CBSE Model Paper – Mathematics : 2008
Model Test Paper – I.
Question 1 to 15 carry 2 marks each.
1.3x + 2y = 6 ;(k + 1 )x + 4y = (2k + 2)
For what value of k, will the above system of equation have infinite solution.
2.Find the median of the prime numbers between 20 – 50.
3.Form a quadratic equation whose roots are 3 /2 and -5.
4.Prove that : Sec2A / tan A – tan A = Cot A
5.Complete the tabel and find CDR.
|
Age group |
Population |
Number of Deaths |
|
0 -10 |
35650 |
310 |
|
10 – 20 |
37750 |
250 |
|
20 – 35 |
- |
110 |
|
35 – 50 |
30450 |
- |
|
above 50 |
20150 |
390 |
|
- |
1,40,000 |
1200 |
6.Find the GCD of x2 – 4x -12 ; x3 + 8
7.Find the value of (sin 44 / cos 46) + (sin 46 / cos 44) without using the trignometric
tables.
8.Given : ëPQS = ëPQR = 900 Show that QS2 + PR2 = PS2 + QR2
9.Given : PQ || YZ and XP / PY = 4 / 3. If XQ = 6.6 cm. Find QZ.
10.If x3 + y3 / x3 – y3 = 91 / 37 . Show that x : y = 4 :3.
11.Aarti buys a saree costing Rs. 2500/- at Rs. 2700/- after paying sales tax.
Calculate the ratio of sales tax paid by her.
12.Find side of square whose diagonal is 12 cm.
13.Quadrilateral ABCD is a cyclic quadrilateral in which ë A = 2ëC.
Find ëA.
14.If the mean of the following data is 14.5 Find the value of k.
Marks obtained (x) 5 10 15 20 25
Number of student (y) 3 6 4 k 3
15.P is the centre of the circle. Seg AB is the diameter, BC = 10, AC = 24. Determine Radius.
SECTION – B
Question number 16 to 25 are of 4 marks each.
16.Calculate cost of living index from the following data :-
Commodity
Quantity
Price in 1999
Price of 2000
P
5
4.20
6.00
R
4
5.00
8.50
A
3
8.00
10.50
G
7
9.00
11.50
S
8
12.50
16.00
17.If Cos245 + Sin 30 = 2 Cos2A , Find Sec2A.
18.Solve graphically 3x – y = 6, 2x + y = 4.
19.Show that : – a2(b + c) + b2 (c + a) + c2 (a + b) +3abc = (a+b+c)(ab + bc + ca).
20.O is the midpoint of seg QR, M is the midpoint of seg OP, seg QS meets side PR at S and QS || OT. Show that PS = 1 / 3 PR.
21.The radius of a circle is less than twice the radius of the other by 1 cm.
The sum of their areas is 34 p sq cm. Find the radius of each circle.
22.Draw a circle with O as a centre and radius 4 cm. Take two points A and B on the
circle such that ëAOB = 800. Draw tangents to the circle at the points A and B.
23.The radius and height of a solid right circular cylinder are 10 cm and 30 cm respectively.
It is melted and solid cones are prepared. If the diametre base of the cone is 2 cm and
its height is 10 cm. Find how many such cones are prepared from the whole metal of the cylinder.
24.Find the mean of the following frequency distribution.
Class
Frequency
00 – 10
3
10 – 20
9
20 – 30
15
30 – 40
8
40 – 50
5
25.If a, b are the roots of the equation 4×2 – 5x + 4 = 0. Form the equation whose roots are a2, b2.
SECTION – C
Question 26 – 30 carry 6 marks each.
26.Sachin’s Annual Income is Rs. 74,600/- (excluding House Rent Allowance).
His contribution to Provident Fund is Rs. 600 per month and he pays
Rs. 2,600 as LIC premium during the year.
Find the tax paid by him during the year.
a) Standard deduction = 1/3 of total income subject to maximum of Rs. 15,000.
b) Rate of Income tax for individual income
i) upto Rs. 35,000 –> No tax
ii) Rs. 35000 to Rs. 60,000 –> 20% of the amount exceeding 35,000
iii) Rs. 60,001 to Rs. 1,00,000 –> Rs. 5000 + 30% of the amount exceeding
Rs. 60,000
c ) Rebate in tax – 20% of the saving to a maximum of Rs. 12000 whichever is less.
27.A vertical tower stands on a horizontal plane and is surmounted by a
vertical flagstaff the elevation of the bottom of the flagstaff is A and
that of the top of the flagstaff is B . Prove that the height of the tower
is h. tanA / tanB – tanA.
28.å a ( x – a ) / ( a – b ) ( a – c )= -1. Prove that.
29.Triangle PQR ëQ = 900, A and B are the midpoints of sides PQ and QR respectively. Prove that 4[ RA2 + PB2 ] = 5PR2
30.In the circle radius 5 cm, AB and AC are two chords such that AB = AC = 6 cm.
Find the length of the chord BC.
Mahatma Gandhi Chitrakoot Gramodaya Vishwavidalya Satna Chitrakoot (MP)
Question Bank of Numerical Methods
Unit-1
BCA 4th Sem
Ques1- (A) Define Errors (B) Truncation Errors
Ques2- Define Absolute, Relative and percentage Errors.
Ques3- (a)How many digits are to taken in computing √21 so that the error does not exceed 0.1%.
(b)Round-off 0.0013478 to four significant figures.
Ques4- If X=8/9 and the exact decimal represent of X is 0.88………..,verify the rule
│X-x│≤1/2X 10-m , numerically when X is rounded-off to three decimal digits.
Ques5- If ۸= 22/7 is approximate as 3.14, find the absolute error, relative error and relative percentage error.
Ques6- If 0.333 is the approximation value of 1/3, find absolute relative and percentage errors.
Ques7- Given the solution of a problem as xa=35.25 with the relative error in the solution at most 2% find to four decimal digits, the range of values with in which the exact value of the solution must lie.
Ques8 (a) Find the difference (√2.01-√2) to three correct digits.
(b) Find the sum of the approximation numbers 0.246, 0.1823, 236.7, 215.4, 13.68 ,0.0783, 0.0214, 0.00354 each correct to the indicate significant digits.
Ques9- (a) If ∆x= 0.005, ∆y= 0.001 be the absolute errors in x=2.11 and y= 4.15 find the relative error in the competition of x+y.
(b) For x=0.4845 and y= 0.4800, calculate the value of x2-y2/x+y using normalized floating point arithmetic compare with the value of (x-y) indicate the error in former.
Ques10- Use the series
Loge (1+x/1-x) = 2(x+x3/3+x5/5+……………..)
To compute the value of the log(1.2) correct to seven decimal places and find the number of forms retained.
Unit-2
Ques1- Find the real root equation f(x)=x 3-2x-5, using bisection method up to fifth approximation.
Ques2- Find a real root of the equation f(x)=x3-4x-9=0, using bisection method up to fourth approximation.
Ques3- Find a real root of the equation f(x)= x3-9x+1=0 by the Regula Falsi method, correct to three decimal places.
Ques4- Find the real root of the equation xlog10x-1.2=0 by the Regula Falsi Method, correct to four decimal places.
Ques5- By using Newton’s Raphson’s method find the root of x4-x-10=0 up to third approximation, correct to three decimal places.
Ques6- Evaluate √(12) to four places of decimal by using Newton-Raphson’s method.
Ques7- Find the cube root of 2 approximation by Newton’s-Raphsons method correct to five decimal places.
Ques8- Solve the following system by Gauss elimination method
6x+3y+2z=6, 6x+4y+3z=0, 20x+15y+12z=0
Ques9 Solve the following system by Gauss elimination method
2x+y+4z=12, 8x-3y+2z=23, 4x+11yz=33
Ques10 – solve by Gauss elimination method
2x-6y+8z=24, 5x+4y-3z=2, 3x+y+2z=16
Ques11- Solve by Jacobie’s Heration method
27x+6y-z=85, 6x+15y+2z=72, x+y+54z=110
Ques12- Solve by Gauss-seidel iteration method
27x+6y-z=85, 6x+15y+2z=72, x+y+54z=110
Ques13- Solve 10x+y+z=12, 2x+10y+z=12, 2x+2y+10x=14 by Gauss-Seidel iteration method.
Ques14- Solve 10x+2y+z=9, 2x+2y-2z=-44 and -2x+3y+10z=22 by jacobie’s itration method.
Unit-3
Ques1- (a) Evaluate ∆tanx, taking unity as interval.
(b) Evaluate ∆ (1-x)(1-2x)(13x), taking using as interval .
Ques2- (a) Evaluate ∆(x+cosx), the interval of differentiating being x.
(b)Evaluate ∆logf(x) =log {1+∆f(x)/f(x}}
Ques3-(a) Evaluate ∆(eaxlogbx) taking interval of differencing being h.
(b) Evalute ∆n(eax+b), taking unity as interval
Ques4- Establish the following Identities.
(a) ∆=E-1 (b) ▼=1-E-1
Ques5- Establish the following Identities .
(a) ehd=1+∆ (B) δ=E1/2-E-1/2
Ques6- Derive NewtonsGregory Formula for forward Interpolation formula.
Ques7- Prove that divided differences of a symmetrical in all their arguments.
Ques8- Prove that the nth divided differences of a polynomial of the nth degree are constant.
Ques9- Given sin45ө=0.7071, sin50=0.7660, sin55=0.8192, sin60=0.8660, find sin52 by using any method of interpolation , where f(x)=sinx,
Ques10- Using Newton’s Forword interpolation formula, find the value of the f(1.6) if
X: 1 1.4 1.8 2.2
Y: 3.49 4.82 5.96 6.5
Ques11- Apply Gauss Forward formula to evaluate e-x when x=1.748 from the following table
X: 1.72 1.73 1.74 1.75 1.76 1.77
Y: 0.1790 0.1773 0.1755 0.1738 0.1720 0.1703
Ques12- The population of town in the year 1931, 1941 …1981 are follows
Year: 1931 1941 1951 1961 1971 1981
Popu: 15 20 27 39 52 70
Ques13- Given-
Ө: 0 5 10 15 20 25 30
tanӨ: 0 0.0875 0.1763 0.2679 0.3640 0.4663 0.5774
Show that tan16=0.2867, with the help of Strinling’s formula
Ques14- the Function x∫∞e-t/t is given in the table below. Find y for x=0.0378 by Strinling’s formula.
X: 0 0.01 0.02 0.03 0.04 0.05 0.06
Y: ∞ 4.0379 3.3547 3.9591 2.6813 2.4679 2.5953
Unit -4
Ques1- Find the first derivative of the function tabulated below, at the point x=1.5
X: 1.5 2.0 2.5 3.0 3.5 4.0
Y=f(x) 3.375 7.000 13.625 24.000 38.875 59.000
Ques2- Calculate the first and second dervatives of the function tabulated below at the point x= 1.1
X: 1.0 1.2 1.4 1.6 1.8 2.0
Y=f(x):0 0.1280 0.5440 1.2960 2.4320 4.0000
Created By Sandeep Maurya BCA (2007-10)batch