A function f: [-7,6) \(\rightarrow\) R is defined as follows.

find 2f(-4) + 3f(2)

A function f: [-7,6) \(\rightarrow\) R is defined as follows.

f(-7) - f(-3)

f(x) = (1+ x)
g(x) = (2x - 1)
Show that fo(g(x)) = gof(x)

A function f: (1,6) \(\rightarrow\)R is defined as follows:

Find the value of f(5),

If R = {(a, -2), (-5, b), (8, c), (d, -1)} represents the identity function, find the values of a, b, c and 

Which of the following list of numbers form an AP? If they form an AP, write the next two terms:
4,10,16, 22, ...

Determine the AP whose 3rd term is 5 and the 7^th term is 9.

If the sum of the first 14 terms of an AP is 1050 and its first term is 10, find the 20th term.

How many terms of the AP: 24, 21, 18, ... must be taken so that their sum is 78?

Find the sum of first 24 terms of the list of numbers whose nth term is given by a_n = 3 + 2n.

The sum of two numbers is 15. If the sum of their reciprocals is \(\frac{3}{10}\), find the numbers.

Seven years ago, Varun's age was five times the square of Swati's age. Three years hence Swati's age will be two fifth of Varun's age. Find their present ages.

A chess board contains 64 equal squares and the area of each square is 6.25 cm², A border round the board is 2 cm wide.

Find two consecutive natural numbers whose product is 20.

A two digit number is such that the product of its digits is 18, when 63 is subtracted from the number, the digits interchange their places. Find the number.

Prove that in a right triangle, the square of 8. the hypotenuse is equal to the sum of the squares of the others two sides.

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

In figure 0 is any point inside a rectangle ABCD. Prove that OB² + OD² = OA² + OC²

In \(\angle ACD={ 90 }^{ 0 }\) and \(CD\bot AB\) Prove that \(\cfrac { { BC }^{ 2 } }{ { AC }^{ 2 } } =\cfrac { BD }{ AD } \)

The perpendicular from A on side BC at a \(\triangle\)ABC intersects BC at D such that DB = 3 CD. Prove that 2AB² = 2AC² + BC².

Find the coordinates at the points of trisection (i.e. points dividing in three equal parts) of the line segment joining the points A(2, -2) and B(-7, 4).

If the points A(6, 1), B(8, 2), C(9, 4) and D(P, 3) are the vertices of a parallelogram, taken in order. Find the value of P.

Find the area of a triangle vertices are(1, -1), (-4, 6) and (-3, -5).

Find the area of the quadrilateral whose vertices, taken in order, are (-4, -2), (-3, -5), (3, -2) and (2, 3).

Find the value of k if the points A(2, 3), B(4, k) and (6, -3) are collinear.

If sin (A - B) = \(\frac12\),  cos (A + B) = \(\frac12\), 0^o < A + ≤  90°, A > B, find A and B.

Evaluate \(\frac { tan{ 65 }^{ o } }{ tan{ 25 }^{ o } } \)

If ATB=90^o then prove that
\(\sqrt { \frac { tanA\quad tanB+tanA\quad cotB }{ sinA\quad secB } } -\frac { { Sin }^{ 2 }A }{ { Cos }^{ 2 }A } =tanA\)

If 15tan² θ+4 sec² θ=23 then find the value of (secθ+cosecθ)² -sin² θ

The angle of elevation of a tower at a point is 45^o, After going 20 meters towards the foot of the tower the angle of elevation of the tower becomes 60^o calculate the height of the tower.

What is the ratio of the volume of a cylinder, a cone, and a sphere. If each has the same diameter and same height?

Find the number of coins, 1.5 cm is diameter and 0.2 cm thick, to be melted to form a right circular cylinder of height 10 cm and diameter 4.5 cm.

A spherical ball of iron has been melted and made into small balls. If the radius of each smaller ball is one-fourth of the radius of the original one, how many such balls can be made?

A wooden article was made by scooping out a hemisphere from each end of a cylinder as shown in figure. If the height of the cylinder is 10 cm and its base is of radius 3.5 cm find the total surface area of the article.

Σx = 99, n = 9, Σ(x - 10)² = 79, then find,
(i) Σx²
(ii) Σ(x - \(\bar { x } \))²

Find the co-efficient of variation for the following data: 16, 13, 17,21, 18.

C.V. of a data is 69%, S.D. is 15.6, then find its mean.

S.D. of a data is 2102, mean is 36.6, then find its C.V.

Team A	50	20	10	30	30
Team B	40	60	20	20	10

Which team is more consistent?

Final the probability of choosing a spade or a heart card from a deck of cards.