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Optional Mathematics Chapter wise Model question Class 10

  • Posted On: Wed Mar 13 2024
  • Posted By: Binay Poudel

Algebra 

For Q.No. 1(a) 

  1. Define an algebraic function. 
  2. Write down the period of function defined as y = tan x. 
  3.  If f = {(2, 1), (4, 1), (5, 1) } Does $f^{-1}$ exist? 
  4. If (x+2) is a factor of f(x) = $x^3$+8, find f(-2). 
  5. If the 10th term of an A.P. is 100 and the common difference is 10, find the first term.
  6. If A.M. between 3x+7 and 5x+8 is $\frac{23}{2}$, find the value of x.

For Q.No. 1(b)

  1. What is the minimum value of the cosine function y = cos x? 
  2. Define a composite function of two functions. 
  3. If f(x) = (x-2)×($x^2$+4x+2)+3, write the degree of f(x).
  4. Find arithmetic mean between the following two terms. -60 and -20
  5. Check if the following sequences are in G.P. or not. 3, 9, 27, 81, ……..
  6. Define common ratio in G.P. 

For Q.No. 6(a) 

  1. If f = (1, 5), (2, 1), (3, 3), (5, 2)} and g = {(1, 3), (2, 1), (3, 2), (5, 5)}, find gof and fog. 
  2. If f(x+2) = 4x+5, find f(x) and (fof) (x)
  3. If k(x) = $\frac{5x+7}{x-2}$, x≠2, find k-1(x) and k-1(4). 
  4. If 4$x^3$-10$x^2$+25x-20 = (4x-3). Q(x)+R(x). Find the value of Q(x) and R(x). 
  5. Find the quotient and remainder in each of the following cases when f(x) divided by d(x) (use synthetic division method): f(x) = 4$x^3$-7$x^2$+6x-2, d(x) = 3x+2
  6. If 2$x^3$+4$x^2$+px+7 has a factor of (x+2), find the value of p. 

For Question No. 6(b) 

  1. Which term of the series is 5+10+15+............+200?
  2. Find the arithmetic means as indicated, If 6,x,y, and 18 are in A.P., find the value of x and y. 
  3.  Find the number of terms in an A.P. which has its first term 16; common difference 4; and the sum, 120. 
  4. How many terms  a G.P. must be taken in the series 64+96+144+216+...........so that the sum may be 2059?
  5. Find the sum of the first 50 natural numbers and 30 even natural numbers. 
  6. Find the  common ratio in the following G.P. $\sqrt{2}+\frac{1}{\sqrt{2}}+\frac{1}{2\sqrt{2}}$

For Question No. 6(c) 

  1. If f(2x+5) = 10x+7, find $f^{-1}$(x) 
  2. Which quadrant does an inequality y ≥ 0 represent as its half plane? 
  3. Find the quotient and remainder in each of the following cases when f(x) divided by d(x) (use synthetic division method):  f(x) = 4$x^3$-7$x^2$+6x-2, d(x) = 3x+2 
  4. Find the three numbers in an A.P. whose sum is 12 and the sum of their squares is 50. 
  5. What will be the point of intersection of the curve f(x) = $x^2$-5x and f(x) = -5?
  6. Write the boundary line equation of 4x+3y ≤ 12. 

For Question No. 11

  1.  If f(x) = $\frac{7x+q}{2}$ and g(x) = x+8, (fog)(4) = 24, find the value of q.
  2. Solve the following polynomial equations:  $x^3-4x^2$+x+6 = 0 
  3. The 6th and the 9th terms of an A.P. 23 and 35. Which term is 67?
  4. The 5th mean between two numbers 7 and 71 is 27. Find the number of A.M’s. 
  5. The first and the second terms of a G.P. are 32 and 8 respectively. Find: 
  1. The first term 
  2. Common ratio
  3. 10th term 

6. The sum of the first 2 terms of a G.P. is 8 and that of the first 4 terms is 80. Find the sum of the first 6 terms. 

For question No. 12 

  1. If g(x) = 5x+3 and (gof)(x) = 2x+5 and f(x) is a linear function, find the value of f(x). 
  2. If f(x) 4x-17 and g(x) = $\frac{2x+8}{5}$ and ($fof^{-1}$)(x) = $g^{-1}$(x), find the value of x. 
  3. When the polynomial 2$x^3$+9$x^2$-7x+k, is exactly divisible by 2x+3, find the value of k by using synthetic division. 
  4. Find the values of a and b in each of the following cases: (x+3) and (2x-7) are factors of a$x^2$-bx-21. 
  5. If x+6, 3x, and 2x+9 are in A.P., find the value of x and the next three terms the progression. 
  6. There are three geometric means between a and b. If the first mean and third mean are $\frac{1}{4}$ and $\frac{1}{64}$, find the values of a and b.

For Question No. 22

  1. The fifth and twelve terms of an A.P. are respectively 17 and 45. Find the sum of the first 15 terms of the progression? 
  2. Graph the following  system of inequalities and find the vertices of convex polygons if they exist.  X+2y≤ 12 and x≥ 6, y ≥0 
  3. 2. In the given diagram, β–³ABC is the feasible region. AB is parallel to the Y-axis and the coordinates of B are (5, 10), one of constraints is x+y ≥5, find the remaining constraints and minimize C = 3x+5y.

4. Draw the graphs for the following quadratic functions. Y = $x^2+2x-3$

5. Find the equation of the parabola under the given condition: Vertex at the origin and passing through the point (1, -4) 

6. Find the equations of parabola under the following stated conditions. Passing through the points (0, -3), (-1, -1), and (3, 3) 

7. Solve the following equation graphically: $x^2-2x-15$ = 0 

8. Solve the following equation graphically: Y = $6x^2$-2x-15, y = 4x-3 

Limit and Continuity

For Question No. 2(a)

  1. What are natural numbers used for? 
  2. Define continuity of a function?
  3. Write down the point of discontinuity of a function given as h(x) = $\frac{1}{x+5}$.
  4. What are the starting and ending numbers in each of the number lines? 
  5. Write conditions for continuity of function f(x) at a point x = a, using notations. 
  6. Find the initial and the terminating points of the curve. 

For Question No. 13

1. Examine the continuity or discontinuity of the following functions at the points mentioned: 

f(x) = $\begin{cases}\frac{x^2-7x}{x-7} & when x\# 7 \\3 & when x = 7 \end{cases} at x = 7$

2. A function is defined as follows: 

f(x) = $\begin{cases}3+2x & for -3/2\leq<0 \\3-2x & for 0\leq x< 3/2 \\ -3-2x & for x\geq 3/2 \end{cases}$

3. Find the value of n, if f(x) is continuous at x = 2

f(x) = $\begin{cases}\frac{x^2-4}{x-2} & for x \# 2 \\n & for x = 0\end{cases}$

4. Draw the graph of p(x) = $\frac{2}{x-5}$ and find, at which point the function is discontinuous? 

Matrices 

For Question No. 2(b)

  1. Evaluate the determinant of the following matrices: $\begin{bmatrix}2 & 3 \\4 & -5 \end{bmatrix}$
  2. Factorise $\begin{bmatrix}2x+3y\\4x-7y \end{bmatrix}$
  3. If D = 4, $D_x$ = $\frac{1}{2}$, $D_y$ = $\frac{1}{4}$ find the values of x and y.
  4. What is the determinant of a square matrix D = [-5]?
  5. If a square matrix is given M = $\begin{bmatrix}a & b \\c & d \end{bmatrix}$ then what does $\begin{bmatrix}d & b \\c & a \end{bmatrix}$ denote? 
  6. Find the value of $D_y$ using Cramer’s rule for the equations 2x+3y = 4 and x+2y = 6

For Question No. 7(a)

  1. Which of the following matrices have their inverse? B =$\begin{bmatrix}4 & 10 \\2& 5 \end{bmatrix}$ 
  2. Find the inverse matrices of the following matrices if possible:  E = $\begin{bmatrix}cos \theta & -sin theta \\ sin \theta & cos \theta \end{bmatrix}$
  3. Define: i. Singular Matrix  ii. Inverse of a matrix 
  4. Find the value of x, when   = 0 
  5. For what value of m, the equations 2x-4y = 5 and x+y = m+3 have $D_x$ = 12
  6. Find the R whose inverse  $R^{-1}$=

For Question No. 7(b)

1. Solve the following system of equations by using Cramer’s rule:

  1. 2x+3y = 17 
  2. $\frac{x}{3}-\frac{y}{4}$  = 2

2. If A = $\begin{bmatrix}1 & 2 \\4 & 5 \end{bmatrix}$ , B = $\begin{bmatrix}2 & 3 \\3 & 4 \end{bmatrix}$ Find the determinants of AB. 

3. For what value of m, matrix  $\begin{bmatrix}m+3 & m \\2& 4 \end{bmatrix}$ has no inverse? Find it.

4. If D = then write the corresponding equations to these values. 

5. Find the inverse of a matrix K =

6. Find the value of y from the equations x +3y = 7 and 2x-y = 3 calculating the value of D and $D_y$.

For Question No.  14

1. If  $\begin{bmatrix}-1 & 2 \\2p & -7 \end{bmatrix}$ and$\begin{bmatrix}q & 2 \\4 & 1 \end{bmatrix}$ are inverse to each other, find the values of o and

2. If A =$\begin{bmatrix}5& 3 \\3 & 2 \end{bmatrix}$ then, show following:

  1. $(A^{-1})^-1$= A 
  2. $(A^{-1})^T$= $(A^T)^{-1}$
  3. $A^{-1}$A = A$A^{-1}$ = I 

3. Solve the following equation by matrix method: 

  1. $\frac{x}{2}+\frac{y}{2}$ = 7
  2. $\frac{x}{6}+\frac{y}{4}$= 1

4. If M = $\begin{bmatrix}2 & 4 \\5 & 2 \end{bmatrix}$, N = $\begin{bmatrix}2 & 1 \\3 & 4 \end{bmatrix}$, Find the determinant:

  1. of 2M +3N 
  2. 3M-2N 
  3. M2-N2 

5. One fourth of the sum of two numbers is 7 and five times of the difference of them is 20. Find the numbers matrix method. 

6. A cinema hall was full of audiences with a capacity of 120 seats a day. The hall had provision of a balcony and special each had to pay Rs. 40 and Rs. 20, respectively, for a ticket. If the ticket of Rs. 3600 was sold altogether on the day. Find the number of audiences in each i.e. balcony and special using Cramer’s rule. 

Coordinate Geometry 

For Q.No. 3(a) 

  1. Write the acute between two lines in each of the following pair of straight lines: 2x+4y = 7 and x+2y = 5 
  2. Find the separate equations of straight lines represented by the following equations: 9$x^2$-25$y^2$ = 0 
  3. Write down the equation of the circle with centre (h, k) and radius r. 
  4. Write the equation of a circle whose ends of a diameter are ($x_1, y_1$) and ($x_2, y_2$). 
  5. Define a homogeneous equation. 
  6. Write the general equation of second degree in x and y. 

For Q. No. 3(b)

  1.  Define circle with respect to conic section. 
  2. State the condition under which the pair of straight lines a$x^2$+2hxy+$y^2$ = 0 will be coincident. 
  3. Write the name of the locus represented by $x^2+y^2$ =$r^2$. 
  4. Write down the formula to find the angle between two lines y = $m_1$x+$c_1$ and y = $m_2$x+$c_2$. 
  5. Find the separate equations of straight lines represented by the following equations: $x^2-y^2$ +x-y= 0 
  6. Write the acute between two lines in each of the following pair of straight lines: 3x+5y = 8 and 2x+y = 6

For Q. No. 8(a) 

  1. Find the acute angle between two lines in each of the following pair of straight lines:  2x+4y= 7 and x+2y = 5 
  2. The pair of straight lines 2x+5y+2 = 0 and kx+y+6 = 0 are parallel. 
  3. Find the value of πœ† when the following equations represents a pair of line perpendicular to each other:  (3πœ†+4)$x^2$-48xy-πœ†$^2$y$^2$ = 0 
  4. Find the equations of circles under the following condition. Centre at (4, -1) and through (-2, -3) 
  5. Find the centre and the radius of a circle having equation $x^2+y^2$+2gx+2fy+c = 0. 
  6. Show that the lines 4x-8y+7 = 0 and x-2y+8 = 0 are parallel to each other.

 

For Q. No. 8(b)

  1. Show the lines x+y = 2 and 2x+2y = 3 are parallel to each other. 
  2. find the equation the straight line which: Passes through the point (4, 3) and parallel to the line 2x+3y+12 = 0 
  3.  Find the two separate equation of two lines represented by the following equations: $x^2$-2xy cot2πžͺ-$y^2$ = 0
  4. Find the equations of circles under the following condition. Touching the coordinate axes at (a, 0) and (a, 0). 
  5. Determine the lines represented by $x^2$-2xy+$y^2$-3x+3y-10 = 0
  6. Draw the conic of parabola. 

For Q. No. 15

  1. Find the separate equations of two lines represented by $x^2$-5xy+4$y^2$ = 0. Find the angle between the lines and the points of intersection of the lines.
  2. Show that the pair of lines, 4$x^2$-9$y^2$ = 0 and 9$x^2$-4$y^2$ = 0 are perpendicular to each other. 
  3. The equation of two diameters of a circle passing through (4, 7) are 2x-3y = 12 and 4x+2y = 10. Determine the equation of the circle. 
  4. Find the equation of a circle that touches the positive X-axis at a distance of 6 units from the origin and cuts off an intercept of 4 units on the Y-axis positively. 
  5. The equation of diagonal PS of a square POST is 3x-5y = 6 and the coordinates of vertex O is O(3, -1). Find the equation of diagonal OT. 
  6. Find the equation of the altitude AD of ABC with vertices A(2, 3), B(-4, 1) and C(2, 0) drawn from the vertex A. 

For Q. No. 23 

  1. Find the centre and radius of circles. Passing through the points P(-4, -2), Q(2, 6) and R(2, -2) 
  2.  Show that the two circles $x^2+y^2$ = 36 and $x^2+y^2$-12x-16y+84 = 0 touch externally.
  3. From point A(5, 6). Perpendicular AB is drawn to the line PQ: 2x+3y = 12. Find the equation of AB. 
  4. FInd the equation of the sides of an equilateral triangle whose vertex is (1, 2) and base is y = 0.
  5. Find the equation of a circle with radius 4 units, whose centre lies on the line 12x+3y = 48 and which touches the line 3x+2y+23 = 0. 
  6. Find the angle between a pair of straight lines represented by a$x^2$+2hxy+b$y^2$ = 0 also derives the condition of the lines being perpendicular and coincident. 

Trigonometry 

For Q.No. 4(a) 

  1. Define multiple angles with an example. 
  2. Express cos πœƒ in terms of cos $\frac{\theta}{2}$. 
  3. Express each of the following as product form: sin x- sin y
  4. Define conditional trigonometric identities with an example.
  5. If Sec $\alpha$  = cosec $\alpha$ , what is the acute value of A?

For Q. No. 4(b)  

  1. Find the value of πœƒ, $0^o$ ≤ πœƒ ≤$90^o$:  sec πœƒ = cosec πœƒ
  2. Find the value of x in the following diagrams: 

3. Express cos 3M-cos2N in the form of a product of sine or cosine. 

4. What is meant by angle of elevation?

5. Express cos 10B in term of sin 5B

For Q.No. 9(a) 

  1. If sin πœƒ = $\frac{\sqrt{3}}{2}$, find the value of sin 3πœƒ and cos 3πœƒ. 
  2. If cos 2πœƒ = $\frac{-1}{2}$ ($p^2$ +$\frac{1}{p^2}$
  3. Prove that: $\frac{1-cos 2πœƒ}{1+cos2 πœƒ}$= $tan^2$πœƒ

For Question No. 9(b)

  1. Prove that: $\frac{1+sin 2πœƒ-cos 2πœƒ}{1+sin 2πœƒ+cos2πœƒ}$ = tanπœƒ
  2. Prove that: Sin x= 3sin ($\frac{x}{3}$) - 4$sin^2(\frac{x}{3})$
  3. Prove that: cot( $\frac{πœƒ}{2}$+$\frac{\pi^c}{4}$) -tan($\frac{πœƒ}{2}$+$\frac{\pi^c}{4})$ =$\frac{2cos \theta }{1+sin \theta}$ 

For question No. 9(c) 

  1. Prove that: $\frac{cos 7A+cos 3A-cos5A-cosA}{sin 7A-sin3A-sin 5A+sinA}$ = cot2A
  2. If A+B+C = $\pi^c$, prove that: cotA.cotB+cotB.cotC+cotC.cotA-1 = 0
  3. Express cos $105^o$. Cos15o into sum or difference of sine or cosine. Hence, find its value.  

For Q.No. (16)

  1. If 2tanπžͺ = 3 tan 𝛃, then prove that, tan(πžͺ+𝛃) = $\frac{5sin2 𝛃}{5cos 2𝛃-1}$
  2. Prove that: $\frac{2 sinπœƒ -sin 2πœƒ}{2sinπœƒ+sin2πœƒ}$ = $tan^2$ $\frac{πœƒ}{2}$
  3. If A+B+C = $\pi^c$, prove that:sinA-sinB-sinC = -4cos $\frac{A}{2}$.sin$\frac{B}{2}$.sin$\frac{C}{2}$
  4. Solve: 0o≤πœƒ≤$360^0$ : 4$cos^2$πœƒ+4sinπœƒ = 5
  5. A pole is divided by a point in the ratio 1:9 from bottom to top. If the two parts of the pole subtend equal angles at 20m away from the foot of the pole, find the height of the pole.

For Q.No. 17

  1. Prove that: $\frac{cos7A+cos3A-cos5A-cosA}{sin7A-sin3A-sin5A+sinA}$ = cot2A
  2. If A+B+C = $\pi^c$, prove that: $cos^2$A-$cos^2$B+$cos^2$C = -1+2cosA.sinB.sinC
  3. Solve for πœƒ: $0^o$≤πœƒ≤$180^o$: Sinπœƒ+sin2πœƒ+sin3πœƒ = 0 
  4. From a helicopter flying vertically above a straight road, the angles of depressions of two consecutive kilometer stones on the same side are found to be $45^o$ and $60^o$. Find the height of the helicopter. 
  5. The shadow of a pole on the ground level increases by x m when the sun's altitude changes from $60^o$ to $45^o$. If the height of the pole is 50 ft, find the value of x. 

For Q.No. 18 

  1. Prove that: (cosB-cosA)$^2$ +(sinA-sinB)$^2$= 4sin$^2$($\frac{A-B}{2}$)
  2. If A+B+C = $\pi^c$, prove that: $\frac{sin 2A+sin2B+sin2C}{4 cos\frac{A}{2}. cos\frac{B}{2}. cos \frac{C}{2}}$ = 8sin $\frac{A}{2}$ sin $\frac{B}{2}$ sin $\frac{C}{2}$
  3. Solve: $0^0$≤x≤$360^o$ : $\sqrt{3}$cosx = $\sqrt{3}$-sinx
  4. From the top and bottom of a tower, the angle of depression of the top of the house and angle of elevation of the house are found to be $60^o$ and $30^0$ respectively. If the height of the building is 20m. Find the height of the tower. 
  5. A tower of a radio station is divided by a point in the ratio 9:1, Form the top if both the parts subtend equal angles at a point on the ground level 600m away from its bottom, find the height of the tower. 

Vectors 

For Q.No. 5(a) 

  1. Define scalar product of two vectors. 
  2.  Find the dot product of |$\vec{a}$| and  |$\vec{b}$|  in following cases:  |$\vec{a}$| = 2, |$\vec{b}$| = 5, angle between them = $90^o$ 
  3. If p = (3, 4) and q = (-1, 6), What is the dot product of p and q? 

For Q.No. 10(a) 

  1. Find the angles between given pair of vectors:  |$\vec{a}$| = 3, |$\vec{b}$| = 5, $\vec{a}$.$\vec{b}$  = 7.5 
  2.  In PQR if $\vec{P}$Q = 5 $\vec{i}$-9$\vec{j}$, $\vec{Q}$R = 4$\vec{i}$+14$\vec{j}$ prove that $\triangle$PQR is a right angled triangle. 
  3.  The position vectors of A and B are 2 $\vec{a}$- 3$\vec{b}$ and 5$\vec{a}$-4$\vec{b}$ respectively. Find the position vector of the point which divides AB in ratio 3:2 internally. 

For Q.No. 10(b) 

  1. In ABC, the coordinates of two ends of a median AD are A(2, 5) and D(7, -1) then find the position vector of centroid G of ABC. 
  2. Find the angle between two vectors P and q when p = 6 $\vec{i}$+8$\vec{j}$ and q = 4$\vec{i}$ +3$\vec{j}$ 
  3. If the position vector of the mid point of the line segment AB is (3$\vec{i}$-2$\vec{j}$), where the position vector of B is (5$\vec{i}$+2$\vec{j}$), find the position vector of A.

For Q. No. 24. 

  1. In the figure O is the centre of the semi-circle. Prove that <PRQ is right angle. 

2. In the adjoining figure, PQRS is  a parallelogram. G is the point of intersection of the diagonals. If O is any point prove that

 

$\vec{O}$G = $\frac{1}{4}$ ($\vec{O}$A+$\vec{O}$B + $\vec{O}$C +$\vec{O}$D) 

  1. Prove by vector method that diagonals KN and ID of a rectangle KIND are equal to each other. 
  2. If a triangle XYZ, <XYZ = $90^o$and A is the midpoint of side XZ, prove by vector method that: XA = YA = ZA. 

Transformations 

For Q.No. 5. (b) 

  1. Define combined transformation. 
  2. Find the image of P(5, 3) under enlargement E[(1, 1), 2]. 
  3. Write down the transformation which is associated with the reflection on Y-axis. 
  4. In a circle with centre ‘O’and radius ‘r’, ‘P’is the inversion point of P. If OP = 2cm and OP’= 18cm, find the value of r. 

For Question No. 19 

  1. Let $T_1$ = $\begin{bmatrix}3\\2 \end{bmatrix}$  and $T_2$ =$\begin{bmatrix}1\\2 \end{bmatrix}$  be two translations, find the image of the following points under the combined translations $T_1$ o $T_2$ and $T_2$o$T_1$: A(-6, 7) 
  2. If $T_1$ =$\begin{bmatrix}1\\2 \end{bmatrix}$  and $T_2$ = $\begin{bmatrix}-2\\4 \end{bmatrix}$and $T_1$ o $T_2$ (x, y) = (8, 8) find the values of x and y. 
  3. Find the image of S(7, 5) under combined transformation $R_2$ o $R_1$, where,
  • R1 = Rotation of 180o about (2, 3)
  • R2 = rotation of +90o about origin. 

4. Find the inverse of the point (2, -5) with respect to the circle $x^2+y^2$ = 1 

5. A triangle with vertices P(2, 1), Q(5, 3), and R(6, 7) is transformed by the matrix $\begin{bmatrix}0 & -1 \\-1 & 0 \end{bmatrix}$ find the image of the quadrilateral PQRS.

For Question No. 25

  1. Let M(1, 1), N(-3, -6) and (6, -1) be the vertices of MNP. The vertices are transformed by a single transformation obtained by the combination of the rotation [(0, 0) , + $90^o$] and in the same direction of a rotation [(0, 0), +$180^o$]. Find the coordinates of the images of these points. 
  2. On a graph paper draw ABC having the vertices A(5, 4), B(2, 2) and C(5, 2). Find the image of ABC by stating coordinates and graphing them after successive reflections on x-axis following by reflection on the line y = x. 
  3. A triangle having vertices A(2,5), B(-1, 5) and C(4, 1) is rotated through +90o about the origin. The image obtained is reflected on the line x = 0. Find the vertices of image triangles. Show all the triangles in the same paper and also write the single transformation to represent these two transformations. 
  4. Find the image of ABC with the vertices A(2, 1), B(3, 5) and C(5, 4) under enlargement $E_1$ [(0, 0), 3/2] followed by another enlargement $E_2$ [(0, 0), -2]. Draw ABC and its images on the same graph paper. 
  5. M(3, 4) , N(1, 1), and P(4, 1) are the vertices of MNP. find the image of MNP. Under the enlargement with centre (1, -1) and scale factor -2 followed by the rotation about the origin through negative quarter turn. Also show the image on the same graph paper. 
  6.  PQR with vertices P(5, 1), Q(12, 4) and R(4, 5) maps onto the  P’Q’R’ with the vertices P’(-5, -1) Q’(-12, -4) and R’(-4, -5). Which is the single transformation for this mapping? Also find the 2×2 matrix that represents the transformation. 

Statistics 

For Q.No. 10(c) 

  1. Define quartile deviation. 
  2. Calculate the coefficient of quartile deviation from the following: $Q_1$ = 20, $Q_3$ = 40 
  3. In a continuous series, mean = 20, N = 50 and ∑f|m$\vec{x}$| = 208, find the mean deviation and its coefficient. 
  4. If the standard deviation of a data is 0.35, find its variance. 

For Question No. 20

1. Calculate the quartile deviation and its coefficient from the following data: 

Volume of water (l) 

5-10

10-15

15-20

20-25

25-30

30-40

No. of families 

4

12

16

6

2

1

 2. Calculate quartile deviation and its coefficient from the following data:

Income (Rs)

Below 50

50-70

70-90

90-110

110-130

130-150

150 above

workers

5

10

20

25

18

12

10

3. Calculate the quartile deviation and its coefficient from the given data: 

Class interval 

20-29

30-39

40-49

50-59

60-69

70-79

frequency

100

80

75

95

70

40

4. Calculate the mean, deviation from (i) mean (ii) median for the following data: 

Marks 

0-10

10-20

20-30

30-40

40-50

Number of students

9

6

4

12

9

5. Calculate mean deviation from median and its coefficient for the following grouped data: 

Mid point 

2

6

10

14

18

22

26

frequency

7

13

10

5

8

4

3

6. Calculate the standard deviation and its coefficient from the following data by

  1. direct method 
  2. short-cut method 
  3. step-deviation 

Marks 

0-10

10-20

20-30

30-40

40-50

No. of. Students 

7

12

24

10

7

7. Calculate the standard deviation and coefficient of variation: 

Hight (cm)

0-8

8-16

16-24

24-32

32-40

No.of plants

6

7

10

8

9

8. Calculate the standard deviation and coefficient of variation from the following

x

Less than 10 

Less than 20

Less than 30 

Less than 40

Less than 50 

f

12

19

24

33

40 
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