11th Standard Syllabus & Materials
11th Standard
TN 11th Tamil இயற்கை வேளாண்மை,சுற்றுச்சூழல் -செய்யுள் - மனோன்மணீயம் Important Questions And Answers Study Material - QB365 Set A
NEW11th Standard
TN 11th Tamil என்னுயிர் என்பேன் -துணைப்பாடம் - இசைத்தமிழர் இருவர் Important Questions And Answers Study Material - QB365 Set A
NEW11th Standard
TN 11th Tamil மொழி கலை -செய்யுள் - ஒவ்வொரு புல்லையும் Important Questions And Answers Study Material - QB365 Set A
NEW11th Standard
TN 11th Tamil பீடு பெற நில் - இலக்கணம் - பகுபத உறுப்புகள் Important Questions And Answers Study Material - QB365 Set A
NEW11th Standard
TN 11th Tamil பீடு பெற நில் - துணைப்பாடம் - வாடிவாசல் Important Questions And Answers Study Material - QB365 Set A
NEW11th Standard
TN 11th Tamil பீடு பெற நில் - செய்யுள் - குறுந்தொகை Important Questions And Answers Study Material - QB365 Set A
Published on: 29/09/2018
Important 1mark -
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 + Answers key
Take MCQ Maths Test1.
In a certain college 4% of the boys and 1% of the girls are taller than 1.8 meter. Further 60% of the students are girls. If a student is selected at random and is taller than 1.8 meters, then the probability that the student is a girl is
\({2\over 11}\)
\({3\over 11}\)
\({5\over 11}\)
\({7\over 11}\)
2.
If X and Y be two events such that P(X/Y) = \({1\over2},P(Y/X)={1\over3}\) and \(P(X\cap Y)={1\over6}\), then P(X\(\cup\)Y) is
\({1\over3}\)
\({2\over5}\)
\({1\over6}\)
\({2\over3}\)
3.
Let A and B be two events such that \(P(\overline{A\cup B})={1\over6}, P(A\cap B)={1\over4}\) and \({P(\overline{A})}={1\over4}\). Then the events A and B are
Equally likely but not independent
Independent but not equally likely
Independent and equally likely
Mutually inclusive and dependent
4.
The function \(f(x)= \begin{cases}\frac{x^{2}-1}{x^{3}+1} & x \neq-1 \\ P & x=-1\end{cases}\)is not defined for x = −1. The value of f(−1) so that the function extended by this value is continuous is
\({2\over3}\)
-\({2\over3}\)
1
0
5.
\(lim_{\alpha \rightarrow {\pi/4}}{sin \alpha -cos \alpha \over \alpha -{\pi\over 4}}\) is
\(\sqrt{2}\)
\(1\over \sqrt{2}\)
1
2
6.
If f(x) = x(-1)\(\left\lfloor 1\over x \right\rfloor \), \(x\le0\), then the value of \(lim_{x\rightarrow 0}f(x)\) is equal to
-1
0
2
4
7.
\(\underset { x\rightarrow \infty }{ lim } \left( \cfrac { { x }^{ 2 }+5x+3 }{ { x }^{ 2 }+x+3 } \right) ^{ x }\)is
e4
e2
e3
1
8.
Area of triangle ABC is _______________
\(\frac{1}{2}\)ab cos C
\(\frac{1}{2}\)ab sin C
\(\frac{1}{2}\)ab cos B
\(\frac{1}{2}\)bc sin B
9.
If in a triangle ABC, ∠B = 60°, then _______________
(a-b)2 = c2- ab
(b-c)2 = a2- bc
(c-a)2 = b2- ac
a2 + b2 = c2
10.
The numerical value of tan-11 + tan-12 + tan-13 = _______________
\(\pi\)
\(\frac{\pi}{2}\)
0
\(\frac{\pi}{4}\)
11.
If cos θ + \(\sqrt{3}\) sin θ = 2 and θ∈[0, 2π] then θ is _______________
\(\frac{\pi}{3}\)
\(\frac{5\pi}{3}\)
\(\frac{2\pi}{3}\)
\(\frac{4\pi}{3}\)
12.
The value of tan 1° tan 2° tan 3°...tan 89° is ____________
\(\infty\)
0
1
\(\sqrt{3}\)
13.
(sec A + tan A-1) (sec A - tan A+1)-2 tan A = _______________
0
1
2
2 tan A
14.
The general solution of cosec\(\theta\) = -2 is _______________
\(2n\pi +(-1)^n({\pi\over 6})\)
\(n\pi +(-1)^n({-\pi\over 6})\)
\(2n\pi \pm({\pi\over 6})\)
\(-{\pi\over 6}+n\pi\)
15.
The quadratic equation whose roots are tan 75° and cot 75° is _______________
x2+4x+ 1 = 0
4x2-x+ 1 = 0
4x2+ 4x - 1 = 0
x2 - 4x + 1 = 0
16.
If tan A = \(\frac { a }{ a+1 } \) and B = \(\frac { 1 }{ 2a+1 } \) then the value of A + B is ___________
0
\(\frac { \pi }{ 2 } \)
\(\frac { \pi }{ 3 } \)
\(\frac { \pi }{ 4 } \)
17.
The angle between the minute and hour hands of a clock at 8.30 is ___________
800
750
600
1050
18.
\(\frac { cos6x+6cos4x+15cos2x+10 }{ cos5x+5cos3x+10cosx } \) is equal to
cos 2x
cos x
cos 3x
2 cos x
19.
cos 2ፀ cos 2ф + sin2(ፀ - ф) - sin2(ፀ + ф) is equal to
sin2(ፀ+\(\phi \))
cos2(ፀ+\(\phi \))
sin2(ፀ-\(\phi \))
cos2(ፀ-\(\phi \))
20.
\(\frac { 1 }{ cos{ 80 }^{ 0 } } -\frac { \sqrt { 3 } }{ sin{ 80 }^{ 0 } } \)=
\(\sqrt{2}\)
\(\sqrt{3}\)
2
4
1.
\(P\left(A_{1}\right)=0.6, \quad P\left(A_{2}\right)=0.4\)
\(A_{1}=\text { Event of selecting a girl }\)
\(\mathrm{B}=\text { Event of student taller than } 1.8 \mathrm{~m}\)
\(A_{2}=\text { Event of selecting a boy }\)
\(P\left(B / A_{1}\right)=\frac{1}{100}, P\left(B / A_{2}\right)=\frac{4}{100}\)
To find \(=\frac{P\left(A_{1}\right) \cdot P\left(B / A_{1}\right)}{P\left(A_{1}\right) \cdot P\left(B / A_{1}\right)+P\left(A_{2}\right) \cdot P\left(B / A_{2}\right)} \)
\(=\frac{0.6 \times \frac{1}{100}}{0.6 \times \frac{1}{100}+0.4 \times \frac{4}{100}} \)
\(=\frac{6}{\frac{6}{1000}+\frac{16}{1000}} \)
\(=\frac{6}{22}=\frac{3}{11} \)
2.
\(P(X / Y)=\frac{1}{2} \Rightarrow \frac{P(X \cap Y)}{P(Y)}=\frac{1}{2} \)
\(P(Y / X)=\frac{1}{3} \Rightarrow \frac{P(X \cap Y)}{P(X)}=\frac{1}{3} \)
\(\text {But } P(X \cap Y)=\frac{1}{6} \Rightarrow \frac{\frac{1}{6}}{P(Y)}=\frac{1}{2}\)
\(P(Y)=\frac{\frac{1}{6}}{\frac{1}{2}}=\frac{1}{3}\)
\(\text {and } P(X)=\frac{\frac{1}{6}}{\frac{1}{3}}=\frac{1}{2}\)
\(P(X \cup Y)=P(X)+P(Y)-P(X \cap Y)\)
\(=\frac{1}{2}+\frac{1}{3}-\frac{1}{6}=\frac{3+2-1}{6} =\frac{2}{3} \)
3.
\(P(\bar{A})=\frac{1}{4}, P(A) =\frac{3}{4}, P(A \cap B)=\frac{1}{4} \)
\(P(A \cup B) =\frac{3}{4}+P(B)-\frac{1}{4} \)
\(=\frac{1}{2}+P(B) \)
\(\frac{5}{6} =\frac{1}{2}+P(B) \)
\(P(B) =\frac{5}{6}-\frac{1}{2}=\frac{2}{6}=\frac{1}{3} \)
\(P(\bar{A})=\frac{1}{4}, P(A)=\frac{3}{4}, P(A \cap B)=\frac{1}{4} \)
\(P(A \cap B)=P(A) \cdot P(B)=\frac{3}{4} \times \frac{1}{3}=\frac{1}{4}=P(\text { Any }) \)
A and B are independent but not equally likely.
4.
\(f(-1) =\lim _{x \rightarrow-1} f(x) \)
\(=\lim _{x \rightarrow-1} \frac{x^{2}-1}{x^{3}+1} \)
\(=\lim _{x \rightarrow-1} \frac{x^{2}-(-1)^{2}}{x^{3}-(-1)^{3}}=\frac{2(-1)^{2-1}}{3(-1)^{3-1}}=\frac{-2}{3}
\)
5.
We know that,
\(\sin \alpha-\cos \alpha =\sqrt{2}\left[\frac{1}{\sqrt{2}} \sin \alpha-\frac{1}{\sqrt{2}} \cos \alpha\right] \)
\(=\sqrt{2}\left[\cos \frac{\pi}{4} \sin \alpha-\sin \frac{\pi}{4} \cos \alpha\right] \)
\(=\sqrt{2} \sin \left(\alpha-\frac{\pi}{4}\right) \)
\(\therefore \lim _{\alpha \rightarrow \frac{\pi}{4}} \frac{\sin \alpha-\cos \alpha}{\alpha-\frac{\pi}{4}} =\lim _{\alpha-\frac{\pi}{4} \rightarrow 0} \frac{\sqrt{2} \sin \left(\alpha-\frac{\pi}{4}\right)}{\left(\alpha-\frac{\pi}{4}\right)}=\sqrt{2}
\)
6.
\(f(x)=x(-1)^{\left\lfloor\frac{1}{x}\right\rfloor}\)
\(=x(\pm 1) \left(\because\left[\frac{1}{x}\right\rfloor \text { is an integer }\right) \)
\(=\pm x \)
\(\therefore \lim _{x \rightarrow 0} f(x)=\lim _{x \rightarrow 0}(\pm x)=0\)
7.
\(\lim _{x \rightarrow \infty}\left(\frac{x^{2}+5 x+3}{x^{2}+x+3}\right)^{x} =\lim _{x \rightarrow \infty}\left(\frac{x^{2}+5 x}{x^{2}+x}\right)^{x} \)
\(=\lim _{x \rightarrow \infty}\left(\frac{1+\frac{5}{x}}{1+1 / x}\right)^{x}=\frac{e^{5}}{e}=e^{4} \)
8.
(b)
\(\frac{1}{2}\)ab sin C
9.
(c)
(c-a)2 = b2- ac
10.
(a)
\(\pi\)
11.
(a)
\(\frac{\pi}{3}\)
12.
(c)
1
13.
(a)
0
14.
(b)
\(n\pi +(-1)^n({-\pi\over 6})\)
15.
(d)
x2 - 4x + 1 = 0
16.
(d)
\(\frac { \pi }{ 4 } \)
17.
(b)
750
18.
\(\text { Numerator }=\cos 6 x+6 \cos 4 x+15 \cos 2 x+10\)
\(=(\cos 6 x+\cos 4 x)+5(\cos 4 x+\cos 2 x)+ 10(\cos 2 x+1) \)
\(=2 \cos 5 x \cos x+5(2 \cos 3 x \cdot \cos x)+10\left(2 \cos ^{2} x\right) \)
\(=2 \cos x[\cos 5 x+5 \cos 3 x+10 \cos x] \)
\(\therefore \frac{\mathrm{Nr}}{\mathrm{Dr}} =\frac{2 \cos x(\cos 5 x+5 \cos 3 x+10 \cos x)}{\cos 5 x+5 \cos 3 x+10 \cos x} \)
\(=2 \cos x \)
19.
\(\cos 2 \theta \cos 2 \phi+\sin ^{2}(\theta-\phi)-\sin ^{2}(\theta+\phi) \)
\(=\cos 2 \theta \cos 2 \phi+\frac{1}{2}-\frac{1}{2} \cos (2 \theta-2 \phi)-\frac{1}{2}+\frac{1}{2} \cos (2 \theta+2 \phi) \)
\(=\cos 2 \theta \cos 2 \phi+\frac{1}{2}[\cos (2 \theta+2 \phi)-\cos (2 \theta-2 \phi)] \)
\(=\cos 2 \theta \cos 2 \phi-\sin 2 \theta \cos 2 \phi \)
\(=\cos (2 \theta+2 \phi) \)
\(=\cos 2(\theta+\phi) \)
20.
\(x =\frac{1}{\cos 80^{\circ}}-\frac{\sqrt{3}}{\sin 80^{\circ}} \)
\(=\frac{\sin 80^{\circ}-\sqrt{3} \cos 80^{\circ}}{\sin 80^{\circ} \cos 80^{\circ}} \)
\(\frac{x}{2} =\frac{\frac{1}{2} \sin 80^{\circ}-\frac{\sqrt{3}}{2} \cos 80^{\circ}}{\frac{1}{2} \sin 80^{\circ} \cos 80^{\circ}} \)
\(=\frac{\sin 80^{\circ} \cos 60^{\circ}-\cos 80^{\circ} \sin 60^{\circ}}{\frac{1}{2} \sin 80^{\circ} \cos 80^{\circ}} \)
\(=\frac{\sin 20^{\circ}}{\frac{1}{2} \sin 80^{\circ} \cos 80^{\circ}} \)
\(=\frac{\sin 160^{\circ}}{\frac{1}{2} \sin 80^{\circ} \cos 80^{\circ}} \)
\(=\frac{2 \sin 80^{\circ} \cos 80^{\circ}}{\frac{1}{2} \sin 80^{\circ} \cos 80^{\circ}}=4 \)
11th Standard Syllabus & Materials
11th Standard
TN 11th Tamil பீடு பெற நில் - செய்யுள் - காவடிச்சிந்து Important Questions And Answers Study Material - QB365 Set A
NEW11th Standard
TN 11th Tamil பீடு பெற நில் - உரைநடை - மலை இடப்பெயர்கள் : ஓர் ஆய்வு Important Questions And Answers Study Material - QB365 Set A
NEW11th Standard
TN 11th Tamil மாமழை போற்றுதும் - துணைப்பாடம் - யானை டாக்டர் Important Questions And Answers Study Material - QB365 Set A
NEW11th Standard
TN 11th Tamil மாமழை போற்றுதும் - செய்யுள் - ஐங்குறுநூறு Important Questions And Answers Study Material - QB365 Set A
Tamilnadu Stateboard 11th Standard Subjects
Maths
Commerce
Economics
Biology
Business Maths and Statistics
Accountancy
Computer Science
Physics
Chemistry
Maths
Biology
Economics
Physics
Chemistry
History
Business Maths and Statistics
Computer Science
Accountancy
Computer Applications
History
Computer Technology
Commerce
Computer Applications
Computer Technology
Tamil
English
French
Tamilnadu Stateboard Standards
