In this question paper, it covers the important one question from the chapter

Matrices and Determinants
Algebra
Analytical Geometry
Trigonometry
Differential Calculus

Download Tamil Nadu 11th Standard Business Maths and Statistics 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

If y = log x then y₂ = ________.

(a)

\(\frac{1}{x}\)

(b)

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

(c)

\(-\frac{2}{x^2}\)

(d)

e²

\(\frac{d}{dx}(\frac{1}{x})\) is equal to ________.

(a)

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

(b)

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

(c)

log x

(d)

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

For what value of x, f(x) = \(\frac{x+2}{x-1}\) is not continuous?

(a)

-2

(b)

(c)

(d)

-1

The graph of f(x) = e^x is identical to that of ________.

(a)

f(x) = a^x, a > 1

(b)

f(x) = a^x, a < 1

(c)

f(x) = a^x, 0 < a < 1

(d)

y = ax +b, a \(\ne\) 0

The range of f(x) = |x|, for all \(x\in R\), is ________.

(a)

(0, \(\infty \))

(b)

(0, \(\infty \))

(c)

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

(d)

(1, \(\infty \))

Which one of the following functions has the property f (x) = \(f\left( \frac { 1 }{ x } \right) \), provided \(x \neq 0\)

(a)

\(f\left( x \right) =\frac { { x }^{ 2 }-1 }{ x } \)

(b)

\(f\left( x \right) =\frac { 1-{ x }^{ 2 } }{ x } \)

(c)

f(x) = x

(d)

\(f\left( x \right) =\frac { { x }^{ 2 }+1 }{ x } \)

The graph of y = 2x² is passing through _______.

(a)

(0,0)

(b)

(2,1)

(c)

(2,0)

(d)

(0,2)

The graph of the line y = 3 is _______.

(a)

Parallel to x-axis

(b)

Parallel to y-axis

(c)

Passing through the origin

(d)

Perpendicular to x-axis

If \(f\left( x \right) =\begin{cases} { x }^{ 2 }-4x\quad ifx\ge 2 \\ x+2\quad ifx<2 \end{cases}\) then f(0) is _______.

(a)

(b)

(c)

-1

(d)

10.

If f(x) = x² - x + 1, then f (x + 1) is _______.

(a)

x²

(b)

(c)

(d)

x² + x + 1

11.

The value of \(\frac{1}{cosec(-45^o)}\) is _______.

(a)

\(\frac{-1}{\sqrt2}\)

(b)

\(\frac{1}{\sqrt2}\)

(c)

\(\sqrt2\)

(d)

\(-\sqrt2\)

12.

If \(\alpha\) and \(\beta\) be between 0 and \(\frac{\pi}{2}\) and if \(\cos(\alpha+\beta)=\frac{12}{13}\) and \(\sin(\alpha-\beta)=\frac{3}{5}\) then \(\sin2\alpha\) is _____.

(a)

\(\frac{16}{15}\)

(b)

(c)

\(\frac{56}{65}\)

(d)

\(\frac{64}{65}\)

13.

The value of \(\frac{3 \tan 10^{\circ}-\tan ^3 10^{\circ}}{1-3 \tan ^2 10^{\circ}}\) is _______,

(a)

\(\frac{1}{\sqrt3}\)

(b)

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

(c)

\(\frac{\sqrt3}2\)

(d)

\(\frac{1}{\sqrt2}\)

14.

If \(\sin A=\frac{1}{2}\) then \(4\cos^3A-3\cos A\) is ________.

(a)

(b)

(c)

\(\frac{\sqrt3}{2}\)

(d)

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

15.

The value of \(\frac{2\tan30^o}{1+tan^230}\) is _____.

(a)

\(\frac12\)

(b)

\(\frac{1}{\sqrt3}\)

(c)

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

(d)

\(\sqrt3\)

16.

The value of 1 - 2sin²45^o is _______.

(a)

(b)

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

(c)

\(\frac14\)

(d)

17.

The value of sec A sin(270^o + A) is ______.

(a)

-1

(b)

cos² A

(c)

sec² A

(d)

18.

The value of \(\sin 28^o\cos 17^o+\cos 28^o\sin 17^o\) is _______.

(a)

\(\frac{1}{\sqrt2}\)

(b)

(c)

\(\frac{-1}{\sqrt2}\)

(d)

19.

The value of \(\sin(-420^o)\) is _______.

(a)

\(\frac{\sqrt3}{2}\)

(b)

\(-\frac{\sqrt3}{2}\)

(c)

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

(d)

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

20.

If \(\tan\theta=\frac{1}{\sqrt5}\) and \(\theta\) lies in the first quadrant, then \(\cos\theta\) is _______.

(a)

\(\frac{1}{\sqrt6}\)

(b)

\(\frac{-1}{\sqrt6}\)

(c)

\(\frac{\sqrt5}{\sqrt6}\)

(d)

\(\frac{-\sqrt5}{\sqrt6}\)

21.

The radian measure of 37^o30^' is ______.

(a)

\(\frac{5\pi}{24}\)

(b)

\(\frac{3\pi}{24}\)

(c)

\(\frac{7\pi}{24}\)

(d)

\(\frac{9\pi}{24}\)

22.

The distance between directrix and focus of a parabola y² = 4ax is _______.

(a)

(b)

(c)

(d)

23.

If the circle touches x axis, y axis and the line x = 6 then the length of the diameter of the circle is _______.

(a)

(b)

(c)

(d)

24.

Combined equation of co-ordinate axes is _______.

(a)

x²-y²= 0

(b)

x²+y²= 0

(c)

xy = c

(d)

xy = 0

25.

If the centre of the circle is (-a, -b) and radius is \(\sqrt{a^2-b^2}\), then the equation of circle is _______.

(a)

x²+y²+2ax+2by+2b²= 0

(b)

x²+y²+2ax +2by-2b²= 0

(c)

x² +y² - 2ax - 2by - 2b² = 0

(d)

x² + y - 2ax - 2by + 2b² = 0

26.

Length of the latus rectum of the parabola y² = - 25x is _______.

(a)

(b)

-5

(c)

(d)

-25

27.

The locus of the point P which moves such that P is always at equidistance from the line x + 2y+ 7 = 0 is _______.

(a)

x+2y+2 = 0

(b)

x - 2y + 1 = 0

(c)

2x - y + 2 = 0

(d)

3x + y + 1 = 0

28.

The locus of the point P which moves such that P is at equidistance from their coordinate axes is _______.

(a)

\(y={1\over x}\)

(b)

y = -x

(c)

y = x

(d)

\(y=-{1\over x}\)

29.

If the lines 2x - 3y - 5 = 0 and 3x - 4y - 7 = 0 are the diameters of a circle, then its centre is _______.

(a)

(-1, 1)

(b)

(1,1)

(c)

(1, -1 )

(d)

(-1, -1)

30.

Sum of the binomial coefficients is ________.

(a)

2ⁿ

(b)

n²

(c)

(d)

n + 17

31.

Sum of Binomial co-efficient in a particular expansion is 256, then number of terms in the expansion is ________.

(a)

(b)

(c)

(d)

32.

The value of (5C₀ + 5C₁) + (5C₁ + 5C₂) + (5C₂ + 5C₃) + (5C₃ + 5C₄) + (5C₄ + 5C₅ ) is ________.

(a)

2⁶-2

(b)

2⁵-1

(c)

2⁸

(d)

2⁷

33.

The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is _________.

(a)

(b)

(c)

(d)

34.

The number of 3 letter words that can be formed from the letters of the word number when the repetition is allowed are ________.

(a)

206

(b)

133

(c)

216

(d)

300

35.

If \(\frac { kx }{ (x+4)(2x-1) } =\frac { 4 }{ x+4 } +\frac { 1 }{ 2x-1 } \) then k is equal to _______.

(a)

(b)

(c)

(d)

36.

The middle term in the expansion of \({ \left( x+\frac { 1 }{ x } \right) }^{ 10 }\) is _______.

(a)

10C₄\(\left( \frac { 1 }{ x } \right) \)

(b)

10C₅

(c)

10C₆

(d)

10C₇x⁴

37.

If n is a positive integer, then the number of terms in the expansion (x + a)ⁿ is _______.

(a)

(b)

n + 1

(c)

n-1

(d)

38.

The greatest positive integer which divide n(n + 1) (n + 2) (n + 3) for n \(\in\) N is ________.

(a)

(b)

(c)

(d)

39.

If nP_r = 720 (nC_r), then r is equal to ______.

(a)

(b)

(c)

(d)

40.

The number of ways selecting 4 players out of 5 is _______.

(a)

(b)

(c)

(d)

41.

If nC₃ = nC₂, then the value of nC₄ is _______.

(a)

(b)

(c)

(d)

42.

If \(\begin{vmatrix} 4 & 3 \\ 3 & 1 \end{vmatrix}=-5\) then value of \(\begin{vmatrix} 20 & 15 \\ 15 & 5 \end{vmatrix}\) is ________.

(a)

-5

(b)

-125

(c)

-25

(d)

43.

If \(\triangle=\begin{vmatrix} {a}_{11} & {a}_{12} & {a}_{13} \\ {a}_{21} & {a}_{22} & {a}_{23} \\ {a}_{31} & {a}_{32} & {a}_{33} \end{vmatrix}\) and A_ij is cofactor of a_ij, then value of \(\triangle\) is given by ________.

(a)

a₁₁ A₃₁ + a₁₂ A₃₂ + a₁₃ A₃₃

(b)

a₁₁ A₁₁ + a₁₂A₂₁ + a₁₃ A₃₁

(c)

a₂₁ A₁₁ + a₂₂ A₁₂ + a₂₃ A₁₃

(d)

a₁₁ A₁₁ + a₂₁ A₂₁ + a₃₁ A₃₁

44.

If A = \(\begin{vmatrix}cos \theta & sin \theta \\ -sin \theta&cons\theta \end{vmatrix},\) then |2A| is equal to ________.

(a)

4 cos 2 \(\theta\)

(b)

(c)

(d)

45.

The value of \(\begin{vmatrix} x & x^2 & -yz & 1 \\ y & y^2 & -zx & 1 \\ z & z^2 & -xy &1 \end{vmatrix}\) is ________.

(a)

(b)

(c)

-1

(d)

-xyz

46.

If A and B are non-singular matrix then, which of the following is incorrect?

(a)

A² = I implies A^-1= A

(b)

I^-1 = I

(c)

If AX = B, then X = B^-1 A

(d)

If A is square matrix of order 3 then |adj A|= |A|²

47.

The inverse matrix of \(\begin{pmatrix} 3 & 1 \\ 5 & 2\end{pmatrix}\) is ________.

(a)

\(\begin{pmatrix} 2 & -1 \\-5 & 3 \end{pmatrix}\)

(b)

\(\begin{pmatrix} -2 & 5 \\1 & -3 \end{pmatrix}\)

(c)

\(\begin{pmatrix} 3 & -1 \\-5 & -3 \end{pmatrix}\)

(d)

\(\begin{pmatrix} -3 & 5 \\1 & -2 \end{pmatrix}\)

48.

If A = \(\begin{pmatrix} a & b \\ c & d \end{pmatrix}\)such that ad - bc \(\neq\) 0 then A^-1 is ________.

(a)

\({{1}\over{ad-bc}}\begin{pmatrix} d & b \\-c & a\end{pmatrix}\)

(b)

\({{1}\over{ad-bc}}\begin{pmatrix} d & b \\c & a\end{pmatrix}\)

(c)

\({{1}\over{ad-bc}}\begin{pmatrix} d & -b \\-c & a\end{pmatrix}\)

(d)

\({{1}\over{ad-bc}}\begin{pmatrix} d & -b \\c & a\end{pmatrix}\)

49.

adj (AB) is equal to ________.

(a)

adj A adj B

(b)

adj A^T adj B^T

(c)

adj B adj A

(d)

adj B^T adj A^T

50.

The value of x if \(\begin{vmatrix} 0 & 1 & 0 \\ x & 2 & x \\ 1 & 3 & x \end{vmatrix}=0\) is_________.

(a)

0, - 1

(b)

0, 1

(c)

- 1, 1

(d)

- 1, - 1

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Answers Key:

Multiple Choice Question

50 x 1 = 50

\(y_1=\frac{1}{x}, y_2=\frac{-1}{x^2}\)

(a)
\(-\frac{1}{x^2}\)

(b)
1

(a)
f(x) = a^x, a > 1

(b)
(0, \(\infty \))

\(f(x)=\frac{x^2+1}{x} \)
\(f\left(\frac{1}{x}\right)=\frac{\frac{1}{x^2}+1}{\frac{1}{x}}=\frac{1+x^2}{x^2} \times \frac{x}{1}=\frac{1+x^2}{x}=f(x) \)

(a)
(0,0)

(a)
Parallel to x-axis

f(0) = 0 + 2 = 2

10.

\(f(x+1) =(x+1)^2-(x+1)+1 \)
\(=x^2+2 x+1-x-1+1 \)
\(=x^2+x+1 \)

11.

\(\frac{-1}{\operatorname{cosec} 45^{\circ}}=\frac{-1}{\sqrt{2}}\)

12.

\(\cos (\alpha+\beta)=\frac{12}{13} \Rightarrow \sin (\alpha+\beta)=\frac{5}{13} \)
\(\sin (\alpha-\beta)=3 / 5 \Rightarrow \cos (\alpha-\beta)=4 / 5 \)
\(\sin 2 \alpha=\sin ((\alpha+\beta)+(\alpha-\beta)) \)
\(= \sin (\alpha+\beta) \cos (\alpha-\beta) +\cos (\alpha+\beta) \sin (\alpha-\beta) \)
\(= \frac{5}{13} \cdot \frac{4}{5}+\frac{3}{5} \cdot \frac{12}{13}=\frac{56}{65}\)

13.

\(\frac{3 \tan 10^{\circ}-\tan ^3 10^{\circ}}{1-3 \tan ^2 10^{\circ}} =\tan 3(10) =\tan 30^{\circ}=\frac{1}{\sqrt{3}} \)

14.

\(\sin A=\frac{1}{2} \Rightarrow A=30^{\circ} \)
\(4 \cos ^3 A-3 \cos \mathrm{A} =\cos 3 \mathrm{~A} \)
\(=\cos 3(30) \)
\(=\cos 90^{\circ} =0\)

15.

\(\frac{2 \tan 30^{\circ}}{1+\tan ^2 30^{\circ}} =\sin 2\left(30^{\circ}\right)=\sin 60^{\circ}=\frac{\sqrt{3}}{2} \)

16.

1 - 2sin²45^o= cos 2(45^o)
= cos 90^o = 0

17.

\(\sec A(-\cos A)=\frac{1}{\cos A}(-\cos A)=-1\)

18.

\(\sin (28+17)=\sin 45^{\circ}=\frac{1}{\sqrt{2}}\)

19.

\(\sin \left(-420^{\circ}\right) =-\sin 420^{\circ}=-\sin (360+60) =-\sin 60^{\circ}=\frac{-\sqrt{3}}{2} \)

20.

\(\sec \theta =\sqrt{1+\tan ^2 \theta}=\sqrt{1+\frac{1}{5}}=\sqrt{\frac{6}{5}} \)

21.

\(37^{\circ} 30^{\prime}=37 \frac{1}{2}^{\circ}=\frac{75}{2} \times \frac{\pi}{180}=\frac{5 \pi}{24}\)

22.

(b)
2a

23.

24.

Equation of x axis y = 0, equation of y axis x = 0
\(\therefore\) combined equation xy = 0

25.

\((x+a)^2+(y+b)^2=a^2-b^2\)
\(x^2+a^2+2 a x+y^2+b^2+2 b y=a^2-b^2\)

26.

4a = 5

27.

(parallel line)

28.

29.

30.

(a)
2ⁿ

31.

2ⁿ = 256 = 2⁸
n = 8
Number of terms = n + 1 = 9

32.

Since sum of all binomial coefficients is 2n
5C₀ + 5C₁ + 5C₂ + 5C₃ + 5C₄ + 5C₅+ (5C₁ + 5C₂ + 5C₃ + 5C₄)
= 2⁵ + (2⁵ - (5C₀ + 5C₅)
= 32 + 32 - (1 + 1)
= 64 - 2 = 2⁶ - 2

33.

The number of parallelograms = 4C₂ x 3C₂

34.

The number of ways = 6 x 6 x 6 = 216

35.

Equality coefficient of x in the numerator
kx = 4 (2n) + 1 (x)
kx = 9x

36.

\(\text { M.T } =t_{\frac{n}{2}}+1=t_{5+1}=t_6 \quad r=5 \)
\(t_6 =10 C_5\left(x^5\right)\left(\frac{1}{x^5}\right)=10 C_5 \)

37.

(b)
n + 1

38.

Since if n = 1 then (1) (2) (3) (4) = 24 is divisible by = 24

39.

\(n P_r =720(\mathrm{nCr}) \)
\(\frac{n !}{(n-r) !} =720\left(\frac{n !}{r !(n-r) !}\right) \)
\(r ! =720 \)
\(r ! =6 ! \)
r = 6

40.

No. of ways = 5C₄ = 5C₁ = 5

41.

x + y = n
3 + 2 = 5 = n
nC₄ = 5C₄ = 5C₁ = 5

42.

\(\left|\begin{array}{cc} 20 & 15 \\ 15 & 5 \end{array}\right|=5 \times 5\left|\begin{array}{ll} 4 & 3 \\ 3 & 1 \end{array}\right|\)
\(=5 \times 5 \times-5\)
\(=-125\)

43.

(Corresponding co-factor)

44.

\(|A|=\cos ^2 \theta+\sin ^2 \theta=1\)
\(|2 A|=2^2(1)=4\)

45.

\(\left|\begin{array}{ccc} x & x^2 & 1 \\ y & y^2 & 1 \\ z & z^2 & 1 \end{array}\right|+\left|\begin{array}{ccc} x & -y z & 1 \\ y & -z x & 1 \\ z & -x y & 1 \end{array}\right|\)
Multiply R₁, R₂, R₃, of second determinant by x, y, z respectively
\(\left|\begin{array}{ccc} x & x^2 & 1 \\ y & y^2 & 1 \\ z & z^2 & 1 \end{array}\right|-\frac{1}{x y z}\left|\begin{array}{ccc} x^2 & x y z & x \\ y^2 & x y z & y \\ z^2 & x y z & z \end{array}\right|\)
\(=\left|\begin{array}{lll} x & x^2 & 1 \\ y & y^2 & 1 \\ z & z^2 & 1 \end{array}\right|-\frac{x y z}{x y z}\left|\begin{array}{ccc} x^2 & 1 & x \\ y^2 & 1 & y \\ z^2 & 1 & z \end{array}\right|\)
\(=\left|\begin{array}{lll} x & x^2 & 1 \\ y & y^2 & 1 \\ z & z^2 & 1 \end{array}\right|-\left|\begin{array}{lll} x & x^2 & 1 \\ y & y^2 & 1 \\ z & z^2 & 1 \end{array}\right|=0\)

46.

(Since \(\mathrm{X}=\mathrm{A}^{-1} \mathrm{~B}\) is the correct answer)

47.

\(|A|=6-5=1\)
\(A^{-1}=\left(\begin{array}{cc} 2 & -1 \\ -5 & 3 \end{array}\right)\)

48.

\(|A|=\frac{1}{a d-b c} ; \quad A^{-1}=\frac{1}{a d-b c}\left(\begin{array}{cc} d & -b \\ -c & a \end{array}\right)\)

49.

50.

\(\left|\begin{array}{lll} 0 & 1 & 0 \\ x & 2 & x \\ 1 & 3 & x \end{array}\right|=0 \Rightarrow-1\left[x^2-x\right]=0\)
\(\Rightarrow x(x-1)=0 \Rightarrow x=0,1\)