Based on the current academic year, the question paper is prepared. In this question paper, it covers some of the important one mark questions from the chapter

Sets, Relations and Functions
Basic Algebra
Trigonometry
Combinatorics and Mathematical Induction
Binomial Theorem, Sequences And Series
Two Dimensional Analytical Geometry

Download Tamil Nadu 11th Standard Maths question papers, model tests, one-mark questions, important questions, and public exam papers in PDF format. Free study materials and answer keys for TN State Board students.

Questions:

Multiple Choice Question

50 x 1 = 50

The locus of a point which is collinear with the points (a, 0) and (0, b) is ______________

(a)

x + y = 1

(b)

\(\frac{x}{a}+\frac{y}{b}=1\)

(c)

x + y = ab

(d)

\(\frac{x}{a}-\frac{y}{b}=1\)

The distance between the parallel lines 3x - 4y + 9 = 0 and 6x - 8y -15 = 0 is ______________

(a)

\(\frac{-33}{10}\)

(b)

\(\frac{10}{33}\)

(c)

\(\frac{33}{10}\)

(d)

\(\frac{33}{20}\)

The value \(\lambda\) for which the equation 12x²- 10xy + 2y²+11x-5y+\(\lambda\) = 0 represent a pair of straight lines is ______________

(a)

\(\lambda\) = 1

(b)

\(\lambda\) = 2

(c)

\(\lambda\) = 3

(d)

\(\lambda\) = 0

Number of solutions of the equation tan x + sec x = 2 cos x lying in the interval [0, 2π] is _______________

(a)

(b)

(c)

(d)

Pair of lines perpendicular to the lines represented by ax²+ 2hxy + by²= 0 and through origin is ______________

(a)

ax²+ 2hxy + by²= 0

(b)

bx²+ 2hxy + ay²= 0

(c)

bx²- 2hxy + ay²= 0

(d)

bx²- 2hxy + ay²= 0

Which one of the following is not a singleton set?

(a)

A = {x : 3x - 5 = 0, x ∈ Q}

(b)

B = {| x | = 1 / x ∈ Z}

(c)

{x : x³ - 1 = 0, x ∈ R}

(d)

{x : 30x = 60, x ∈ N}

If \(f(x)={1-x\over 1+x},(x\neq0)\) then f^-1(x) =

(a)

f(x)

(b)

\(1\over f(x)\)

(c)

-f(x)

(d)

-\(1\over f(x)\)

The equation of a line which makes an angle of 135° with positive direction of x-axis and passes through the point (1, 1) is ______________

(a)

x+y=2

(b)

x-y=0

(c)

\(2\sqrt {2x}-\sqrt {2y}=0\)

(d)

x-3y=0

If ⁿP_t = 720 nCr, then the value of r = _________

(a)

(b)

(c)

(d)

10.

The number of squares which can form on a chess a board is _________

(a)

(b)

160

(c)

224

(d)

204

11.

The value of n for which \(\frac{a^{n+1}+b^{n+1}}{a^n+b^n}\) is the arithmetic mean of a and b is ______________

(a)

(b)

(c)

(d)

12.

The number of real solutions of the equation |x²| - 3|x| + 2 = 0 is ___________

(a)

(b)

(c)

(d)

13.

The slope of the line joining A and B where A is (-1, 2) and B is the point of intersection of the lines 2x + 3y = 5 and 3x + 4y = 7 is ______________

(a)

-2

(b)

(c)

\(\frac{1}{2}\)

(d)

-\(\frac{1}{2}\)

14.

The value of \(1-\frac{1}{2}(\frac{3}{4})+\frac{1}{3}(\frac{3}{4})^2-\frac{1}{4}(\frac{3}{4})^3+...\)is ______________

(a)

\(\frac{3}{4}log(\frac{7}{4})\)

(b)

\(\frac{4}{3}log(\frac{7}{4})\)

(c)

\(\frac{1}{3}log(\frac{7}{4})\)

(d)

\(\frac{4}{3}log(\frac{4}{7})\)

15.

With usual notation C₀ + C₂ + C₄+ ... is ______________

(a)

2^n-1

(b)

2ⁿ

(c)

2ⁿ⁺¹

(d)

2ⁿ⁺²

16.

In \(\triangle\)ABC, \(\hat{C}\) = 90° then a cos A + b cos B is _______________

(a)

2R sin B

(b)

2 sin B

(c)

(d)

2a sin B

17.

The quadratic equation whose roots are tan 75° and cot 75° is _______________

(a)

x²+4x+ 1 = 0

(b)

4x²-x+ 1 = 0

(c)

4x²+ 4x - 1 = 0

(d)

x² - 4x + 1 = 0

18.

If ⁿP_r=k x ^n-1P_r-1 what is k:

(a)

(b)

(c)

n+1

(d)

r+1

19.

\(\sqrt [ 4 ]{ { \left( -2 \right) }^{ 4 } } \times { \left( -1000 \right) }^{ \frac { 1 }{ 3 } }\) is ___________

(a)

(b)

-20

(c)

2^-10

(d)

100

20.

Find the other root of x²- 4x + 1 = 0 given that 2 +\(\sqrt{3}\) is a root ___________

(a)

\(\sqrt{3}\) + 2

(b)

-\(\sqrt{3}\) -\(\sqrt{2}\)

(c)

2 - \(\sqrt{3}\)

(d)

\(\sqrt{3}\) - 2

21.

The coefficient of x⁸y¹² in the expansion of (2x + 3y)²⁰ is

(a)

(b)

2⁸3¹²

(c)

2⁸3¹² + 2¹²3⁸

(d)

²⁰C₈ 2⁸ 3¹²

22.

If the lines x + q = 0, y - 2 = 0 and 3x + 2y + 5 = 0 are concurrent, then the value of q will be ______________

(a)

(b)

(c)

(d)

23.

Distance between the lines 5x + 3y - 7 = 0 and 15x + 9y + 14 = 0 is ______________

(a)

\(\frac{35}{\sqrt{34}}\)

(b)

\(\frac{1}{3\sqrt{34}}\)

(c)

\(\frac{35}{2\sqrt{34}}\)

(d)

\(\frac{35}{3\sqrt{34}}\)

24.

If the two straight lines x + (2k -7)y + 3 = 0 and 3kx + 9y - 5 = 0 are perpendicular then the value of k is

(a)

k = 3

(b)

\(k=\frac13\)

(c)

\(k=\frac23\)

(d)

\(k=\frac32\)

25.

The image of the point (2, 3) in the line y = -x is

(a)

(-3, -2)

(b)

(-3, 2)

(c)

(-2, -3)

(d)

(3, 2)

26.

If \(\Sigma n=210\) then \(\Sigma { n }^{ 2 }\)= ______________

(a)

2870

(b)

2160

(c)

2970

(d)

none of these

27.

The product of r consecutive positive integers is divisible by _________

(a)

(b)

r!+1

(c)

(r+1)

(d)

none of these

28.

Which of the following point lie on the locus of 3x²+ 3y²- 8x - 12y + 17 = 0

(a)

(0, 0)

(b)

(-2, 3)

(c)

(1, 2)

(d)

(0, -1)

29.

The equation of the locus of the point whose distance from y-axis is half the distance from origin is

(a)

x²+ 3y²= 0

(b)

x²- 3y²= 0

(c)

3x²+ y²= 0

(d)

3x²- y²= 0

30.

If P_r stands for ^r P_r then the sum of the series 1+ P₁ + 2P₂ + 3P₃ +...+ nP_n is

(a)

P_n+1

(b)

P_n+1-1

(c)

P_n-1+1

(d)

⁽ⁿ⁺¹⁾P_(n-1)

31.

The number of ways of choosing 5 cards out of a deck of 52 cards which include at least one king is

(a)

⁵²C₅

(b)

⁴⁸C₅

(c)

⁵²C₅ + ⁴⁸C₅

(d)

⁵²C₅ - ⁴⁸C₅

32.

The n^th term of the sequence \(\frac { 1 }{ 2 } ,\frac { 3 }{ 4 } ,\frac { 7 }{ 8 } ,\frac { 15 }{ 6 } \),......is

(a)

2ⁿ- n - 1

(b)

1 - 2^-ⁿ

(c)

2^-n+ n - 1

(d)

2^n-1

33.

The number of ways in which a host lady invite 8 people for a party of 8 out of 12 people of whom two do not want to attend the party together is

(a)

2 \(\times\) ¹¹ C₇+¹⁰C₈

(b)

¹¹C₇+¹⁰C₈

(c)

¹²C₈-¹⁰C₆

(d)

¹⁰C₆+2!

34.

The number of 5 digit numbers all digits of which are odd is

(a)

(b)

5⁵

(c)

5⁶

(d)

625

35.

In an examination there are three multiple choice questions and each question has 5 choices. Number of ways in which a student can fail to get all answer correct is

(a)

125

(b)

124

(c)

(d)

36.

If S_n denotes the sum of n terms of an AP whose common difference is d, the value of S_n- 2S_n-1+ S_n-2 is

(a)

(b)

(c)

(d)

d²

37.

(x²-2x+2)(x²+2x+2) are the factors of the polynomial ___________

(a)

(x²-2x)²

(b)

x⁴-4

(c)

x⁴+4

(d)

(x²-2x+2)²

38.

\((\sqrt { 5 } -2)(\sqrt { 5 } +2)\) is equal to ___________

(a)

(b)

(c)

(d)

39.

If cos x = \(\frac { -1 }{ 2 } \) \(0 < x < 2\pi\) and, then the solutions are _______________

(a)

x = \(\frac { \pi }{ 3 } ,\frac { 4\pi }{ 3 } \)

(b)

x = \(\frac { 2\pi }{ 3 } ,\frac { 4\pi }{ 3 } \)

(c)

x = \(\frac { 2\pi }{ 3 } ,\frac { 7\pi }{ 6 } \)

(d)

x = \(\frac { 2\pi }{ 3 } ,\frac { 5\pi }{ 3 } \)

40.

The value of sin²\(\frac { 5\pi }{ 12 } -sin^{ 2 }\frac { \pi }{ 12 } \) is ___________

(a)

\(\frac { 1 }{ 2 } \)

(b)

\(\frac { \sqrt { 3 } }{ 2 } \)

(c)

(d)

41.

The number of solution of x²+ |x - 1| = 1 is

(a)

(b)

(c)

(d)

42.

If |x+2| \(\le\) 9, then x belongs to

(a)

\((-\infty ,-7)\)

(b)

[-11, 7]

(c)

\((-\infty ,-7)\cup (11,\infty)\)

(d)

(-11, 7)

43.

A wheel is spinning at 2 radians/second. How many seconds will it take to make 10 complete rotations?

(a)

10\(\pi \) seconds

(b)

20\(\pi \) seconds

(c)

5\(\pi \) seconds

(d)

15\(\pi \) seconds

44.

If cos pፀ + cos qፀ = 0 and if p ≠ q, then ፀ is equal to (n is any integer)

(a)

\(\frac { \pi (3n+1) }{ p-q } \)

(b)

\(\frac { \pi (2n+1) }{ p\pm q } \)

(c)

\(\frac { \pi (n\pm 1) }{ p\pm q } \)

(d)

\(\frac { \pi (n+2) }{ p+q } \)

45.

The maximum value of 4sin²x + 3 cos²x + \(sin\frac { x }{ 2 } +cos\frac { x }{ 2 } \) is

(a)

\(4 + \sqrt{2}\)

(b)

\(3+ \sqrt{2}\)

(c)

(d)

46.

Let R be the universal relation on a set X with more than one element. Then R is

(a)

not reflexive

(b)

not symmetric

(c)

transitive

(d)

none of the above

47.

Let f : R➝R be given by f(x) = x + \(\sqrt { { x }^{ 2 } } \) is __________

(a)

injective

(b)

Surjective

(c)

bijective

(d)

none of these

48.

Let R be a relation on the set N given by R = {(a,b) : a = b - 2, b > 6}. Then ____________

(a)

(2,4)∈R

(b)

(3,8)∈R

(c)

(6,8)∈R

(d)

(8,7)∈R

49.

The function f:R➝R is defined by f(x)=\(\frac { \left( { x }^{ 2 }+cosx \right) \left( 1+{ x }^{ 4 } \right) }{ \left( x-sinx \right) \left( 2x-{ x }^{ 3 } \right) } +{ e }^{ -\left| x \right| }\) is

(a)

an odd function

(b)

neither an odd function nor an even function

(c)

an even function

(d)

both odd function and even function.

50.

The number of constant functions from a set containing m elements to a set containing n elements is

(a)

(b)

(c)

(d)

m+n

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Answers Key:

Multiple Choice Question

50 x 1 = 50

(b)
\(\frac{x}{a}+\frac{y}{b}=1\)

(b)
\(\lambda\) = 2

(b)
B = {| x | = 1 / x ∈ Z}

(a)
f(x)

(a)
x+y=2

(a)
6

10.

(d)
204

11.

(d)
0

12.

(d)
4

13.

(d)
-\(\frac{1}{2}\)

14.

(b)
\(\frac{4}{3}log(\frac{7}{4})\)

15.

(a)
2^n-1

16.

(d)
2a sin B

17.

(d)
x² - 4x + 1 = 0

18.

(b)
n

19.

(b)
-20

20.

21.

\((2 x+3 y)^{20} \text { the term containing } x^{8} y^{12} \text { is }\)
\({ }^{20} C_{12}(2 x)^{20-12}(3 y)^{12}={ }^{20} C_{12} 2^{8} \cdot 3^{12} \cdot x^{8} y^{12}\)
\(\left(\because{ }^{20} \mathrm{C}_{12}={ }^{20} \mathrm{C}_{8}\right)\)
\(\text { Coefficient of } x^{8} y^{12} \text { is }{ }^{20} \mathrm{C}_{8} 2^{8} 3^{12}\)

22.

23.

24.

\(\text { Slope of first line }=\frac{-1}{(2 k-7)}\)
\(\text { Slope of second line }=\frac{-3 k}{9}\)
\(\text { They are perpendicular } \mathrm{m}_{1} \mathrm{~m}_{2}=-1\)
\(\frac{3 k}{9(2 k-7)} =-1 \)
\(k =-3(2 k-7) \)
\(k =-6 k+21 \)
\(7 k =21 \)
\(k=3 \)

25.

The required point is (-3, -2)

26.

(a)
2870

27.

(a)
r!

28.

\((1,2) \text { lies on } 3 x^{2}+3 y^{2}-8 x-12 y+17=0\)
\(\text { Because, } 3(1)^{2}+3(2)^{2}-8(1)-12(2)+17\)
\(=3+12-8-24+17=0\)

29.

Let the point be (x, y)
Its distance from origin is \(\sqrt{x^{2}+y^{2}}\)
Given \(x =\frac{1}{2} \sqrt{x^{2}+y^{2}} \)
\(\Rightarrow 2 x =\sqrt{x^{2}+y^{2}} \)
\(4 x^{2} =x^{2}+y^{2} \)
\(3 x^{2}-y^{2}=0 \) is the required equation of the locus

30.

\(1+1 \mid 1+2\lfloor 2+3\lfloor 3+\ldots \ldots . n\lfloor n \quad=\lfloor n+1\)
\(\text { Let } \mathrm{n}=1, \quad \text { L.H.S }=1+1=2\)
\(\text { R.H.S }=\lfloor 2=2\)
It is true for n = 1, In fact it is true for n = 0 also let us assume that it is true for n=k
\(1+1 \mid 1+2\lfloor 2+3\lfloor 3+\ldots \ldots . n\lfloor n=\lfloor k+1\)
\(1+1 \mid 1+2\lfloor 2+3\lfloor 3+\ldots \ldots k \mid k+(k+1)\lfloor k+1\)
\(=\lfloor k+1+(k+1)\lfloor k+1=\lfloor k+1[1+k+1]\)
\(\lfloor k+1 (k+ 2)\)
\(\lfloor k+2\)
It is true for (k + 1)
Also by mathematical induction, it is true for all value of \(n \geq 0, n \in Z\)

31.

\({ }^{52} \mathrm{C}_{5} \text { includes all possibilities (zero king, }1 \text { king, } 2 \text { kings, } 3 \text { kings, } 4 \text { kings }){ }^{48} C_{5} \text { has no kings}\)
\(\text { Réquired possibilities }{ }^{52} \mathrm{C}_{5}-{ }^{48} \mathrm{C}_{5}\)

32.

\(n^{\text {th }} \text { term }=1-\frac{1}{2^{n}}=1-2^{-n}\)

33.

Number of ways of selecting 8 people from 12 in ¹²C₈ ways.
Let A and B both attend the party
Out of 10 remaining people 8 can attend in ¹⁰C₆ ways.
.'. Number of ways in which two of them do not attend together = ¹²C₈ - ¹⁰C₆

34.

(b)
5⁵

35.

No. of ways of answering = 5³ = 125
Correct answer - 1
.'. Number of incorrect answer = 125 - 1 = 124

36.

\(\mathrm{S}_{\mathrm{n}} =\frac{\mathrm{n}}{2}[2 a+(\mathrm{n}-1) \mathrm{d}] \)
\(\mathrm{S}_{\mathrm{n}-1} =\frac{\mathrm{n}-1}{2}[2 a+(\mathrm{n}-2) \mathrm{d}] \)
\(\mathrm{S}_{\mathrm{n}-2} =\frac{\mathrm{n}-2}{2}[2 a+(\mathrm{n}-3) \mathrm{d}] \)
\(\mathrm{S}_{\mathrm{n}}-2 \mathrm{~S}_{\mathrm{n}-1}+\mathrm{S}_{\mathrm{n}-2} =2 a\left[\frac{\mathrm{n}-2(\mathrm{n}-1)}{2}+\frac{(\mathrm{n}-2)}{2}\right]+\frac{\mathrm{d}}{2}[\mathrm{n}(\mathrm{n}-1)-2(\mathrm{n}-1)(\mathrm{n}-2)+(\mathrm{n}-2)(\mathrm{n}-3)] \)
\(=2 a\left[\frac{\mathrm{n}-2 \mathrm{n}+2+\mathrm{n}-2}{2}\right]+\frac{\mathrm{d}}{2}\left[\mathrm{n}^{2}-\mathrm{n}-2 \mathrm{n}^{2}+6 \mathrm{n}-4+\mathrm{n}^{2}-5 \mathrm{n}+6\right] \)
\(= 0+\frac{\mathrm{d}}{2}(2)=\mathrm{d} \)

37.

38.

(a)
1

39.

(b)
x = \(\frac { 2\pi }{ 3 } ,\frac { 4\pi }{ 3 } \)

40.

(b)
\(\frac { \sqrt { 3 } }{ 2 } \)

41.

\(x^{2}+|x-1| =1\)
\(|x-1| =1-x^{2} \)
\(1-x^{2} =x-1 \text { (or) } 1-x^{2} =-x+1 \)
\(x^{2}+x-2 =0 \ x^{2}-x =0 \)
\((x+2)(x-1) =0 \ x(x-1) =0 \)
\(x =-2 \text { (or) } 1 \ x=0 ; x =1 \)
The roots are -2, 0, 1. Since -2 does not satisfy. The roots are 0 and 1.
.'. Number of solution is 2.

42.

\(|x+2| \leq 9 \)
\( \Rightarrow-9 \leq x+2 \leq 9 \)
\( \Rightarrow-11 \leq x \leq 7 \)
\(x \text { belongs to }[-11,7]\)

43.

In one second it rotates = 2 radians.
For 2 radians it takes 1 second.
\(\text { For } 2 \pi \text { ( } 1 \text { revolution) it will take } \frac{2 \pi}{2}=\pi \text { second. }\)
\(\therefore \text { For } 10 \text { revolutions it takes } 10 \pi \text { seconds. }\)

44.

\(\cos p \theta+\cos q \theta=0 \)
\(2 \cos \left(\frac{p+q}{2}\right) \theta \cdot \cos \left(\frac{p-q}{2}\right) \theta=0 \)
\(\Rightarrow 2 \cos \left(\frac{p+q}{2}\right) \theta=0 \)
\(\cos \left(\frac{\mathrm{p}-\mathrm{q}}{2}\right) \theta=0\)
\(\text { Principal angle is } \pi / 2\)
\(\therefore\left(\frac{p+q}{2}\right) \theta =n \pi \pm \pi / 2 \)
\(\Rightarrow(p+q) \cdot \theta =2 n \pi \pm \pi \)
\(\theta =\frac{\pi(2 n \pm 1)}{p+q} \)
\(\text { Similarly, } \theta=\frac{\pi(2 n \pm 1)}{p-q}\)

45.

\(4 \sin ^{2} x+3 \cos ^{2} x+\sin \frac{x}{2}+\cos \frac{x}{2} \)
\(=3\left(\sin ^{2} x+\cos ^{2} x\right)+\sin ^{2} x+\sin \frac{x}{2}+\cos \frac{x}{2} \)
\(=3+\sin ^{2} x+\sin \frac{x}{2}+\cos \frac{x}{2} \)
\(\text { Maximum of } \sin x=1\)
\(\text { Maximum value of } \sin ^{2} x=1\)
\(\text { Maximum value of } \sin \frac{x}{2} \text { occurs where } x=45^{\circ}\)
\(\text { Maximum value is } 3+1+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}}=4+\frac{2}{\sqrt{2}}=4+\sqrt{2}\)

46.

Let X = (a,b,c)
Then R = Universal relation
= {(a, a), (a, b), (a, c), (b, a), (b, b), (b, c), (c, a), (c, b), (c, c)}.
It is transitive

47.

(d)
none of these

48.

49.

\(f(x) =\frac{\left(x^{2}+\cos x\right)\left(1+x^{4}\right)}{(x-\sin x)\left(2 x-x^{3}\right)}+e^{-|x|} \)
\(f(-x) =\frac{\left[(-x)^{2}+\cos (-x)\right]\left[1+(-x)^{4}\right]}{[-x-\sin (-x)]\left[-2 x-\left(-x^{3}\right)\right]}+e^{+x \mid} \)
\(=\frac{\left(x^{2}+\cos x\right)\left(1+x^{4}\right)}{(x-\sin x)\left(2 x-x^{3}\right)}+e^{-|x|} \)
\(=f(x) \)
Hence f(x) is an even function

50.