The blanks of river are parallel. A swimmer starts from a point on one of the banks and swims in a straight line to the bank at 45^o and reaches the opposite bank at a point 20 m, from the point opposite to the straight point. The breadth of the river is equal to ____________

In one thousand lottery tickets, there are 50 prizes to be given. The probability of happenning of the event is ___________

In a competition containing two events A and B, the probability of winning the events A and B are \(\frac { 1 }{ 3 } \) and \(\frac { 1 }{ 4 } \) respectively and the probability if winning both events is ___________

A spherical steel ball is melted to make 8 new identical balls. Then the radius each new ball is how much times the radius of the original ball?

The y-intercept of the line 3x - 4y + 8 = 0 is ___________

Find the equation of the line passing through the point (0, 4) and is parallel to 3x+5y+15 = 0 the line is ___________

In the given figure if OC = 9 cm and OB = 15 cm then OB + BD is equal to ____________

A line which intersects a circle at two distinct points is called ____________

If \(A=\left[ \begin{matrix} y & 0 \\ 3 & 4 \end{matrix} \right] \) and \(I=\left[ \begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix} \right] \) then A² = 16 for ___________

If \(\frac { p }{ q } =a\) then \(\frac { { p }^{ 2 }+{ q }^{ 2 } }{ { p }^{ 2 }-{ q }^{ 2 } } \) ___________

Sum of infinite terms of G.P is 12 and the first term is 8. What is the fourth term of the G.P?

In the arithmetic series Sn = k + 2k + 3k +...+ 100, k is positive integer and k is a factor 100 then S_n is ____________

If f is constant function of value \(\frac { 1 }{ 10 } \), the value of f(1) + f(2) + ... + f(100) is _________

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 ___________

The radius of base of a cone 5 cm and height is 12 cm. The slant height of the cone ___________

If cos A = \(\frac{4}{5}\), then the value of tan A is ___________

Kamalam went to play a lucky draw contest. 135 tickets of the lucky draw were sold. If the probability of Kamalam winning is \(\frac{1}{9}\), then the number of tickets bought by Kamalam is

The standard deviation of a data is 3. If each value is multiplied by 5 then the new variance is

If the ratio of the height of a tower and the length of its shadow is \(\sqrt{3}: 1\), then the angle of elevation of the sun has measure

The value of \(si{ n }^{ 2 }\theta +\frac { 1 }{ 1+ta{ n }^{ 2 }\theta } \) is equal to

The next term of the sequence \(\frac { 3 }{ 16 } ,\frac { 1 }{ 8 } ,\frac { 1 }{ 12 } ,\frac { 1 }{ 18 } \), ..... is

If the HCF of 65 and 117 is expressible in the form of 65m - 117 , then the value of m is

Consider four straight lines
(i) l₁ : 3y = 4x + 5
(ii) l₂ : 4y = 3x - 1
(iii) l₃ : 4y + 3x =7
(iv) l₄ : 4x + 3y = 2
Which of the following statement is true?

The slope of the line which is perpendicular to a line joining the points (0, 0) and (– 8, 8) is

If \(\triangle\)ABC is an isosceles triangle with \(\angle\)C = 90^o and AC = 5 cm, then AB is

In ∆LMN, \(\angle\)L = 60^o, \(\angle\)M = 50^o. If ∆LMN ~ ∆PQR then the value of \(\angle\)R is

A frustum of a right circular cone is of height 16 cm with radii of its ends as 8 cm and 20 cm. Then, the volume of the frustum is

If the radius of the base of a cone is tripled and the height is doubled then the volume is

Let f(x) = \(\sqrt { 1+x^{ 2 } } \) then

If {(a, 8 ),(6, b)}represents an identity function, then the value of a and b are respectively

Graph of a linear equation is a ____________

The square root of \(\frac { 256{ x }^{ 8 }{ y }^{ 4 }{ z }^{ 10 } }{ 25{ x }^{ 6 }{ y }^{ 6 }{ z }^{ 6 } } \) is equal to