Duration: 2h
Choose the correct answer for the following question.
The roots of x^{2} + kx + k = 0 are real and equal, find k.
0
4
0 or 4
2
Chapter: [2] Quadratic Equations
Choose the correct alternative answer for the following question .
For an given A.P. a = 3.5, d = 0, n = 101, then t_{n} = ....
0
3.5
103.5
14.5
Chapter: [1] Arithmetic Progression
Write the correct alternative for the following.
In the format of GSTIN there are ... alphanumerals.
15
10
16
9
Chapter: [6] Financial Planning
The formula to find mean from a grouped frequency table is
(A)
\[\frac{x_i + A}{g}\]

(B)
\[\left( x_i  A \right)\]

(C)
\[\frac{x_i  A}{g}\]

(D)
\[\frac{A  x_i}{g}\]

Chapter: [5] Statistics
Solve the following simultaneous equation.
3a + 5b = 26; a + 5b = 22
Chapter: [3] Linear equations in two variables
Decide whether the following equation is quadratic equation or not.
\[y^2 + \frac{1}{y} = 2\]
Chapter: [2] Quadratic Equations
The arrow is rotated and it stops randomly on the disc. Find out on which colour it may stop.
Chapter: [4] Probability
The following table shows the number of students and the time they utilized daily for their studies. Find the mean time spent by students for their studies by direct method.
Time (hrs.)  0  2  2  4  4  6  6  8  8  10 
No. of students  7  18  12  10  3 
Chapter: [5] Statistics
Solve the Following Word Problem.
Places A and B are 30 km apart and they are on a st raight road. Hamid travels from A to B on bike. At the same time Joseph starts from B on bike, travels towards A. They meet each other after 20 minutes. If Joseph would have started from B at the same time but in the opposite direction (instead of towards A) Hamid would have caught him after 3 hours. Find the speed of Hamid and Joseph.
Chapter: [3] Linear equations in two variables
A tank fills completely in 2 hours if both the taps are open. If only one of the taps is open at the given time, the smaller tap takes 3 hours more than the larger one to fill the tank. How much time does each tap take to fill the tank completely?
Chapter: [2] Quadratic Equations
The 11^{th} term and the 21^{st} term of an A.P. are 16 and 29 respectively, then find the 41^{th}term of that A.P.
Chapter: [1] Arithmetic Progression
Solve the following simultaneous equation.
49x – 57y = 172; 57x – 49y = 252
Chapter: [3] Linear equations in two variables
Solve the following quadratic equation by factorisation.
2x^{2} – 2x +\[\frac{1}{2}\]=0
Chapter: [2] Quadratic Equations
Find the fourth term from the end in an A.P. –11, –8, –5,...., 49.
Chapter: [1] Arithmetic Progression
The following table shows the income of farmers in a grape season. Find the mean of their income.
Income
(Thousand Rupees)

20  30  30  40  40  50  50  60  60  70  70  80 
Farmers  10  11  15  16  18  14 
Chapter: [5] Statistics
Grouped frequency distribution of supply of milk to hotels and the number of hotels is given in the following table. Find the mode of the supply of milk.
Age (years)  Less than 5  5  9  10  14  15  19  20  24  25  29 
No. of patients  38  32  50  36  24  20 
Chapter: [5] Statistics
Solve the following simultaneous equations.
\[ \frac{2}{x}  \frac{3}{y} = 15; \frac{8}{x} + \frac{5}{y} = 77\]
Chapter: [3] Linear equations in two variables
Find quadratic equation such that its roots are square of sum of the roots and square of difference of the roots of equation
\[2 x^2 + 2\left( p + q \right)x + p^2 + q^2 = 0\]
Chapter: [2] Quadratic Equations
Fill in the blanks given in the contract note of salepurchase of shares.
(B  buy S  sell)
No. of
shares

MV of
shares

Total
value

Brokerage
0.2%

9% CGST
on
brokerage

9% SGST
on
brokerage

Total
value of
shares

100 B  Rs 45  
75 S  Rs 200 
Chapter: [6] Financial Planning
In a game of chance, a spinning arrow comes to rest at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8. All these are equally likely outcomes. Find the probability that it will rest at an odd number.
Chapter: [4] Probability
In a game of chance, a spinning arrow comes to rest at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8. All these are equally likely outcomes. Find the probability that it will rest at a number greater than 2.
Chapter: [4] Probability
In a game of chance, a spinning arrow comes to rest at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8. All these are equally likely outcomes. Find the probability that it will rest at a number less than 9.
Chapter: [4] Probability
The pie diagram in figure shows the proportions of different workers in a town. Answer the following questions with its help.
(1) If the total workers is 10,000; how many of them are in the field of construction ?
(2) How many workers are working in the administration ?
(3) What is the percentage of workers in production ?
Chapter: [5] Statistics
The following table shows the ages of the patients admitted in a hospital during a year:
age (in years) 
5 − 15 
15 − 25 
25 − 35 
35 − 45 
45 − 55 
55 − 65 
Number of patients 
6 
11 
21 
23 
14 
5 
Find the mode and the mean of the data given above. Compare and interpret the two measures of central tendency.
Chapter: [5] Statistics
Solve the following pairs of equations by reducing them to a pair of linear equations
`5/(x1) + 1/y2 = 2`
`6/(x1)  3/(y2) = 1`
Chapter: [3] Linear equations in two variables
For the given trading chain prepare the tax invoice I, II, III, GST at the rate of 12% was chanrged for the article supplied.
Prepare the statement of GST payable under each head by the wholesaler, distributor and retailer at the time of filing the return to the government.
Chapter: [6] Financial Planning
Two dice, one blue and one grey, are thrown at the same time.
(i) Write down all the possible outcomes and complete the following table:
Event : ‘Sum on 2 dice’ 
2  3  4  5  6  7  8  9  10  11  12 
Probability  1/36  5/36  1/36 
Chapter: [4] Probability
Ranjana wants to distribute 540 oranges among some students. If 30 students were more each would get 3 oranges less. Find the number of students.
Chapter: [2] Quadratic Equations
The A.P. in which 4^{th} term is –15 and 9^{th} term is –30. Find the sum of the first 10 numbers.
Chapter: [1] Arithmetic Progression
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