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All Questions and Answers

Class 9 Maths Chapter 1 to 30

Exercise 1 (A)

3 Qs

Without doing any actual division, find which of the following rational numbers have terminating decimal representation :
(i) $\frac{7}{1 6}$ (ii) $\frac{2 3}{1 2 5}$
(iii) $\frac{9}{1 4}$ (iv) $\frac{3 2}{4 5}$
(v) $\frac{4 3}{5 0}$ (vi) $\frac{1 7}{4 0}$
(vii) $\frac{6 1}{7 5}$ (viii) $\frac{1 2 3}{2 5 0}$

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The correct number in the $5^{t h}$ decimal place of the number $\frac{2}{7}$ $=$ $0 . \overline{285714}$

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State whether True or False
$\frac{8}{1 3}$ can be represented as $0 . \overline{615384}$

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Exercise 1 (B)

15 Qs

State whether True or False
The square of $5 - 2$ is $9 - 45$

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State whether True or False
The square of $3 + 25$ is $29 + 125$

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Given universal set $= {- 6, - 5 \frac{3}{4}, - 4, - \frac{3}{5}, - \frac{3}{8}, 0, \frac{4}{5}, 1, 1 \frac{2}{3}, 8, 3.01, π, 8.47}$
From the given set, find the set of irrational numbers.

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Given universal set $= {- 6, - 5 \frac{3}{4}, - 4, - \frac{3}{5}, - \frac{3}{8}, 0, \frac{4}{5}, 1, 1 \frac{2}{3}, 8, 3.01, π, 8.47}$
From the given set, find the set of integers.

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Use division method to show that $3$ and $5$ are irrational numbers.

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Use division method of contradiction to show that $3$ and $5$ are irrational numbers. Also find the value of $15 \times 3 \times 5$

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Simplify : ( $3 + 2$ ) $\times$ ( $3 - 2$ ).

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Find the sum of the irrational numbers : $3 - 2$ and $5 + 2$

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State whether true or false
The pair of irrational numbers gives difference which is irrational are $2 + 23$ and $3 - 32$

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If the following statement is True, enter 1 else enter 0.
The difference between these two irrational numbers, $7 + 52$ and $- 3 + 52$ is rational.

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check whether the following statement is True or False:
The product of these two irrational numbers $3 + 32$ and $2 - 3$ is also an irrational number.

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Insert two irrational numbers between $5$ and $6$ .

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Insert five irrational numbers between $25$ and $33$ .

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Say true or false:
$1.5$ is rational number between $2$ and $3$ .

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Write three rational numbers between $3$ and $5 .$

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Exercise 1 (C)

31 Qs

State true or false: $3 + 2$ is a surd.

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If the lowest rationalizing factor of $52$ is $m$ , then find the value of $m$ .

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If the lowest rationalising factor of $24$ is $m$ , then find the value of $m$ .

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The diagonals of a rhombus are $12$ cm and $16$ cm. Find :

$5 - 3$ is $5 + m$
m is

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If $7 - 7$ is $m + 7$ , then $m$ is

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Write the lowest rationalising factor of :

$18 - 50$ is $m$

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Write the lowest rationalising factor of :

$5 - 2$ is $5 + m$
$m$ is

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Write the lowest rationalising factor of :

$13 + 3$ is $13 - m$
$m$ is

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Write the lowest rationalising factor of :
$15 - 32$ is $m + 2$
$m$ is

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32√+23√ is

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Find the value of 'a' in the following equation:
$\frac{2 + 3}{2 - 3} = a + b 3$

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Find the values of 'a' in each of the following :
If $\frac{7 - 2}{7 + 2} = a 7 + b$ , then $a = - \frac{m}{3}$
where m is

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Find the values of 'a' in each of the following :
$\frac{3}{3 - 2} = a 3 - b 2$

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Find the value of 'a' in $\frac{5 + 3 2}{5 - 3 2} = a + b 2$ , then $a = \frac{m}{7}$ where m is rational number.

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$\frac{2 2}{2 3 + 1} + \frac{1 7}{2 3 - 1}$ is equal to $\frac{7 8 3 - 5}{m}$
then the value of m if m is rational number

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If $\frac{2}{6 - 2} - \frac{3}{6 + 2}$ is equal to $\frac{2 3 + 2 - 3 2 + 6}{m}$ then value of m is

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$x = \frac{5 - 2}{5 + 2}$ and $y = \frac{5 + 2}{5 - 2}$ .
If $x^{2}$ is $161 - 72 m$ , then value of $m$ is ?

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If $x = \frac{5 - 2}{5 + 2}$ , $y = \frac{5 + 2}{5 - 2}$ and $y^{2}$ is $(161 + 72 m)$ , then value of $m$ is ___.

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$x = \frac{5 - 2}{5 + 2}$ and $y = \frac{5 + 2}{5 - 2}$ .
Find the value of $x y$ .

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$x = \frac{5 - 2}{5 + 2}$ and $y = \frac{5 + 2}{5 - 2}$ .
Find the value of $x^{2} + y^{2} + x y$ .

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If $x = 5 - 46$ , find value of m:
$\frac{1}{x}$ $= - \frac{5 + 4 6}{m}$ .

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Given: $x = 5 - 46$ .

If $x - \frac{1}{x}$ is equal to $\frac{3 6 0}{7 1} - \frac{2 8 0}{7 1} m$ , then the value of $m$ is ?

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If $x = 5 - 46$ , $x + \frac{1}{x}$ is equal to $\frac{3 5 0}{7 1} - \frac{2 8 8}{7 1} m$ .
Find the value of m.

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If $m = \frac{1}{3 - 8}$ and $n = \frac{1}{3 + 8}$ .
If $m^{2}$ is equal to $17 + 6 n$ , then value of $n$ is?

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If $m = \frac{1}{3 - 8}$ and $n = \frac{1}{3 + 8}$ , find if $n^{2}$ is equal to $17 - 6 m$ , then value of m is?

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Solve:
$m n = \frac{1}{( 3 - 8 ) \times ( 3 + 8 )}$ .

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If $x = 23 + 22$ and $\frac{1}{x}$ is equal to $\frac{3 - 2}{m}$ , then value of $m$ is :

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If $x = 23 + 22,$ find :

If $x + \frac{1}{x}$ is equal to $\frac{5 3 + 3 2}{m}$ , then value of $m$ is :

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If $x = 23 + 22$ and $(x + \frac{1}{x})^{2}$ is equal to $\frac{9 3 + 3 0 6}{m}$ , then value of $m$ is?

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If $x = 5 - 26,$ find the value of : $(x - \frac{1}{x})^{2}$

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If $x = 5 - 26,$ find $x^{2} + \frac{1}{x ^{2}}$ .

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Exercise 30 (A)

47 Qs

For equation given below, name the dependent and independent variables.
$y = \frac{4}{3} x - 7$

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For equation given below, $y$ is the independent variable and $x$ is the dependent variable.
$x = 9 y + 4$

If above statement is true then write 1 and if false then write 0.

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For equation given below, name the dependent and independent variables.
$x = \frac{5 y + 3}{2}$

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For each equation given below, name the dependent and independent variables.
$y = \frac{1}{7} (6 x + 5)$

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If $(8, 7)$ is plotted in correct place of graph then write answer is $1,$ else $0$ .

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By using graph find the quadrant(in number) in which the point $(3, 6)$ lies.

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By using graph we can locate $(0, 4)$ on the y-axis.

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By using graph we find that the point P $(0, - 4)$ lies on the x-axis.

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By using graph, (in numbers) find the quadrant or axis in which $(3, - 2)$ lies.

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By using graph, the quadrant (in number) in which $(- 2, 5)$ lies is ____.

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Plot the following point on a graph paper : $(- 3, 0)$

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By using graph, the quadrant (in number) in which $(3, 6)$ lies is ___ .

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Plot the following point on a graph paper :
$(- 4, - 3)$

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Find the values of $x$ and $y$ if $(x - 1, y + 3) = (4, 4)$ .

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Find the values of x and y if $(3 x + 1, 2 y - 7) = (9, - 9)$

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Find the values of x and y if (5x - 3y, y - 3x) = (4, -4)

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The abscissa is $2$ , the point is $(2, 2)$ and $(2, - 4)$ .
If true then enter $1$ and if false then enter $0$ .

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Use the graph given alongside, to find the coordinates of the point(s) satisfying the given condition:

The ordinate is 0.
The point is (5,0)

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Find the coordinates with ordinate as $3$ .

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The ordinate is -4. The point is (2,-4).
If true then enter $1$ and if false then enter $0$ .

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Find the coordinates with abscissa is 5.

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The abscissa is equal to the ordinate, then $A = (2, 2), H = (5, 5)$ and $I = (4, 4)$ .
If true, then enter $1$ and if false, then enter $0$ .

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The ordinate is half of the abscissa, then the point $E = (6, 3)$ .
If true, then enter $1$ and if false, then enter $0$ .

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The ordinate of a point is its x-co-ordinate.

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State true or false:
The origin is in the first quadrant.

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The y-axis is the vertical number line.

If above statement is true then enter $1$ and if false then enter $0$ .

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Every point is located in one of the four quadrants.

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If the ordinate of a point is equal to its abscissa; the point lies either in the first quadrant or in the second quadrant.

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The origin $(0, 0)$ lies on the $x$ -axis.

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The point $(a, b)$ lies on the $y$ -axis if $b = 0$ .

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In the following, find the co-ordinates of the point whose abscissa is the solution of the first equation and ordinate is the solution of the second equation :
$3 - 2 x = 7; 2 y + 1 = 10 - 2 \frac{1}{2} y .$

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In the following, find the coordinates of the point whose abscissa is the solution of the first equation and ordinate is the solution of the second equation:

$\frac{2 a}{3} - 1 = \frac{a}{2}; \frac{1 5 - 4 b}{7} = \frac{2 b - 1}{3}$

Claim : Solution is $(6, 2)$

If true then enter $1$ and if false then enter $0$

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In the following, find the coordinates of the point whose abscissa is the solution of the first equation and ordinate is the solution of the second equation :

$5 x - (5 - x) = \frac{1}{2} (3 - x); 4 - 3 y = \frac{4 + y}{3}$
solution is $(1, \frac{4}{5})$
If true then enter $1$ and if false then enter $0$

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In the following, the coordinates of the three vertices of a rectangle ABCD are given. By plotting the given points; find, the coordinates of the fourth vertex:

A (2, 0), B (8, 0) and C (8, 4)
Claim: The co-ordinates of the fourth vertex are (2,4)
If true then enter $1$ and if false then enter $0$

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A (4, 2), B (-2, 2) and D (4, -2) is (-2,-2)
If true then enter $1$ and if false then enter $0$

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In the following, the coordinates of the three vertices of a rectangle ABCD are given. By plotting the given points; find, the coordinates of the fourth vertex:

A (-4, -6), C (6, 0) and D (-4, 0)
Claim: The co-ordinates of the fourth vertex are ( $x$ ,-6).
Find $x$ .

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In the following, the coordinates of the three vertices of a rectangle ABCD are given. By plotting the given points; find, the coordinates of the fourth vertex:

B (10, 4), C (0, 4) and D (0, -2)
Claim: The co-ordinates of the fourth vertex are (10,-2).
If true then enter $1$ and if false then enter $0$

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$A (- 2, 2), B (8, 2)$ and $C (4, - 4)$ are the vertices of a parallelogram $A B C D$ . By plotting the given points on a graph paper; find the co-ordinates of the fourth vertex $D$ .
Also, from the same graph, state the co-ordinates of the mid-points of the sides $A B$ and $C D$ .

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Use the graphical method to find the co-ordinate of the fourth vertex B
Claim : Answer is (4,4)
If true then enter $1$ and if false then enter $0$

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A (-2, 4), C (4, 10) and D (-2, 10). are the vertices of a square ABCD.

The co-ordinates of the mid-point of BC is (4,7)

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The co-ordinates of the mid-point of CD is (1, 10)
If true then enter $1$ and if false then enter $0$

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The co-ordinates of the point of intersection of the diagonals of the square ABCD is (1,7)
If true then enter $1$ and if false then enter $0$

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By plotting the following points on the same graph paper, check whether they are collinear or not
If true then enter $1$ and if false then enter $0$
$$(3, 5), (1, 1) and (0, -1)$$

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(-2, -1), (-1, -4) and (-4,-1)

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Plot the point A (5, -7). From point A, draw AM perpendicular to x-axis and AN perpendicular to y-axis. Write the co-ordinates of points M and N.

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In square ABCD; A = (3, 4), B = (-2, 4) and C = (-2, -1). By plotting these points on a graph paper, find the co-ordinates of vertex D. Also, find the area of the square.

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In rectangle OABC; point O is the origin, OA = 10 units along x-axis and AB = 8 units. Find the co-ordinates of vertices A, B and C.

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Exercise 30 (B)

45 Qs

Draw the graph for the linear equation given below: $x = 3$

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Draw the graph for the linear equation given below: $x + 3 = 0$

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$x - 5 = 0$ and find the value of x co-ordinate where it crosses $x - a x i s$

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Draw the graph for the linear equation given below:
$2 x - 7 = 0$
Which of the following points lie on this line?

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y = 4 is parallel to x axis.If true enter 1 else 0.

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y + 6 = 0 is parallel to x axis.If true enter 1 else 0.

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y - 2 = 0 is parallel to x axis.If true enter 1 else 0.

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Draw the graph for the linear equation given below: $3 y + 5 = 0$ .

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2y - 5 = 0 is parallel to x axis.If true enter 1 else 0.

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Draw the graph for the linear equation given below:
$y = 0$
Which of the following points lie on this line?

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x = 0 is y axis.If true enter 1 else 0.

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$y = 3 x$

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$y = - x$

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$y = x$

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$5 x + y = 0$

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$x + 2 y = 0$

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$4 x - y = 0$

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The line $3 x + 2 y = 0$

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Draw the graph for the linear equation $x = - 2 y$

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Which of the following is/are true regarding the following linear equation:
$y = 2 x + 3$

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The equation of the line $y = \frac{2}{3} x - 1$ , passes through

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Which of the following is/are true regarding the following linear equation:

$y = - x + 4$

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Which of the following is/are true regarding the following linear equation:

$y = 4 x - \frac{5}{2}$

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Which of the following is/are true regarding the following linear equation:
$y = \frac{3}{2} x + \frac{2}{3}$

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The line $2 x - 3 y = 4$

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Which of the following is/are true regarding the following linear equation:
$\frac{x - 1}{3} - \frac{y + 2}{2} = 0$

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Which of the following is/are true regarding the following linear equation:
$x - 3 = \frac{2}{5} (y + 1)$

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Which of the following is/are true regarding the following linear equation:
$x + 5 y + 2 = 0$

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$3 x + 2 y = 6$

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Draw the graph for the equation given below :
The co-ordinates of the points where the line meets the $X$ -axis and the $Y$ -axis are respectively. $\frac{1}{2} x + \frac{2}{3} y = 5$

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$\frac{2 x - 1}{3} - \frac{y - 2}{5} = 0$

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7 - 3 (1 - y) = - 5 + 2x

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The pair of linear equations are:
$y = 3 x - 1$
$y = 3 x + 2$

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$y = x - 3$
$y = - x + 5$

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The pair of linear equations are
$2 x - 3 y = 6$
$\frac{x}{2} + \frac{y}{3} = 1$

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The pair of linear equations are
$3 x + 4 y = 24$
$\frac{x}{4} + \frac{y}{3} = 1$

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On the same graph paper, plot the graphs of $y = 2 x - 1, y = 2 x a n d y = 2 x + 1$ from $x = - 2 t o x = 4$ . Are the graph (line) drawn parallel to each other ? If yes enter 0 otherwise 1,

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The graph of 3x + 2y = 6 meets the x-axis at point P and the y-axis at point Q. Use the graphical method.
Statement : Then the co-ordinates of points P and Q are P = (2, 0) and Q = (0, 3)
If statement is true then enter $1$ and if false then enter $0$

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Find the value of y, when $x = - 3$ in the graph of equation $x + 2 y - 3 = 0$

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Draw the graph of equation $x + 2 y - 3 = 0$ . From the graph, find $x_{2}$ .
Also find the value of $x$ , when $y = - 2$

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Draw the graph of equation $3 x - 4 y = 12$ and use the graph drawn to find $y_{1}$ , when $x = 4$

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Draw the graph of equation $3 x - 4 y = 12$ . use the graph drawn to find the value of $x$ , when $y = - 3$ .

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For $\frac{x}{4} + \frac{y}{5} = 1$ . then find the value of $y$ , when $x = - 4$ .

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the value of $x$ , when $y = - 5$ .

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The graph of 3x + 2y = 6 meets the x-axis at point P and the y-axis at point Q. Use the graphical method,then the co-ordinates of points P and Q are P = (2, 0) and Q = (0, 3)
If true then enter $1$ and if false then enter $0$

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Exercise 30 (C)

30 Qs

Write the inclination of a line which is parallel to x-axis.

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Write the inclination of a line which is perpendicular to x-axis.

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Write the inclination of a line which is Parallel to y-axis.

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Write the inclination of a line which is Perpendicular to y-axis

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The slope of the line whose inclination is $0^{\circ}$

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The slope of the line whose inclination is $3 0^{\circ}$ is $\frac{1}{m}$ . Find the value of $m$ .

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The slope of the line whose inclination is $4 5^{\circ}$

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The slope of the line whose inclination is $6 0^{\circ}$ is $k 3$ , find $k$

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Find the inclination of the line whose slope is 1

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Find the inclination of the line whose slope is $3$

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Find the inclination of the line whose slope is $\frac{1}{3}$

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perpendicular to x-axis is not defined.If true enter 1 else 0.

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Write the slope of the line which is parallel to y-axis.

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Write the slope of the line which is perpendicular to y-axis.

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Given slope of $x + 3 y + 5 = 0$ is $- \frac{1}{3}$
find intercept of y.

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Find the slope of $$3x - y - 8 = 0$$

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Given equation is $5 x = 4 y + 7$ , then the slope is $\frac{5}{m}$ find the value of m.

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Given equation is $x = 5 y - 4$ , then the slope is $\frac{1}{m}$ . Find the value of $m$ .

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The slope of $y = 7 x - 2$ is ____ .

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Find the slope of $3 y = 7$

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The slope of $4 y + 9 = 0$ is ____.

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Slope $= 2$ and y-intercept $= 3$ , then the equation of line is $y = m x + c$ . Find $c - m$ .

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Slope $= 5$ and y-intercept $= - 8$ , then the equation of line is $y = m x + c$ . Find $m - c$ .

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Slope $= - 4$ and y-intercept $= 2$ , then the equation of line is $m x + y = c$ . Find $m + c$ .

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Slope = -3 and y-intercept = -1, then the equation is kx + y+ 1 =0
Find $k$

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Slope = 0 and y-intercept = -5, then the equation is y + k = 0
Find $k$

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Slope = 0 and y-intercept = 0, then equation of line is y = k
Find k

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Draw the line $3 x + 4 y = 12$ on a graph paper. From the graph paper, read the y-intercept of the line.

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Draw the line $2 x - 3 y - 18 = 0$ on a graph paper. From the graph paper read the y-intercept of the line?

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Draw the graph of line x + y = 5. Use the graph paper drawn to find the inclination and the y-intercept of the line.

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Exercise 29 (A)

35 Qs

Find value of 10x

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Value of 100x is 3464,

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.

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(ii)

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(in degrees)

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Find angle 'x' if :

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Find the length of $A D$ from the above figure.

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The length of $A D$ is

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Given : $∠ A B C = 6 0^{\circ}$
$∠ D B C = 4 5^{\circ}$
and BC = 40 cm.Find the length of AD (in cm)

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Find lengths of BD. Given AB = 60 cm and $∠ B A D = 6 0^{\circ}$

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AB is 54.64
If true then enter $1$ and if false then enter $0$

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Length of AB in cm

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Distance between AB and DC is 17.32 cm.
If true then write 1 and if false then write 0.

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The length of AB is 25.32 cm
If true then enter $1$ and if false then enter $0$

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The length of AB is 81.96 cm.
If true then enter $1$ and if false then enter $0$

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Calculate AB

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AC is 2.83 cm
If true then enter $1$ and if false then enter $0$

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AE is 2.31 cm
If true then enter $1$ and if false then enter $0$

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BE (in cm)

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AC is 24.25 cm
If true then enter $1$ and if false then enter $0$

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BC is 20.78 cm
If true then enter $1$ and if false then enter $0$

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Find the value of $A C$ (in cm) for given figure.

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In right-angled triangle $A B C; B = 9 0^{\circ}$ . Find the magnitude of angle $A$ , if:
$A B$ is $3$ times of $B C$ .

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BC is $3$ times of AB

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A ladder is placed against tower. If the ladder makes an angle of $3 0^{\circ}$ with the ground and reaches upto a height of 15 m of the tower; find length of the ladder.

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A kite is attached to a 100 m long string, then the greatest height reached by the kite when its string makes an angle of $6 0^{\circ}$ with the level ground is 86.6 m
If true then enter $1$ and if false then enter $0$

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AB is 27.32 cm
If true then enter $1$ and if false then enter $0$

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AB is 17.32 cm
If true then enter $1$ and if false then enter $0$

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Ab is 47.32 cm
If true then enter $1$ and if false then enter $0$

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Find PQ, if AB = 150 m, $∠ P = 3 0^{\circ} a n d ∠ Q = 4 5^{\circ}$

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If $t a n x^{\circ} = \frac{5}{1 2}, t a n y^{\circ} = \frac{3}{4}$ and AB = 48 m; find the length of CD.

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The perimeter of a rhombus is 96 cm and the obtuse angle of it is $12 0^{\circ}$ .
Find the length of its smallest diagonal.

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AB is a ladder of length 4 m, leaning on a vertical wall. End A of the ladder is on the floor and end B is on the wall. If the ladder slipped to the position A'B', the top end of the ladder has come down to 1.46 cm
If true then enter $1$ and if false then enter $0$

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In the following figure; angle $B = 9 0^{\circ}, ∠ A D B = 3 0^{\circ} a n d ∠ A C B = 6 0^{\circ}$ .
If CD = 40 m, then AB is 34.64 m
If true then enter $1$ and if false then enter $0$

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Exercise 29 (B)

10 Qs

$sin 5 7^{\circ} - cos 3 3^{\circ}$

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$cos^{2} 4 2^{\circ} - sin^{2} 4 8^{\circ}$

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$sin^{2} 6 2^{\circ} - cos^{2} 2 8^{\circ}$

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$cos^{2} 1 0^{\circ} - sin^{2} 8 0^{\circ} + tan^{2} 4 5^{\circ}$

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$\frac{2 cos 7 5 ^{\circ}}{sin 1 5 ^{\circ}} - \frac{sin 3 5 ^{\circ}}{2 cos 5 5 ^{\circ}}$ is $1 \frac{1}{m}$ . m is

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$3 - sin^{2} 4 8^{\circ} + cos^{2} 4 2^{\circ}$

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$2 sin^{2} 5 4^{\circ} - 2 cos^{2} 3 6^{\circ} + 4 sin^{2} 3 0^{\circ}$

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$c o s 5 8^{\circ} c o s 3 2^{\circ} - c o s 5 8^{\circ} s i n 5 8^{\circ}$

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$(\frac{sin 5 0 ^{\circ}}{cos 4 0 ^{\circ}})^{2} + (\frac{cos 2 8 ^{\circ}}{sin 6 2 ^{\circ}})^{2} - 2 tan^{2} 4 5^{\circ}$

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Evaluate: $cos 2 0^{\circ} cos 7 0^{\circ} - sin 2 0^{\circ} sin 7 0^{\circ}$

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Exercise 28 (A)

42 Qs

If $sin 3 0^{\circ} cos 3 0^{\circ}$ is $\frac{3}{m}$ , then $m$ is:

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The value of $tan 3 0^{\circ} tan 6 0^{\circ}$ is ____.

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Find the value of $cos^{2} 6 0^{\circ} + sin^{2} 3 0^{\circ}$ .

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Find the value of $c o s e c^{2} 6 0^{\circ} - tan^{2} 3 0^{\circ}$

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Find the value of $(sin^{2} 3 0^{\circ} + cos^{2} 3 0^{\circ} + cot^{2} 4 5^{\circ})$

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If $cos^{2} 6 0^{\circ} + sec^{2} 3 0^{\circ} + tan^{2} 4 5^{\circ}$ is $m \frac{7}{1 2}$ , then $m$ is:

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If $tan^{2} 3 0^{\circ} + tan^{2} 4 5^{\circ} + tan^{2} 6 0^{\circ}$ is $m \frac{1}{3}$ , then $m$ is:

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Find the value of $\frac{tan 4 5 ^{\circ}}{c o s e c 3 0 ^{\circ}} + \frac{sec 6 0 ^{\circ}}{cot 4 5 ^{\circ}} - \frac{5 sin 9 0 ^{\circ}}{2 cos 0 ^{\circ}}$

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If $3 sin^{2} 3 0^{o} + 2 tan^{2} 6 0^{\circ} - 5 cos^{2} 4 5^{\circ}$ is $4 \frac{m}{4}$ then, $m$ is

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Find the value of:
$sin 6 0^{\circ} cos 3 0^{\circ} + cos 6 0^{\circ} \cdot sin 3 0^{\circ}$

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Find the value of:
$cosec^{2} 4 5^{\circ} - cot^{2} 4 5^{\circ}$

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The value of: $cos^{2} 3 0^{\circ} - sin^{2} 3 0^{\circ}$ is $cos 6 0^{o}$ or $\frac{1}{2}$ .( Enter 1 if true or 0 otherwise)

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State true or false:
$[\frac{tan 6 0 ^{\circ} + 1}{tan 6 0 ^{\circ} - 1}] = \frac{1 + tan 3 0 ^{\circ}}{1 - tan 3 0 ^{\circ}}$

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Find he value of: $3 cosec^{2} 6 0^{\circ} - 2 cot^{2} 3 0^{\circ} + sec^{2} 4 5^{\circ}$

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$s i n (2 \times 3 0^{\circ}) = \frac{2 t a n 3 0 ^{\circ}}{1 + t a n ^{2} 3 0 ^{\circ}}$ , if true then write 1 and if false then write 0

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$c o s (2 \times 3 0^{\circ}) = \frac{1 - t a n ^{2} 3 0 ^{\circ}}{1 - t a n ^{2} 3 0 ^{\circ}}$ , if true then write 1 and if false then write 0

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$t a n (2 \times 3 0^{\circ}) = \frac{2 t a n 3 0 ^{\circ}}{1 - t a n ^{2} 3 0 ^{\circ}}$ , if true then write 1 and if false then write 0

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ABC is an isosceles right-angled triangle. Assuming AB = BC = x, find the value of each of the following trigonometric ratios : $s i n 4 5^{\circ}$ is $\frac{1}{m}$ , m is

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ABC is an isosceles right-angled triangle. Assuming AB = BC = x, find the value of each of the following trigonometric ratios : $c o s 4 5^{\circ}$ is $\frac{m}{2}$ , m is

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ABC is an isosceles right-angled triangle. Assuming AB = BC = x, find the value of each of the following trigonometric ratios : $t a n 4 5^{\circ}$

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$s i n 6 0^{\circ} = 2 s i n 3 0^{\circ} c o s 3 0^{\circ}$
If true then write 1 and if false then write 0.

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Calculate the value of the expression $4 (sin^{4} 3 0^{\circ} + cos^{4} 3 0^{\circ}) - 3 (cos^{2} 4 5^{\circ} - sin^{2} 9 0^{\circ})$

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If $s i n x = c o s x$ and $x$ is acute, state the value of $x$ in degrees.

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If sin x = cos x and x is acute, state the value of x.

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If sec A = cosec A and $0^{\circ} \leq A \leq 9 0^{\circ}$ , state the value of A.

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If $t a n θ = c o t θ$ and $0^{\circ} \leq θ \leq 9 0^{\circ}$ , state the value of $θ$

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If $sin x = cos y$ and both the angles $x$ and $y$ are acute, then find the value of $x + y$ .
Where, $x, y$ are in degrees.

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If $s i n (x) = c o s (y)$ , then $x + y$ = $4 5^{\circ}$ , write true or false.

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$s e c θ \cdot c o t θ = c o s e c θ$ Write $1$ if true else $0$

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For any angle $θ$ , state the value of : $s i n^{2} θ + c o s^{2} θ$ .

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$s i n θ$ increases as $θ$ increases
If true then write 1 and if false then write 0.

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$c o s θ$ increases as $θ$ increases.
If true then write 1 and if false then write 0

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$t a n θ$ increases as $θ$ increases.
If true then write 1 and if false then write 0

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If $3 = 1.732$ , find (correct to two decimal places) the value of each of the following :
$s i n 6 0^{\circ}$ is 0.87
State true or false.

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The value of $\frac{2}{t a n 3 0 ^{\circ}}$ is ________

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$K = \frac{c o s 3 A - 2 c o s 4 A}{s i n 3 A + 2 s i n 4 A}$ , when A = $1 5^{\circ}$ , $K = \frac{1 - 2}{1 + 6}$
write 1 for true and 0 for false

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If the value of $\frac{3 sin 3 B + 2 cos ( 2 B + 5 ^{\circ} )}{2 cos 3 B - sin ( 2 B - 1 0 ^{\circ} )}$ ; when $B =$ $2 0^{\circ}$ is $3 m + 22$ , then find the value of $m$ .

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If $A =$ $6 0^{\circ}$ and $B =$ $3 0^{\circ}$ , find the value of $(sin A cos B + cos A sin B)^{2} + (cos A cos B - sin A sin B)^{2}$ .

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State true or false.

If A = $3 0^{\circ}$ , then $s i n (6 0^{\circ} + A) - s i n (6 0^{\circ} - A) = c o s A$ .

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If A = $3 0^{\circ}$ then
$sin (A + 3 0^{\circ}) + cos (A + 6 0^{\circ}) = cos A$
State true or false.

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If $x =$ $1 5^{\circ}$ , evaluate : $4 cos 2 x \cdot sin 4 x \cdot tan 3 x - 1$

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If $x =$ $2 0^{\circ}$ , evaluate : $12 sin \frac{3 x}{2} cos 3 x + 5 tan (2 x + 5^{\circ}) - 3 cot^{2} 3 x$ .

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Exercise 28 (B)

20 Qs

sin (A + B) = sin A cos B + cos A sin B
If true then write 1 and if false then write 0.

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If A = $6 0^{\circ}$ and B = $3 0^{\circ}$ then cos (A + B) = cos A cos B - sin A sin B.
If above statement is true then write 1 and if false then write 0.

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cos (A - B) = cos A cos B + sin A sin B
If true then write 1 and if false then write 0

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Construct a circle of radius $7$ cm . Draw two perpendicular tangent to it.

View solution

If A= $3 0^{\circ}$ ,then: $s i n 2 A =$

Class 9 Maths Chapter 1 to 30

Exercise 1 (A)

Related questions

Without doing any actual division, find which of the following rational numbers have terminating decimal representation : (i) 167​ (ii) 12523​ (iii) 149​ (iv) 4532​ (v) 5043​ (vi) 4017​ (vii) 7561​ (viii) 250123​

The correct number in the 5th decimal place of the number 72​ = 0.285714

State whether True or False138​ can be represented as 0.615384

Exercise 1 (B)

Related questions

State whether True or FalseThe square of 5​−2 is 9−45​

State whether True or FalseThe square of 3+25​ is 29+125​

Given universal set ={−6,−543​,−4​,−53​,−83​,0,54​,1,132​,8​,3.01,π,8.47}From the given set, find the set of irrational numbers.

Given universal set ={−6,−543​,−4​,−53​,−83​,0,54​,1,132​,8​,3.01,π,8.47}From the given set, find the set of integers.

Use division method to show that 3​ and 5​ are irrational numbers.

Use division method of contradiction to show that 3​ and 5​ are irrational numbers. Also find the value of 15​×3​×5​

Simplify : (3​+2​) × (3​−2​).

Find the sum of the irrational numbers : 3−2​ and 5+2​

State whether true or falseThe pair of irrational numbers gives difference which is irrational are 2+23​ and 3−32​

If the following statement is True, enter 1 else enter 0.The difference between these two irrational numbers, 7+52​ and −3+52​ is rational.

check whether the following statement is True or False:The product of these two irrational numbers 3​+32​ and 2​−3​ is also an irrational number.

Insert two irrational numbers between 5 and 6.

Insert five irrational numbers between 25​ and 33​.

Say true or false:1.5 is rational number between 2​ and 3​.

Write three rational numbers between 3​ and 5​.

Exercise 1 (C)

Related questions

State true or false: 3+2​​ is a surd.

If the lowest rationalizing factor of 52​ is m​, then find the value of m.

If the lowest rationalising factor of 24​ is m​, then find the value of m.

The diagonals of a rhombus are 12 cm and 16 cm. Find : 5​−3 is 5​+m m is

If 7−7​ is m+7​, then m is

Write the lowest rationalising factor of : 18​− 50​ is m​

Write the lowest rationalising factor of : 5​−2 is 5​+m m is

Write the lowest rationalising factor of : 13​+3 is 13​−m m is

Write the lowest rationalising factor of :15−32​ is m+2​ m is

Write the lowest rationalising factor of :3√2+2√332√+23√ is

Find the value of 'a' in the following equation:2−3​2+3​​=a+b3​

Find the values of 'a' in each of the following :If 7​+27​−2​=a7​+b, then a=−3m​ where m is

Find the values of 'a' in each of the following :3​−2​3​=a3​−b2​

Find the value of 'a' in 5−32​5+32​​=a+b2​, then a=7m​ where m is rational number.

23​+122​+23​−117​ is equal to m783​−5​ then the value of m if m is rational number

If 6​−2​2​​−6​+2​3​​ is equal to m23​+2−32​+6​​ then value of m is

x=5​+25​−2​ and y=5​−25​+2​.If x2 is 161−72m​, then value of m is ?

If x=5​+25​−2​, y=5​−25​+2​ and y2 is (161+72m​), then value of m is ___.

x=5​+25​−2​ and y=5​−25​+2​.Find the value of xy.

x=5​+25​−2​ and y=5​−25​+2​.Find the value of x2+y2+xy.

If x=5−46​, find value of m:x1​ =−m5+46​​.

Given: x=5−46​. If x−x1​ is equal to 71360​−71280​m​, then the value of m is ?

If x=5−46​, x+x1​ is equal to 71350​−71288​m​. Find the value of m.

If m=3−8​1​ and n=3+8​1​.If m2 is equal to 17+6n​, then value of n is?

If m=3−8​1​ and n=3+8​1​, find if n2 is equal to 17−6m​, then value of m is?

Solve:mn=(3−8​)×(3+8​)1​.

If x=23​+22​ and x1​ is equal to m3​−2​​, then value of m is :

If x=23​+22​, find : If x+x1​ is equal to m53​+32​​, then value of m is :

If x=23​+22​ and (x+x1​)2 is equal to m93+306​​, then value of m is?

If x=5−26​, find the value of :(x−x1​)2

If x=5−26​, find x2+x21​.

Exercise 30 (A)

Related questions

For equation given below, name the dependent and independent variables. y=34​x−7

For equation given below, y is the independent variable and x is the dependent variable.x=9y+4 If above statement is true then write 1 and if false then write 0.

For equation given below, name the dependent and independent variables. x=25y+3​

For each equation given below, name the dependent and independent variables. y=71​(6x+5)

If (8,7) is plotted in correct place of graph then write answer is 1, else 0.

By using graph find the quadrant(in number) in which the point (3,6) lies.

By using graph we can locate (0,4) on the y-axis.

By using graph we find that the point P(0,−4) lies on the x-axis.

By using graph, (in numbers) find the quadrant or axis in which (3,−2) lies.

By using graph, the quadrant (in number) in which (−2,5) lies is ____.

Plot the following point on a graph paper : (−3,0)

By using graph, the quadrant (in number) in which (3,6) lies is ___ .

Plot the following point on a graph paper :(−4,−3)

Find the values of x and y if (x−1,y+3)=(4,4).

Find the values of x and y if (3x+1,2y−7)=(9,−9)

Find the values of x and y if (5x - 3y, y - 3x) = (4, -4)

The abscissa is 2, the point is (2,2) and (2,−4). If true then enter 1 and if false then enter 0.

Use the graph given alongside, to find the coordinates of the point(s) satisfying the given condition: The ordinate is 0. The point is (5,0)

Find the coordinates with ordinate as 3.

The ordinate is -4. The point is (2,-4). If true then enter 1 and if false then enter 0.

Find the coordinates with abscissa is 5.

The abscissa is equal to the ordinate, then A=(2,2),H=(5,5) and I=(4,4). If true, then enter 1 and if false, then enter 0.

The correct number in the $5^{t h}$ decimal place of the number $\frac{2}{7}$ $=$ $0 . \overline{285714}$

State whether True or False
$\frac{8}{1 3}$ can be represented as $0 . \overline{615384}$

State whether True or False
The square of $5 - 2$ is $9 - 45$

State whether True or False
The square of $3 + 25$ is $29 + 125$

Given universal set $= {- 6, - 5 \frac{3}{4}, - 4, - \frac{3}{5}, - \frac{3}{8}, 0, \frac{4}{5}, 1, 1 \frac{2}{3}, 8, 3.01, π, 8.47}$
From the given set, find the set of irrational numbers.

Given universal set $= {- 6, - 5 \frac{3}{4}, - 4, - \frac{3}{5}, - \frac{3}{8}, 0, \frac{4}{5}, 1, 1 \frac{2}{3}, 8, 3.01, π, 8.47}$
From the given set, find the set of integers.

Use division method to show that $3$ and $5$ are irrational numbers.

Use division method of contradiction to show that $3$ and $5$ are irrational numbers. Also find the value of $15 \times 3 \times 5$

Simplify : ( $3 + 2$ ) $\times$ ( $3 - 2$ ).

Find the sum of the irrational numbers : $3 - 2$ and $5 + 2$

State whether true or false
The pair of irrational numbers gives difference which is irrational are $2 + 23$ and $3 - 32$

If the following statement is True, enter 1 else enter 0.
The difference between these two irrational numbers, $7 + 52$ and $- 3 + 52$ is rational.

check whether the following statement is True or False:
The product of these two irrational numbers $3 + 32$ and $2 - 3$ is also an irrational number.

Insert two irrational numbers between $5$ and $6$ .

Insert five irrational numbers between $25$ and $33$ .

Say true or false:
$1.5$ is rational number between $2$ and $3$ .

Write three rational numbers between $3$ and $5 .$

State true or false: $3 + 2$ is a surd.

If the lowest rationalizing factor of $52$ is $m$ , then find the value of $m$ .

If the lowest rationalising factor of $24$ is $m$ , then find the value of $m$ .

The diagonals of a rhombus are $12$ cm and $16$ cm. Find :

$5 - 3$ is $5 + m$
m is

If $7 - 7$ is $m + 7$ , then $m$ is

Write the lowest rationalising factor of :

$18 - 50$ is $m$

Write the lowest rationalising factor of :

$5 - 2$ is $5 + m$
$m$ is

Write the lowest rationalising factor of :

$13 + 3$ is $13 - m$
$m$ is

Write the lowest rationalising factor of :
$15 - 32$ is $m + 2$
$m$ is

32√+23√ is

Find the value of 'a' in the following equation:
$\frac{2 + 3}{2 - 3} = a + b 3$

Find the values of 'a' in each of the following :
If $\frac{7 - 2}{7 + 2} = a 7 + b$ , then $a = - \frac{m}{3}$
where m is

Find the values of 'a' in each of the following :
$\frac{3}{3 - 2} = a 3 - b 2$

Find the value of 'a' in $\frac{5 + 3 2}{5 - 3 2} = a + b 2$ , then $a = \frac{m}{7}$ where m is rational number.

$\frac{2 2}{2 3 + 1} + \frac{1 7}{2 3 - 1}$ is equal to $\frac{7 8 3 - 5}{m}$
then the value of m if m is rational number

If $\frac{2}{6 - 2} - \frac{3}{6 + 2}$ is equal to $\frac{2 3 + 2 - 3 2 + 6}{m}$ then value of m is

$x = \frac{5 - 2}{5 + 2}$ and $y = \frac{5 + 2}{5 - 2}$ .
If $x^{2}$ is $161 - 72 m$ , then value of $m$ is ?

If $x = \frac{5 - 2}{5 + 2}$ , $y = \frac{5 + 2}{5 - 2}$ and $y^{2}$ is $(161 + 72 m)$ , then value of $m$ is ___.

$x = \frac{5 - 2}{5 + 2}$ and $y = \frac{5 + 2}{5 - 2}$ .
Find the value of $x y$ .

$x = \frac{5 - 2}{5 + 2}$ and $y = \frac{5 + 2}{5 - 2}$ .
Find the value of $x^{2} + y^{2} + x y$ .

If $x = 5 - 46$ , find value of m:
$\frac{1}{x}$ $= - \frac{5 + 4 6}{m}$ .

Given: $x = 5 - 46$ .

If $x - \frac{1}{x}$ is equal to $\frac{3 6 0}{7 1} - \frac{2 8 0}{7 1} m$ , then the value of $m$ is ?

If $x = 5 - 46$ , $x + \frac{1}{x}$ is equal to $\frac{3 5 0}{7 1} - \frac{2 8 8}{7 1} m$ .
Find the value of m.

If $m = \frac{1}{3 - 8}$ and $n = \frac{1}{3 + 8}$ .
If $m^{2}$ is equal to $17 + 6 n$ , then value of $n$ is?

If $m = \frac{1}{3 - 8}$ and $n = \frac{1}{3 + 8}$ , find if $n^{2}$ is equal to $17 - 6 m$ , then value of m is?

Solve:
$m n = \frac{1}{( 3 - 8 ) \times ( 3 + 8 )}$ .

If $x = 23 + 22$ and $\frac{1}{x}$ is equal to $\frac{3 - 2}{m}$ , then value of $m$ is :

If $x = 23 + 22,$ find :

If $x + \frac{1}{x}$ is equal to $\frac{5 3 + 3 2}{m}$ , then value of $m$ is :

If $x = 23 + 22$ and $(x + \frac{1}{x})^{2}$ is equal to $\frac{9 3 + 3 0 6}{m}$ , then value of $m$ is?

If $x = 5 - 26,$ find the value of : $(x - \frac{1}{x})^{2}$

If $x = 5 - 26,$ find $x^{2} + \frac{1}{x ^{2}}$ .

For equation given below, name the dependent and independent variables.
$y = \frac{4}{3} x - 7$

For equation given below, $y$ is the independent variable and $x$ is the dependent variable.
$x = 9 y + 4$

If above statement is true then write 1 and if false then write 0.

For equation given below, name the dependent and independent variables.
$x = \frac{5 y + 3}{2}$

For each equation given below, name the dependent and independent variables.
$y = \frac{1}{7} (6 x + 5)$

If $(8, 7)$ is plotted in correct place of graph then write answer is $1,$ else $0$ .

By using graph find the quadrant(in number) in which the point $(3, 6)$ lies.

By using graph we can locate $(0, 4)$ on the y-axis.

By using graph we find that the point P $(0, - 4)$ lies on the x-axis.

By using graph, (in numbers) find the quadrant or axis in which $(3, - 2)$ lies.

By using graph, the quadrant (in number) in which $(- 2, 5)$ lies is ____.

Plot the following point on a graph paper : $(- 3, 0)$

By using graph, the quadrant (in number) in which $(3, 6)$ lies is ___ .

Plot the following point on a graph paper :
$(- 4, - 3)$

Find the values of $x$ and $y$ if $(x - 1, y + 3) = (4, 4)$ .

Find the values of x and y if $(3 x + 1, 2 y - 7) = (9, - 9)$

The abscissa is $2$ , the point is $(2, 2)$ and $(2, - 4)$ .
If true then enter $1$ and if false then enter $0$ .

Use the graph given alongside, to find the coordinates of the point(s) satisfying the given condition:

The ordinate is 0.
The point is (5,0)

Find the coordinates with ordinate as $3$ .

The ordinate is -4. The point is (2,-4).
If true then enter $1$ and if false then enter $0$ .

The abscissa is equal to the ordinate, then $A = (2, 2), H = (5, 5)$ and $I = (4, 4)$ .
If true, then enter $1$ and if false, then enter $0$ .

The ordinate is half of the abscissa, then the point $E = (6, 3)$ .
If true, then enter $1$ and if false, then enter $0$ .

State true or false:
The origin is in the first quadrant.

The y-axis is the vertical number line.

If above statement is true then enter $1$ and if false then enter $0$ .

The origin $(0, 0)$ lies on the $x$ -axis.

The point $(a, b)$ lies on the $y$ -axis if $b = 0$ .

In the following, find the co-ordinates of the point whose abscissa is the solution of the first equation and ordinate is the solution of the second equation :
$3 - 2 x = 7; 2 y + 1 = 10 - 2 \frac{1}{2} y .$

In the following, the coordinates of the three vertices of a rectangle ABCD are given. By plotting the given points; find, the coordinates of the fourth vertex:

A (2, 0), B (8, 0) and C (8, 4)
Claim: The co-ordinates of the fourth vertex are (2,4)
If true then enter $1$ and if false then enter $0$

A (4, 2), B (-2, 2) and D (4, -2) is (-2,-2)
If true then enter $1$ and if false then enter $0$

In the following, the coordinates of the three vertices of a rectangle ABCD are given. By plotting the given points; find, the coordinates of the fourth vertex:

A (-4, -6), C (6, 0) and D (-4, 0)
Claim: The co-ordinates of the fourth vertex are ( $x$ ,-6).
Find $x$ .

$A (- 2, 2), B (8, 2)$ and $C (4, - 4)$ are the vertices of a parallelogram $A B C D$ . By plotting the given points on a graph paper; find the co-ordinates of the fourth vertex $D$ .
Also, from the same graph, state the co-ordinates of the mid-points of the sides $A B$ and $C D$ .

Use the graphical method to find the co-ordinate of the fourth vertex B
Claim : Answer is (4,4)
If true then enter $1$ and if false then enter $0$

A (-2, 4), C (4, 10) and D (-2, 10). are the vertices of a square ABCD.

The co-ordinates of the mid-point of BC is (4,7)