- This question paper contains
**50**questions out of which**40**questions are to be attempted. All questions carry**equal**marks. - This question paper contains
**three**Sections:**A**,**B**, and**C.** - Section
**A**has**20**questions. Attempt any**16**questions from Q.No.**1**to**20.** - Section
**B**has**20**questions. Attempt any**16**questions from Q.No.**21**to**40.** - Section
**C**contains**two**Case Studies containing 5 Questions in each case. Attempt any**4**questions from Q.No.**41**to**45**and**4**another from Q.No.**46**to**50.** - There is only
**one**correct option for every multiple choice question (MCQ). Marks will not be awarded for answering more than one option. - There is no negative marking.

Q. No. 1 to 20 are of 1 mark each. Attempt any 16 from Q. 1 to 20.

- 3
- 4
- 5
- 6

Ans: (b)

- 1
- 2
- 3
- 5

Ans: (d)

Sol: The number of zeroes of P(x) is 5.

- –1, 2
- –1, 4
- 1, –2
- –1, –4

Ans: (a)

- 2
- –3
- –√3
- –√2

Ans: (c)

- 4 : 25
- 2 : 3
- 9 : 4
- 25 : 4

Ans: (d)

- 1
- $\frac{40}{9}$
- $\frac{38}{9}$
- $5\frac{1}{3}$

Ans: (d)

- 2464 m
^{2} - 1232 m
^{2} - 616 m
^{2} - 308 m
^{2}

Ans: (c)

- –2
- 2
- 1
- –1

Ans. (a)

- 17 m/min
- 19 m/min
- 23 m/min
- 13 m/min

Ans: (b)

- 1
- 2
- 3
- 4

Ans: (c)

- 9x + 8y = 7
- –12x – 8y = 7
- –12x + 8y = 7
- 12x + 8y = 7

Ans: (c)

- 8
- 9
- 7
- 6

Ans: (b)

- Congruent, but not similar.
- Similar, but not congruent.
- Neither congruent nor similar.
- Congruent as well as similar.

Ans: (b)

- $\frac{7}{25}$
- $\frac{24}{25}$
- $\frac{7}{24}$
- $\frac{24}{7}$

Ans: (a)

- 44 cm
- 88 cm
- 132 cm
- 176 cm

Ans: (c)

- $\frac{9}{13}$
- $\frac{35}{52}$
- $\frac{10}{13}$
- $\frac{19}{26}$

Ans: (a)

- 4 : 00 pm
- 4 : 30 pm
- 5 : 00 pm
- 5 : 30 pm

Ans: (c)

- k [x
^{2}– 8x + 5] - k [x
^{2}+ 8x + 5] - k [x
^{2}– 5x + 8] - k [x
^{2}+ 5x + 8]

Ans: (a)

- 1, –7
- –1, 7
- 2, 7
- –2, –7

Ans: (b)

Ans: (a)

Section – B

Q. No. 21 to 40 are of 1 mark each. Attempt any 16 from Q. 21 to 40.

- 575
- 450
- 750
- 625

Ans: (d)

- 0.01
- 3%
- $\frac{16}{17}$
- $\frac{17}{16}$

Ans: (d)

- 10
^{4} - 10
^{5} - 10
^{6} - 10
^{3}

Ans: (b)

Ans: (c)

- 3 : 2
- 2 : 3
- 3 : 4
- 4 : 3

Ans: (c)

- a = 5, b = –1
- a = 9, b = –5
- a = 7, b = –3
- a = 3, b = 1

Ans: (b)

- Coprime
- Not coprime
- Even
- Odd

Ans: (a)

- 321 cm
^{2} - 642 cm
^{2} - 128 cm
^{2} - 256 cm
^{2}

Ans: (c)

- equilateral triangle
- isosceles triangle
- right angled triangle
- isosceles right angled triangle

Ans: (c)

- –7
- 7
- -3
- 3

Ans: (b)

- 1
- 4
- 3
- 2

Ans: (d)

- 3 : 1
- 3 : 4
- 3 : 2
- 3 : 5

Ans: (d)

- a
^{2}– b^{2} - b
^{2}– a^{2} - a
^{2}+ b^{2} - b – a

Ans: (b)

- 22 : 7
- 11 : 7
- 7 : 11
- 7 : 22

Ans: (d)

- $\frac{11}{36}$
- $\frac{1}{3}$
- $\frac{13}{36}$
- $\frac{25}{36}$

Ans: (d)

Sol: A dice is rolled twice. Then possible outcomes are :

- 300
- 400
- 500
- 600

Ans: (c)

- $\frac{56}{7}$ cm
- $\frac{7}{56}$ cm
- $\frac{25}{7}$ cm
- $\frac{24}{7}$ cm

Ans: (d)

- 107°
- 135°
- 155°
- 145°

Ans: (a)

- $\frac{{\mathrm{p}}^{2}+1}{2\mathrm{p}}$
- $\frac{{\mathrm{p}}^{2}-1}{2\mathrm{p}}$
- $\frac{{\mathrm{p}}^{2}-1}{{\mathrm{p}}^{2}+1}$
- $\frac{{\mathrm{p}}^{2}+1}{{\mathrm{p}}^{2}-1}$

Ans: (b)

Ans: (c)

Section – C

Q. No. 41-45 are based on Case Study–I, you have to answer any (4) four questions. Q. No. 46-50 are based on Case Study-II, you have to answer any (4) four questions.

Case Study-I

A book store shopkeeper gives books on rent for reading. He has variety of books in his store related to fiction, stories and quizzes etc. He takes a fixed charge for the first two days and an additional charge for subsequent day. Amruta paid ₹22 for a book and kept for 6 days; while Radhika paid ₹16 for keeping the book for 4 days.

Assume that the fixed charge be ₹x and additional charge (per day) be ₹y.

Based on the above information, answer any four of the following questions :

Based on the above information, answer any four of the following questions :

Given information:

Let, fixed charge for 2 days = ₹x.

and additional charge (per day) = ₹y.

- x – 4y = 16
- x + 4y = 16
- x – 2y = 16
- x + 2y = 16

Ans: (d)

The amount paid by Radhika, for keeping the book for 4 days = ₹16

$\Rightarrow $ Fixed charge for two days + additional charge (per day) for next 2 days = ₹16

$\Rightarrow $ x + 2y = 16

- x – 2y = 11
- x – 2y = 11
- x + 4y = 22
- x – 4y = 11

Ans: (c)

Sol: The amount paid by Amruta, for keeping the book for 6 days = ₹22

$\Rightarrow $ Fixed charge for two days + additional charge (per day) for next 4 days = ₹22.

$\Rightarrow $ x + 4y = 22

- ₹9
- ₹10
- ₹13
- ₹15

Ans: (b)

- ₹6
- ₹5
- ₹4
- ₹3

Ans: (d)

Sol: The additional charges for each subsequent day for a book = y = ₹3 (As solved in Q. 43 equation (3).)

- ₹35
- ₹52
- ₹50
- ₹58

Ans: (c)

Sol: Total amount = Amount paid by Radhika for keeping the book for 6 days + Amruta for keeping the book for 8 days

= Radhika for keeping the book for 4 days + 2 days additional

+ Amruta keeping the book for 6 days + 2 days additional

= 16 + 2y + 22 + 2y

= 38 + 4y

= 38 + 4 × 3

= 38 + 12

= ₹50

Case Study – II

A farmer has a field in the shape of trapezium, whose map with scale 1 cm = 20 m, is given below : The field is divided into four parts by joining the opposite vertices.

Based on the above information, answer any four of the following questions :

- Similar by AA criterion
- Similar by AA criterion
- Similar by RHS criterion
- Not similar

Ans: (a)

- 4 : 1
- 1 : 4
- 1 : 2
- 2 : 1

Ans: (b)

- AB = 2 CD
- AB = 4 CD
- CD = 2 AB
- CD = 4 AB

Ans: (d)

- $\u2206\mathrm{AOD}~\u2206\mathrm{BOC}$
- $\u2206\mathrm{AOD}~\u2206\mathrm{BCO}$
- $\u2206\mathrm{ADO}~\u2206\mathrm{BCO}$
- $\u2206\mathrm{ODA}~\u2206\mathrm{BCO}$

Ans: (b)

- The ratio of their perimeters is 3 : 4.
- The corresponding altitudes have a ratio 1 : 2.
- The medians have a ratio 1 : 4.
- The angle bisectors have a ratio 1 : 16.

Ans: (b)