XI CBSE Math - Half Yearly Sample Paper

No. 1 Choice of Top Rankers Medical Cut-Off

|

Engineering Cut-Off

Shreya. R PSBB KKN 492/500 | CBSE XI

|

Target 98+%

Arjjun. B PSBB Mill 490/500 |

Maths

| Target CGPA 10

Harish.N Jawahar 1171/1200

Max Marks: 100

Time Allowed : 3 Hours

Pre-Half Yearly Exam Chapters 1-11 & 15 (Code – 135A1) General Instructions: Questions 1 – 6 (1 Marks), 7 – 19 (4 Marks), 20 – 26 (6 Marks) SECTION: A 1.

Find the range of the function f (x) = 2 – 3x, x R, x > 0.

2.

Evaluate

3.

If a  {2, 4, 6, 9} and b  {4, 6, 18, 27}, then form the set of all ordered pairs (a, b) such that a divides b and a < b.

4.

If nC4 = nC6, find 12Cn

5.

Find the slope of a line, which passes through the origin, and the mid-point of the line segment joining the points P (0, – 4) and B (8, 0).

6.

Find the type and the eccentricity of the conic 16x2 + y2 = 16

    tan     tan     4  4 

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CBSE XII, XI

2017

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7.

15-HY101-QP- 2

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SECTION: B In a town of 10,000 families it was found that 40% families buy newspaper A, 20% families buy newspaper B and 10% families but newspaper C. 5% families buy A and B, 3% buy B and C and 4% buy A and C. If 2% families buy all the three news papers, find the number of families which buy (i) A only (ii) B only (iii) none of A, B and C x2  4

8.

Find the domain and range of the real function f(x) =

9.

In any triangle ABC prove that  a(b2 + c2)cosA = 3abc

10.

Prove that sin20o sin40o sin60o sin80o =

11.

Prove that 102n – 1 + 1 is divisible by 11 for all nN

12.

Find the square root of -8 – 6i

13.

Solve: -5 ≤

3 16

2  3x ≤9 4

(OR) Find the mean deviation about the mean for the following data: Marks obtained: 10-20 20-30 30-40 40-50 50-60 Number of students 2 3 8 14 8

60-70 3

70-80 2

14.

The letters of the word ‘RANDOM are written in all possible orders and these words are written out as in dictionary. Find the rank of the word ‘RANDOM’ in this dictionary.

15.

Find the sum to n terms of the series: 5 + 11 + 19 + 29 + 41 …

16.

If pth, qth, rth and sth terms of an A.P. are in G.P., then show that (p - q), (q – r), (r - s) are also in G.P.

17.

Find the image of the point (-8, 12) with respect to the line mirror 4x + 7y + 13 = 0.

18.

Find the distance of the line 4x – y = 0 from the point P (4, 1) measured along the line making an angle of 1350 with the positive x-axis.

19.

Find the type of the conic and also fond coordinates of the foci and the vertices, the eccentricity, the length of the latus rectum, equation of LR

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Test Part Trigonometry, Differential Calculus Integral Calculus

Det22A1 - 3

kilan Institute

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SECTION: C 1  x , if x  0 , if x  0 . Draw the graph of f (x).  x  1 , if x  0 

20.

The function f is defined by f (x) = 1

21.

If A + B + C =  , prove that sin2A – sin2B + sin2C = 4cosA sin B cos C (OR)

1 =0 4 Find the linear inequations for which the solution set is the shaded region given in fig.

3x + 2y ≤ 150, x + 4y ≤ 80, x ≤ 15, y ≥ 0 Solve sin2  - 2 cos  +

22.

(OR) Calculate the mean and standard deviation for the following distribution: Marks: 20 – 30 30 – 40 40 – 50 50 – 60 60 – 70 70 – 80 No. of students 3 6 13 15 14 5

80 – 90 4

23.

If the coefficients of 5th, 6th and 7th terms in the expansion of (1 + x)n are in A.P. Find n.

24.

The sum of n terms of two arithmetic progressions are in the ratio (3n + 8) : (7n + 15). Find the ratio of their 12th terms.

25.

Two lines passing through the point (2, 3) intersect each other at an angle of 600. If slope of one line is 2, find the equation of the other line.

Find the equation of the circle passing through the points (1, 1), (2, -1) and (3, 2)

26.

CBSE XII 2015 RK

Name (CBSE XII)

School

Tot RK

Name (CBSE XII)

School

Tot

1

Arjjun.B

490

12

Sahana.T.K

DAV Gop

465

2

Priyanka

479

13

Aparna

PSBB KKN

464

3

Visweshwar.S

PSBB Mill The Global Indian Intl, Singapore DAV Gop

478

14

Vasudha Mishra

PSBB KKN

464

4

Praveen.J

Chinmya Taylor

477

15

Anirudh.K.K

PSBB Mill

461

5

Sandana.P

DAV Gop

474

16

Rohit.A.R.

PSBB Mill

461

6

Raghul.S

PSBB Mill

473

17

Anjali Devi.S

Amrita

457

7

Bhavana.S

Omega

472

18

Swetha.S

PSBB KKN

457

8

Amrutha.A

PSBB KKN

467

19

Indumathi.P

Amrita

441

9

Dwarak Bharadwaj

NPS

467

20

Neeraj.M

PSBB Mill

441

10

Souptik Kar

PSBB Mill

466

21

Rishab.S

PSBB KKN

423

11

Sivaranjani.S

PSBB KKN

466

22

KrishnaKumar.R

PSBB KKN

448

Akilan Institute

15-HY101-QP- 4

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Pre-Half Yearly Exam Chapters 1-11 & 15 (Code – 135A2) General Instructions: Questions 1 – 6 (1 Marks), 7 – 19 (4 Marks), 20 – 26 (6 Marks) SECTION: A B = { x / x3 + 8 = 0, x  N }. Find A  B

1.

Given A = { x/ - 4 ≤ x < 3, x  Z},

2.

Find the general and principal solutions of cosec x = - 2

3.

Solve of x: x2 + x +

4.

Find the angle between the x-axis and the line joining the points (3,–1) and (4,–2).

5.

Find the sum to infinity of the series

1 2

=0 1 1 1 1 1 1 + + + + + +…

3 52 32 54 35 56

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SHREYA. R PSBB KKN

ARJJUN.B PSBB Mill

492/500

490/500

7 Southern Region Rank 2 State Rank 2

7 Southern Region Rank 4 State Rank 4

All India Rank

All India Rank

Det22A1 - 5

kilan Institute

6.

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The income of a person is Rs. 3,00,000, in the first year and he receives an increase of Rs.10,000 to his income per year for the next 19 years. Find the total amount, he received in 20 years.

SECTION: B  

 x   ; x  R  be a function from R into R. Determine the range of f.

2  1 x    2

7.

Let f(x) =  x,

8.

Solve

9.

Prove by Mathematical induction 12 + 22 + 32 + … + n2 =

10.

Find real θ such that

11.

A manufacturer has 600 litres of a 12% solution of acid. How many litres of a 30% acid solution must be added to it so that acid content in the resulting mixture will be more than 15% but less than 18%?

(OR) The following values are calculated in respect of heights and weights of the students of a section of class XI: Height Weight Mean 162.6 cm 52.36 kg Variance 127.69 cm2 23.1361 kg2 Can we say that the weight s show greater variation than the heights?

12.

A class contains 12 boys and 10 girls. From the class 10 students are to be chosen for a competition under the condition that at least 4 boys and at least 4 girls must be represented. The 2 girls who won the prizes last year should be included. In how many ways can the selection are made?

13.

Show that the middle term of (1 + x)2n is

14.

If a, b, c, d and p are different real numbers such that (a2 + b2 + c2) p2 – 2 (ab + bc + cd) p + (b2 + c2 + d2) ≤ 0, then show that a, b, c and d are in G.P.

15.

Find the values of k for which the line (k–3) x –(4 – k2) y + k2 –7k + 6 = 0 is (a) Parallel to the x-axis, (b) Parallel to the y-axis, (c) Passing through the origin.

16.

Find the points on y-axis whose perpendicular distance from the straight line 4x – 3y – 12 = 0 is 3.

17.

Show that the straight lines 3x + y + 4 = 0, 3x + 4y – 15 = 0 and 24x – 7y – 3 = 0 form an isosceles triangle.

18.

Find the equation of the parabola if the focus is (2, -3) and the directrix

19.

Find the equation of the hyperbola where foci are (0, ±12) and the latus rectum is of length 36.

20.

In a class of 35 students, 18 speak Tamil, 12 speak Hindi and 15 speak English.

2 students speak Tamil and Hindi, 4 Hindi and English and 5 speak English and Tamil. Calculate the number of students who speak all the three languages. Also find the number of students who speak Hindi and English but not Tamil.

 

2 sec  + tan  = 1

3  2i sin  is purely real.

1  2i sin 

n(n  1)(2n  1) for all n  N 6

1.3.5...(2n  1)2n x n n!

is 2y – 3 = 0

Akilan Institute

15-HY101-QP- 6

aim100.com

SECTION: C 21.

22.

1 If A + B = 45 , show that (1 + tanA) (1 + tanB) = 2 and hence deduce the value of tan22 2 Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the latus rectum of the ellipse 9x2 + 4y2 = 36.

o

o

23.

Find the co-ordinates of the orthocenter of the triangle formed by the straight lines x + y – 1 = 0, x + 2y – 4 = 0 and x + 3y – 9 = 0.

24.

How many numbers are there between 500 and 1000 which have exactly one of their digits as 8?

25.

Find the equation of the circle whose centre is on the line x = 2y and which passes through the points ( -1, 2) and (3, -2).

26.

The diameters of circles (in mm) drawn in a design are given below Diameters 33-36 37-40 41-44 45-48 49-52 No. of circles 15 17 21 22 25 Find the standard deviation and mean diameter of the circles by using short-cut method Aim100.com Result: CBSE XII 2014

RK

Name (CBSE XII)

School

Tot RK

Name (CBSE XII)

School

Tot

1

Shreya.R

PSBB KKN

492

19

Srinivasan.S

PSBB KKN

473

2

Rangeesh.V

PSBB Nung

488

20

Harish.K

CPS

472

3

Harish.N

Jawahar

1171

21

Suryaa Raman

PSBB KKN

470

4

Nivedita.S

PSBB KKN

484

22

Nishanth.S

PSBB KKN

469

5

Avanthikaa.R

PSBB KKN

483

23

Abinaya.S

PSBB KKN

469

6

Aishwarya.R

PSBB KKN

482

24

Hari Charan.S

PSBB KKN

469

7

Adithya.M

PSBB KKN

480

25

Vasumathi.B

PSBB KKN

468

8

Krishna.S

PSBB KKN

480

26

Raja Gopal.J

MVM

468

9

Rinitha.G.L

PSBB KKN

480

27

Sriraksha V S

PSBB KKN

468

10

Ashwini Raja

PSBB KKN

478

28

Shruthi Harharan

PSBB KKN

467

11

Sukanya P

Omega

478

29

Pooja.R

PSBB KKN

467

12

Sharmi.C

DAV Gop

478

30

Sangavi.V

PSBB KKN

466

13

Susmitha.B

PSBB KKN

476

31

Pranav Srinivas.R

PSBB KKN

466

14

Jayanth.P

Devi Academy

476

32

Praneeth.P

PSBB KKN

466

15

Sandhya.R

PSBB KKN

475

33

Vignesh.J

PSBB KKN

466

16

Aishwarya.S

PSBB KKN

474 34

Siddharth.S

PSBB KKN

465

17

Akshay Kumar.S

PSBB KKN

474 35

Priyadharshini.J.S

Devi Academy

464

18

Amruth Varshini.M

PSBB KKN

473 36

Rohan Chandhoke

PSBB KKN

462

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