Algebra Model Set 5 on shaalaa.com 2019-2020 SSC (English Medium) 10th Standard Board Exam Question Paper Solution

Choose the correct answer for the following question.

The roots of x² + kx + k = 0 are real and equal, find k.

0

4

0 or 4

2

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

104.5

In the format of GSTIN, there are ______ alpha-numerals.

15

10

16

9

Find the correct answer from the alternatives given.

The formula to find mean from a grouped frequency table is  \[X = A + \frac{\sum f_i u_i}{\sum f_i} \times hg\] .

\[\frac{x_i + A}{g}\] 

\[\left( x_i - A \right)\] 

\[\frac{x_i - A}{g}\]

Solve the following simultaneous equation.

3a + 5b = 26; a + 5b = 22

Decide whether the following equation is quadratic equation or not.

`"y"^2 + 1/"y" = 2`

The arrow is rotated and it stops randomly on the disc. Find out on which colour it may stop.

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.

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.

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?

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.

Solve the following simultaneous equation.
49x – 57y = 172; 57x – 49y = 252

Solve the following quadratic equation by factorization.

`2"x"^2 - 2"x" + 1/2 = 0`

Find the fourth term from the end in an A.P. –11, –8, –5,...., 49.

The following table shows the income of farmers in a grape season. Find the mean of their income. 

The following frequency distribution table gives the ages of 200 patients treated in a hospital in a week. Find the mode of ages of the patients.

Solve the following simultaneous equation.

\[ \frac{2}{x} - \frac{3}{y} = 15; \frac{8}{x} + \frac{5}{y} = 77\]

Find quadratic equation such that its roots are square of sum of the roots and square of difference of the roots of equation \[2 x^2 + 2\left( p + q \right)x + p^2 + q^2 = 0\]

Fill in the blanks given in the contract note of sale-purchase of shares. 
(B - buy S - sell)

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.

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.

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.

The pie diagram in figure shows the proportions of different workers in a town. Answer the following question with its help.
 If the total workers is 10,000; how many of them are in the field of construction ?

The following table shows the ages of the patients admitted in a hospital during a year:

Find the mode and the mean of the data given above. Compare and interpret the two measures of central tendency.

Solve the following pairs of equations by reducing them to a pair of linear equations

`5/(x-1) + 1/y-2 = 2`

`6/(x-1) - 3/(y-2) = 1`

For the given trading chain prepare the tax invoice I, II, III, GST at the rate of 12% was charged 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.

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:

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.

The A.P. in which 4^th term is –15 and 9^th term is –30. Find the sum of the first 10 numbers.