The function t which maps temperature in degree Celsius into temperature in degree Fahrenheit is defined Fahrenheit degree is 95, then the value of  C \(t(C)=\frac { 9c }{ 5 } +32\) is ___________

44 ≡ 8 (mod12), 113 ≡ 85 (mod 12), thus 44 x 113 ≡______(mod 12):

Graphically an infinite number of solutions represents ___________

The perimeter of a right triangle is 36 cm. Its hypotenuse is 15 cm, then the area of the traiangle is ____________

In figure \(\angle OAB={ 60 }^{ o }\) and OA = 6cm then radius of the circle is ____________

If the points (0, 0), (a, 0) and (0, b) are colllinear, then ____________

The value of the expression \(\left[ \frac { { sin }^{ 2 }{ 22 }^{ o }+{ sin }^{ 2 }{ 68 }^{ o } }{ { cos }^{ 2 }{ 22 }^{ 0 }+{ cos }^{ 2 }{ 68 }^{ 0 } } +{ sin }^{ 2 }{ 63 }^{ o+ }{ cos }63^{ 0 }{ sin27 }^{ 0 } \right] \)is ___________

A cone of height 9 cm with diameter of its base 18 cm is carved out from a wooden solid sphere of radius 9 cm. The percentage of wood wasted is

A purse contains 10 notes of Rs. 2000, 15 notes of Rs. 500, and 25 notes of Rs. 200.One note is drawn at random. What is the probability that the note is either a Rs. 500, note or Rs. 200 note?

If the smallest value and co-efficient of range a data are 25 and 0.5 respectively. Then the largest value is ___________

Let A = {0, 1, 2, 3} and B = {1, 3, 5, 7, 9} be two sets. Letf: A \(\rightarrow\)B be a function given by  f(x) = 2x + 1. Represent this function as  a table .

Prove that \(\sqrt { 3 } \) is irrational

Using quadratic formula solve the following equations.9x²-9(a+b)x+(2a²+5ab+2b²)=0

In figure OA· OB = OC·OD
Show that \(\angle A=\angle C\ and\ \angle B=\angle D\)

Find a relation between x and y such that the point (x, y) is equidistant from the points (7, 1) and (3, 5).

Show that \(\\ \frac { { cos }^{ 2 }({ 45 }^{ 0 }+\theta ){ +cos }^{ 2 }({ 45 }^{ 0 }-\theta ) }{ tan({ 60 }^{ 0 }+\theta )tan({ 30 }^{ 0 }-\theta ) } =1\)

Find the depth of a cylindrical tank of radius 28 m, if its capacity is equal to that of a rectangular tank of size 28 m x 16 m x 11 m.

The marks scored by 5 students in a test for 50 marks are 20, 25, 30, 35, 40. Find the S.D for the marks. If the marks are converted for 100 marks, find the S.D. for newly obtained marks.

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

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

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

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.

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

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

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.

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

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

Find the value of f(5),

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

Find two consecutive natural numbers whose product is 20.

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.

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

From a point on a bridge across a river, the angles of depression of the banks on opposite sides at the river are 30° and 45°, respectively. If the bridge is at a height at 3 m from the banks, find the width at the river.

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.

Which team is more consistent?