Term I (2024-25)

STD: XI Marks: 80
Subject: Mathematics Time: 3hrs
General Instructions:
1. The question paper consists of 45 questions divided into 4 sections A, B, C, D.
2. All questions are compulsory.
3. Section A comprises of 20 questions of 1 mark each.
* There are 15 questions of 1 mark each. Overall Internal choice has been provided in some questions.
* 2 case study-based questions each has internally 4 multiple choice questions of 1 mark.
4. Section B comprises of 10 questions of 2 marks each. Internal choice has been provided in some questions.
5. Section C comprises of 7 questions of 3 marks each. Internal choice has been provided in some questions.
6. Section D comprises of 5 questions of 4 marks each. Attempt any 4 out of 5 questions.
Section A
Q.1 to Q.15 is very short answer question of 1 mark each. Internal choice has been given.
Q.1 Find the multiplicative inverse of the √5+ 3i. 1m
Q.2 Find the difference of (- 4 + 7i), ( -11 -23i). 1m
1
Q.3 Solve | 3x – 2 | ≤ . 1m
2
OR
Q.3 solve the linear inequality 5x +7 > 27.
Q.4 Check whether the given plane 3x – 6y ≤ 0 contains th point (3,1). 1m
Q.5 Find the indicated term of given AP. a = 3, d = 2, Tn, T10. 1m
OR
Q.5 How many terms are there in AP 20,25,30, … .... 100?
Q.6 Find the sum of an infinite GP 1, 1, 1, …………...∞. 1m
3 9
Q.7 Find the area of ∆ ABC, whose vertices are A (6,3) B (-3, 5) and C (4, -2). 1m
OR
Q.7 Find the new coordinates of point (3, -5) if the origin is shifted to the point (-3, -2).
Q.8 Prove that the points A (1,4), B (3, -2), C (4, -5) are collinear. 1m
Q.9 Find the slope of a line perpendicular to the line, which passes through (0,8) and (-5,2). 1m
Q.10 Find the modulus and principal argument of (1, -2i). 1m
Q.11 Find the common ratio and 9th term for sequence 3,6,12, 24……. 1m
OR
Q.11Find the equation of the line which have slope ½ and cut off an intercept -5 on y axis. 1m
Q.12 Represent the complex number z = 1 + i√3 in the polar form. 1m
Q.13 If a, b, c are in AP, then prove that b+c, c+a, a+b is also in AP. 1m
Q.14 Find the sum to infinity of GP 6, 1.2, 0.24, ……∞. 1m
Q.15 If two poles standing at the points A (1, -2) and B (-3 ,5), then find the distance between the places. 1m

Read the Case study given below and attempt all 4 sub parts:
CASE 1 - In drilling world’s deepest hole, the Kola Superdeep Borehole, the deepest manmade hole on Earth
and deepest artificial point on Earth, as a result of a scientific drilling project, it was found that the
temperature T in degree Celsius, x km below the surface of Earth, was given by:
T = 30 + 25 (x – 3), 3 < x < 15.
If the required temperature lies between 200o C and 300o C, then
Q.16The depth, x will lie between 1m
1. 9 km and 13 km 2. 9.8 km and 13.8 km 3. 9.5 km and 13.5 km 4. 10 km and 14 km
Q.17Solve for x. -9x+2> 18 OR 13x+15 ≤−4 1m
1. x ≤ −1913 2. x < −1613 3. −1613 < x < −1913 4. There are no solution.
Q.18 Find the inequality represented by the graph 1m

1. y ≤ 12x+2 2. y > 12x+2 3. y ≥ 12x+2 4. y < 12x+2

Q.19 If |x| < 5 then the value of x lies in the interval 1m
1. (-∞, -5) 2. (∞, 5) 3. (-5, ∞) 4. (-5, 5)
CASE 2 -Villages of Shanu and Arun’s are 50km apart and are situated on Delhi Agra highway as shown in
the following picture. Another highway YY’ crosses Agra Delhi highway at O (0,0). A small local road PQ
crosses both the highways at pints A and B such that OA=10 km and OB =12 km. Also, the villages of Barun
and Jeetu are on the smaller high way YY’. Barun’s village B is 12km from O and that of Jeetu is 15 km from
O

Now answer the following questions:

Q.20What are the coordinates of A? 1m
1. (10, 0) 2. (10, 12) 3. (0,10) 4. (0,15)
Q.21 What is the equation of line AB? 1m
1. 5x + 6y = 60 2. 6x + 5y = 60 3. x = 10 4. y = 12
Q.22What is the distance of AB from O (0, 0)? 1m
1. 60 km 2. 60/√61 km 3. √61 km 4. 60 km
Q.23What is the slope of line AB? 1m
1. 6/5 2. 5/6 3. -6/5 4. 10/12
Section B
Q.24 to Q.33 has 2-mark questions.
Q.24 Show that the points (1,4) and (0, -3) lies on the opposite sides of the line x + 3y + 7 = 0. 2m
Q.25 The base of an equilateral triangle with side 2a lies along the Y- axis such that the midpoint of the base
is at the origin. Find vertices of the triangle. 2m
| 𝑥| − 1
Q.26 Solve the inequality ≥ 0, xs 𝑅 𝑎𝑛𝑑 𝑥 G ± 2 2m
|𝑥|− 2
OR
Q.26 Solve the system of inequalities. 7 (2 – 3x) > 18 – 19x and 5 +3x < 5x +6 2m

Q.27 Solve √3 x2 - √2 x + 3√3 = 0 2m

Q.28 Let z1 and z2 be two complex numbers, such that 𝑧1 + i𝑧2 = 0 and arg (z1, z2) = 𝜋. Then find arg (z1). 2m
Q.29 Insert 6 arithmetic means between 3 and 24. 2m
Q.30 Find 12th term of a GP, whose 8th term is 192 and common ratio is 2. 2m
OR
Q.30 Insert three GMs between 1 and 256.
Q.31 Coefficient of variation of distributions are 50 and 60 and their arithmetic means are 30 and 25,
Respectively. Find the difference of their standard deviation. 2m
Q.32 The mean of 100 observations is 50 and their standard deviation is 5. Find the sum of all squares of all
the observations. 2m

Q.33 If x +iy = 𝑎+i , then prove that ay -1 = x. 2m

𝑎−i
OR
Q.33 Find the sum of n terms of the series 1.2 + 2.3+3.4+4.5+……. 2m
Section C
Q.34 to Q.40 has 3-mark questions.
Q.34 Mean and standard deviation of 100 observations were found to be 40 and 10, respectively. IF at the
timeof calculation, two observations were wrongly taken as 30 And 70 in place of n3 and 27
respectively, then find the correct standard deviation. 3m
Q.35 A line passes through the point (3, -2). Find the locus of the middle point of the portion of the line
intercepted between the axes. 3m
OR
Q.35 Find the equations of the lines, which cut-off intercepts on the axes whose sum and product are 1 and -6,
respectively. 3m
Q.36 The mean and standard deviation of 6 observations is 8 and 4, respectively. If each observation is
multiplied by 3, find the new mean and new standard deviation of the resulting observations. 3m
Q.37 Calculate the mean deviation from the median for the following data. 3m
Wages per day Number of workers
20-30 3
30-40 8
40-50 12
50-60 9
 60-70 8
Q.38 The marks obtained to 7 students are 8,9,11,13,14,15,21. Find the variance and standard deviation of
these marks. 3m
OR
Q.38 Find the standard deviation for the following data.
xi 3 8 13 18 23
fi 7 10 15 10 6
Q.39 Find all pairs of consecutive even positive integers, both of which are larger than 5, such that their sum
is less than 23. 3m
Q.40 Find the sum of the series 13 + 33 + 53+ …. + (2n – 1 )3. 3m
OR
Q.40 Let Sn denotes the sum of the first n terms of an AP. If S2n = 3 Sn, then find the ratio S3n : Sn.
Section D
Q.41 to Q.45 has 4-mark questions. Attempt any four questions from given five questions.
Q.41 Express 4m
(i) 5(cos2700 + i sin2700) in Cartesian form.
(ii) (sin 1350 – i cos 1350) in polar form.
1+𝑥
Q.42 Solve the following system of linear inequalities -2 - 𝑥 ≥ and 3 - x < 4(x – 3). 4m
4 3
Q.43 The Fibonacci sequence is defined by 1 = a1 = a2 and an = an- 1 + an -2, n > 2. Find 𝑎𝑛+1 for n=1...,5. 4m
𝑎𝑛
Q.44 In the ∆ ABC with vertices A (2,3), B (4, -1) and C (1,2), find the equation and length of altitude from
the vertex A. 4m
Q.45 The AM and SD if 100 items were recorded as 40 and 5.1, respectively. Later on, it was discovered that
one observation 40 was wrongly copied down as 50. Find the correct SD. 4m