculate her annual dividend. If she had bought these shares at 40% permium, what is the return she gets as percent on her investment ? Give your answer to the nearest integer.

Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time at different speeds. If the caras travel in the same direction, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars?

If alpha + beta =6 " and " alpha^2 + beta^2 =72, find a quadratic equation whose roots are alpha " and " beta.

If tan 2A =cot (A-18^(@) )where 2A is an acute angle, Find the value of A .

Metallic spheres of radii 6cm, 8 cm and 10cm, respectively are melted to form a single solid sphere. Find the radius of the resulting sphere.

Expand the following. log((p^2q^3)/r^4)

Using ruler and compasses only, construct construct a circle of radius 2.5 cm which touches the arms of the angle BAC ofDelta ABC .

A man buys 400, twenty-rupee shares at a premium of 4rs each and receives a dividend of 12% . Find : (i) the amount invested by him (ii) his total income from the shares (iii) percentage return on his money.

State the co-ordinates of the following points under reflection in the line x = 0 : (i) (-6, 4) (ii)(0,5) (iii)(3, -4)

The sides of a right angle triangle PQR are PQ = 7cm , PR =25 cm andangle Q = 90 ^(@)respectively , Then find tan P -tan R

Solve the simultaneous equations. 10/(x+y) = 2/(x-y)=4, 15/(x+y) - 5/(x-y) =-2

For the following frequency distribution, draw a cumulative frequency curve of more than type and hence obtain the median value:

What is ratio of circumcircle radius and radius of incircle of equilateral traingle?

The radii of two circle are 8 cm and 6 cm respectively. Find the radius of the circle having are equal to sum of the areas of two cicles.

P and Q are two points on the opposite sides of a 90 m high tower AB .The base B, of the tower AB , and points P and Q as observed from top A of tower AB are60 ^(@)and 30 ^(@)respectively. Find correct to the nearest .the distance between P and Q.

Choose the best alternative as the answer- A hill always has

A man invests Rs. 4,500 in shares of a company which is playing 7.5% dividend. If Rs. 100 sharesare available at a discount of 10% Find : (i) number of shares he purchases.(ii) his annual income.

A die is thrown 200 times and the following outcomes are noted with their frequencies: {:("Outcomes",1,2,3,4,5,6),("Frequency",56,22,30,42,32,18):} (i) What is the emperical probability of getting 1 in the above case?

Find which term of G.P. 3-6+12-24+. . . . . . . . . . . Is -384 ?

If A=[{:(,-1,1),(,a,b):}] and A^2=I, find a and b.

A wooden cube is painted BLUE on all six faces. The side of this cube is 4 cms. It is cut into smaller cubes of side 1 cm. Answer the following questions based on this statement. How many cubes have no face coloured?

A wooden cube is painted BLUE on all six faces. The side of this cube is 4 cms. It is cut into smaller cubes of side 1 cm. Answer the following questions based on this statement. How many cubes have only one face coloured?

A wooden cube is painted BLUE on all six faces. The side of this cube is 4 cms. It is cut into smaller cubes of side 1 cm. Answer the following questions based on this statement. How many cubes have two faces painted?

A wooden cube is painted BLUE on all six faces. The side of this cube is 4 cms. It is cut into smaller cubes of side 1 cm. Answer the following questions based on this statement. How many cubes have three faces coloured?

If a+b+c =0, find the value of (a^(4) + b^(4) + c^(4) )/( a^(2) b^(2) + c^(2) ( a^(2) + b^(2) ) )

Determine the value of the following. log_(x)sqrtx

Find two consecutive positive integers, sum of whose squares is 613.

A ladder is place against a wall such that its foot is 2.5 m distance from the wall, and its top reaches a window 6m above the ground. Find the length of the ladder.

How many terms of the geometric progression 1+4+16+64+ . . . . .. . . must be added to get sum equal to 5461 ?

Justify that line overset(" "hArr)(AB)line segment formed by given points is parallel to Y -axis . What can you say about their slope ? Why ?(AS_(2))

The total surface area of a hollow cylinder, which is open from both the sides, is 3575 cm", area of its base ring is 357.5 cm^(2)and its height is 14 cm. Find the thickness of the cylinder.

A fig. (X) is given, followed by four complex figures in such a way that fig. (X) is embedded in one of them. Choose that one.

A fig. (X) is given, followed by four complex figures in such a way that fig. (X) is embedded in one of them. Choose that one.

A fig. (X) is given, followed by four complex figures in such a way that fig. (X) is embedded in one of them. Choose that one.

A fig. (X) is given, followed by four complex figures in such a way that fig. (X) is embedded in one of them. Choose that one.

From an external point P, tangents PA and PB are drawn to a circle with centre O. If |__PAB=50^(@), find |__AOB.

In trapezium KLMN ,KL and MN are parallel sides. A line is drawn, from the point A on LN, parallel to MN meeting LM at B. KN :LM is equal to _________.

Pointing towards a person in the photograph, Anita said, “He is the only son of the father of my sister's brother." How is the person related to Anita?

A card is picked up randomly from well shuffled pack of cards. Write the n(S), n(A), n(B) and n(C ). Event A: A red face card. Event B : An ace of spade Event C: Not a black king.

A friction elutch is in the form of a frustum of a coce with radii 16 cm and 10 cm and height 8 cm. find its lateral surface area and its volumein multiples of pi.

If a>0 then the shape of ax^2+bx+c=0 is ……

From an external point P, tangents PA and PB are drawn to a circle with centre O. If |PAB=50^(@), find |AOB.