-
3x + 2y = 6 ;(k + 1 )x + 4y = (2k + 2)
For what value of k, will the above system of equation have infinite solution.
-
Find the median of the prime numbers between 20 - 50.
-
Form a quadratic equation whose roots are 3 /2 and -5.
-
Prove that : Sec2A / tan A - tan A = Cot A
-
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 |
-
Find the GCD of x2 - 4x -12 ; x3 + 8
-
Find the value of (sin 44 / cos 46) + (sin 46 / cos 44) without using the trignometric
tables.
- .
Given : ëPQS = ëPQR
= 900
Show that QS2
+ PR2
= PS2
+ QR2
Given : PQ || YZ and XP / PY = 4 / 3. If XQ = 6.6 cm. Find QZ.
-
If x3 + y3 / x3 - y3 = 91 / 37 . Show that x : y = 4 :3.
-
Aarti buys a saree costing Rs. 2500/- at Rs. 2700/- after paying sales tax.
Calculate the ratio of sales tax paid by her.
-
Find side of square whose diagonal is 12 cm.
-
Quadrilateral ABCD is a cyclic quadrilateral in which ë A = 2ëC.
Find ëA.
-
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
P is the centre of the circle. Seg AB is the diameter, BC = 10, AC = 24. Determine
Radius.
SECTION
- B
-
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
|
-
If Cos245 + Sin 30 = 2 Cos2A , Find Sec2A.
-
Solve graphically 3x - y = 6, 2x + y = 4.
-
Show that : - a2(b + c) + b2 (c + a) + c2 (a + b) +3abc = (a+b+c)(ab + bc + ca).
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.
-
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.
-
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.
-
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.
-
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 |
-
If a, b are the roots of the equation 4x2 - 5x + 4 = 0. Form the equation whose roots are a2, b2.
-
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.
-
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.
-
å a ( x - a ) / ( a - b ) ( a - c )= -1. Prove that.
Triangle PQR ëQ = 900,
A and B are the midpoints of sides PQ and QR respectively. Prove that 4[ RA2
+ PB2
] = 5PR2
-
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.