*Maximum Marks: 40**Time allowed: One and a half hours**Answers to this Paper must be written on the paper provided separately.**You will not be allowed to write during the first 10 minutes.**This time is to be spent in reading the question paper.**The time given at the head of this Paper is the time allowed for writing the answers*

*Attempt all questions from Section A and any three questions from Section B.**The intended marks for questions or parts of questions are given in brackets [ ].*

**Section A [16 Marks] [16×1] **

Question 1. If matrix A is of order 3 x 2 and matrix B is of order 2 x 2 then the matrix AB is of order

(a) 3 x 2 (b) 3 x 1 (c) 2 x 3 (d) 1 x 3

Answer:

Question 2. The percentage share of SGST of total GST for an Intra-State sale of an article is

(a) 25% (b) 50% (c) 75% (d) 100%

Answer:

GST is Goods and service Tax Applicable on all the goods and services which comes under GST regime.

There are different rate of GST for different category of product and services 5% , 12% , 18% and 28%

GST for Intra-State Transactions ( Transactions with in same state) are Equally divided in 2 categories CGST and SGST.

CGST = SGST = GST/2

CGST = SGST = 50% of GST

CGST = Central GST

SGST = State GST

The percentage share of SGST of total GST for an Intra-State sale of an article is 50% .

Question 3. ABCD is a trapezium with AB parallel to DC. Then the triangle similar to is

(a) (b) (c) (d)

Answer:

Given that, ABCD is trapezium with AB parallel to DC .

Therefore , In and we have,

( Vertically opposite angles. )

( since , alternate angles. )

Therefore ( By AA similarity )

Hence, is similar to .

Question 4. The mean proportion between 9 and 16 is

(a) 25 (b) 144 (c)7 (d) 12

Answer:

When four numbers say are in similar quantities such that then they are said to be in proportion.

When are in continued proportion then is said to be the mean proportional.

So, the mean proportional of 9 and 16 is 12.

Question 5. A man deposited Rs. 500 per month for 6 months and received Rs. 3300 as the maturity value. The interest received by him is:

(a) 1950 (b) 300 (c) 2800 (d) none of these

Answer:

Total money deposited

Money received at maturity

Hence the interest received by him

Question 6. The solution set representing the following number line is

(a) (b)

(c) (d)

Answer:

The convention is that a hollow circle marks the end of the range with a strict inequality and a darkened circle marks the end of a range involving an equality as well

Question 7. The first three terms of an arithmetic progression (A. P.) are 1, 9, 17, then the next two terms are

(a) 25 and 35 (b) 27 and 37 (c) 25 and 33 (d) none of these

Answer:

Question 8. If then the corresponding proportional sides are

Answer:

When two triangles are similar, their corresponding angle are equal and corresponding sides are proportional.

For example: If is similar to

Question 9. If , then the solution set of the inequation , is

(a) (b) (c) (d)

Answer:

Given: To find: the solution set of

Simplify the given inequality:

Know that the symbol *W *represents a set of whole number that range from

Therefore, The solution set of will be

Question 10. The roots of the quadratic equation are 1.390, 0. 359.The roots correct to 2 significant figures are

(a) 1.39 and 0.36 (b) 1.3 and 0.35 (c) 1.4 and 0.36 (d) 1.390 and 0.360

Answer:

Root of the equation are :

Question 11. and are in proportion, then is equal to

(a) 6 (b) 4 (c) 4.5 (d) 16

Answer:

Question 12. If a polynomial is divided by , then the remainder is

(a) – 4 (b) 38 (c) -3 (d) 2

Answer:

Question 13. If 73 is the nth term of the arithmetic progression 3, 8, 13, 18…, then ‘n’ is

(a) 13 (b) 14 (c) 15 (d) 16

Answer:

So, AP is

We know that, common difference is the difference of the consecutive terms.

Now,

Applying the given formula,

Question 14. The roots of the quadratic equation are

(a) Real and distinct (b) Real and equal (c) Distinct (d) Not real/imaginary

Answer:

Here

Therefore the roots are real and equal.

Question 15. Which of the following statement is not true?

(a) All identity matrices are square matrix

(b) All null matrices are square matrix

(c) For a square matrix number of rows is equal to the number of columns

(d) A square matrix all of whose elements except those in the leading diagonal are zero is the diagonal matrix

Answer:

A matrix which has equal number of rows and columns is called a square matrix.

If each of the elements of a matrix is zero, it is call a null matrix. Examples could be:

In the first case it is a square matrix while in the other case it is not a square matrix..

Question 16. If is a factor of the polynomial , then is equal to

(a) -10 (b) 26 (c) -26 (d) 10

Answer:

Since is a factor of the polynomial then

**Section B [12 Marks] [6×2]**

Question 17. A man deposited Rs.1200 in a recurring deposit account for 1 year at 5% per annum simple interest. The interest earned by him on maturity is

(a) 14790 (b) 390 (c) 4680 (d) 780

Answer:

Question 18. If is a factor of polynomial , then its factors are

(a) (b)

(c) (d)

Answer:

Question 19. The following bill shows the GST rates and the marked price of articles A and B:

The total amount to be paid for the above bill is: –

(a) 1548 (b) 1596 (c) 1560 (d) 1536

Answer:

Question 20. The solution set for the linear inequation is

(a) (b)

(c) (d)

Answer:

Answer:

Applying Componendo and dividendo

Answer:

**Section C [12 Marks] [3×4]**

Question 23. The distance between station A and B by road is 240 km and by train it is 300 km. A car starts from station A with a speed x km/hr whereas a train starts from station B with a speed 20 km/hr more than the speed of the car.

(i) The time taken by car to reach station B is

Answer:

(ii) The time taken by train to reach station A

Answer:

(iii) If the time taken by train is 1 hour less than that taken by the car, then the quadratic equation formed is

(a) (b)

(c) (d)

Answer:

(iv) The speed of the car is

(a) 60 km/hr (b) 120 km/hr (c) 40 km/hr (d) 80 km/hr

Answer:

Question 24. In the given triangle and AR intersects CB at O.

Using the given diagram answer the following question:

(i) The triangle similar to is

(a) (b) (c) (d)

Answer:

( Alternate angles)

( Alternate angles)

( by AAA axiom)

(ii) by axiom

(a) SAS (b) AAA (c) SSS (d) AAS

Answer

( Alternate angles)

( Alternate angles)

( by AAA axiom)

(iii) If QC =6 cm, CR = 4 cm, BR = 3 cm. The length of RP is

(a) 4.5 cm (b) 8 cm (c) 7.5 cm (d) 5 cm

Answer:

(iv) The ratio PQ: BC is

(a) 2 : 3 (b) 3 : 2 (c) 5 : 2 (d) 2 : 5

Answer:

Question 25. The nth term of an arithmetic progression (A.P.) is (3n + 1)

(i) The first three terms of this A. P. are

(a) 5, 6, 7 (b) 3, 6, 9 (c) 1, 4, 7 (d) 4, 7, 10

Answer:

Given

(ii) The common difference of the A.P. is

(a) 3 (b) 1 (c) -3 (d) 2

Answer:

(iii) Which of the following is not a term of this A.P.

(a) 25 (b) 27 (c) 28 (d) 31

Answer:

Hence 27 is not the term of this A.P.

(iv) Sum of the first 10 terms of this A.P. is

(a) 350 (b) 175 (c) -95 (d) 70

Answer: