11th Standard Syllabus & Materials
11th Standard
Tamilnadu 11th Standard Tamil மொழி கலை -செய்யுள் - ஒவ்வொரு புல்லையும் Important Questions And Answers Study Material - QB365
NEW11th Standard
Tamilnadu 11th Standard Tamil கேடில் விழுச்செல்வம் - உரைநடை - தமிழகக் கல்வி வரலாறு Important Questions And Answers Study Material - QB365
NEW11th Standard
Tamilnadu 11th Standard Tamil பீடு பெற நில் - இலக்கணம் - பகுபத உறுப்புகள் Important Questions And Answers Study Material - QB365
NEW11th Standard
Tamilnadu 11th Standard Tamil பீடு பெற நில் - செய்யுள் - குறுந்தொகை Important Questions And Answers Study Material - QB365 Set B
NEW11th Standard
Tamilnadu 11th Standard Tamil பீடு பெற நில் - செய்யுள் - குறுந்தொகை Important Questions And Answers Study Material - QB365 Set A
NEW11th Standard
Tamilnadu 11th Standard Tamil பீடு பெற நில் - செய்யுள் - காவடிச்சிந்து Important Questions And Answers Study Material - QB365 Set B
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.
\(\int \sin \sqrt{x} d x\) is
\(2(-\sqrt{x}cos\sqrt{x}+sin\sqrt{x})+c\)
\(2(-\sqrt{x}cos\sqrt{x}-sin\sqrt{x})+c\)
\(2(-\sqrt{x}sin\sqrt{x}-cos\sqrt{x})+c\)
\(2(-\sqrt{x}sin\sqrt{x}+cos\sqrt{x})+c\)
2.
\(\int \tan ^{-1} \sqrt{\frac{1-\cos 2 x}{1+\cos 2 x}} d x\) is
x2+c
2x2+c
\({x^2\over2}+c\)
\(-{x^2\over2}+c\)
3.
If \(\overrightarrow{a}=\hat{i}+2\hat{j}+2\hat{k},|\overrightarrow{b}|=5\) and the angle between \(\overrightarrow{a}\) and \(\overrightarrow{b}\) is \({\pi\over 6},\) then the area of the triangle formed by these two vectors as two sides, is
\(7\over4\)
\(15\over4\)
\(3\over4\)
\(17\over4\)
4.
If \(|\overrightarrow{a}+\overrightarrow{b}|=60,\) \(|\overrightarrow{a} - \overrightarrow{b}|=40\) and \(|\overrightarrow{b}|=46\) , then \(|\overrightarrow{a}|\) is
42
12
22
32
5.
Two vertices of a triangle have position vectors \(3\hat{i}+4\hat{j}-4\hat{k}\) and \(2\hat{i}+3\hat{j}+4\hat{k}\) . If the position vector of the centroid is \(\hat{i}+2\hat{j}+3\hat{k}\), then the position vector of the third vertex is
\(-2\hat{i}-\hat{j}+9\hat{k}\)
\(-2\hat{i}-\hat{j}-6\hat{k}\)
\(2\hat{i}-\hat{j}+6\hat{k}\)
\(-2\hat{i}+\hat{j}+6\hat{k}\)
6.
A vector \(\overrightarrow{OP}\) makes 60° and 45° with the positive direction of the x and y axes respectively. Then the angle between \(\overrightarrow{OP}\)and the z-axis is
45°
60°
90°
30°
7.
The unit vector parallel to the resultant of the vectors \(\hat{i}+\hat{j}-\hat{k}\) and \(\hat{i}-2\hat{j}+\hat{k}\) is
\({\hat{i}-\hat{j}+\hat{k}\over\sqrt{5}}\)
\({2\hat{i}+\hat{j}\over\sqrt{5}}\)
\({2\hat{i}-\hat{j}+\hat{k}\over\sqrt{5}}\)
\({2\hat{i}-\hat{j}\over\sqrt{5}}\)
8.
The domain and range of the function \(f(x)={|x-4|\over x-4}\)
R, [-1, 1]
R \ {4};{-1,1}
R \ {4};{-1,l}
R, (-1,1)
9.
If A and B are any two finite sets having m and n elements respectively then the cardinality of the power set of A \(\times\) B is ___________
2m
2n
mn
2mn
10.
For any four sets A, B, C and D, which of the following is not true?
A x C ⊂ B x D
(A x B) ∩ (C x D) = (A ∩ C) x (B ∩ D)
A x (B U,C) = (A x B) U (A x C)
A x (B ∩ C) = (A x B) ∩ (A x C)
11.
Let f and g be two odd functions then the function of f o g is ___________
an even function
an odd function
neither even nor odd
a periodic function
12.
The condition that the equation ax2 + bx + c = 0 may have one root is the double the other is ___________
2b2 = 9ac
b2 = ac
b2 = 4ac
9b2 = 2ac
13.
\(n(A\cap B)=4\) and \((A\cup B)=11\) then \(n(p(A\triangle B))\) is __________
44
256
64
128
14.
If \(f:R\rightarrow R\) is defined by \(f(x)=2x-3\) __________
\({1\over 2x-3}\)
\({1\over 2x+3}\)
\({x+3\over 2}\)
\({x-3\over 2}\)
15.
16.
Let R be the relation over the set of all straight lines in a plane such that l1Rl2 ⇔ l1丄l2 . Then R is __________
symmetric
reflexive
transitive
an equivalent relation
17.
For real numbers x and y, define xRy if x - y + √2 is an irrational number. Then the relation R is __________
reflexive
symmetric
transitive
none of these
18.
Let X = {1, 2, 3, 4}, Y = {a, b, c, d} and f = {(1, a), (4, b), (2, c), (3, d), (2, d)}. Then f is
an one-to-one function
an onto function
a function which is not one-to-one
not a function
19.
The function f:[0,2π]➝[-1,1] defined by f(x) = sin x is
one-to-one
on to
bijection
cannot be defined
20.
The number of constant functions from a set containing m elements to a set containing n elements is
mn
m
n
m+n
1.
\(\text { Let } \sqrt{x}=t\)
\(\text { Then } x=t^{2}\)
\(\therefore \frac{d x}{d t}=2 t\)
\(\therefore d x=2 t d t\)
\(\therefore \int \sin \sqrt{x} d x=\int \sin t \times 2 t d t\)
\(=2 \int t \sin t d t\)
\(\text { Applying Bernoulli's formula }\)
\(=2[t(-\cos t)-1(-\sin t)]+c\)
\(\text { Putting } t=\sqrt{x}\)
\(=2[-\sqrt{x} \cos \sqrt{x}+\sin \sqrt{x}]+c\)
2.
\(\int \tan ^{-1} \sqrt{\frac{1-\cos 2 x}{1+\cos 2 x}} d x =\int \tan ^{-1} \sqrt{\tan ^{2} x} d x \\ \)
\(=\int \tan ^{-1}(\tan x) d x \)
\(=\int x d x=\frac{x^{2}}{2}+c \)
3.
(b)
\(15\over4\)
4.
\(\text { W.K.T }|\vec{a}+\vec{b}|^{2}+|\vec{a}-\vec{b}|^{2}=2\left[|\vec{a}|^{2}+|\vec{b}|^{2}\right]\)
\(60^{2}+40^{2} =2\left(|\vec{a}|^{2}+46^{2}\right) \)
\(3600+1600 =2\left(|\vec{a}|^{2}+2116\right) \)
\(\frac{5200}{2} =|\vec{a}|^{2}+2116 \)
\(2600-2116 =|\vec{a}|^{2} \)
\(|\vec{a}|^{2} =484\)
\(|\vec{a}| =22 \)
5.
\(\left(\frac{3+2+x_{1}}{3},\right. \left.\frac{4+3+x_{2}}{3}, \frac{-4+4+x_{3}}{3}\right)=(1,2,3) \)
\(3+2+x_{1} =3 ; 4+3+x_{2}=6 ;-4+4+x_{3}=9 \)
\(5+x_{1}=3 7+x_{2}=6 \)
\(x_{1}=-2 \quad x_{2}=-1 \)
\(\therefore \text { Third vertex is }(-2,-1,9)\)
6.
\(\cos ^{2} \alpha+\cos ^{2} \beta+\cos ^{2} \gamma=1 \)
\(\cos ^{2} 60^{\circ}+\cos ^{2} 45^{\circ}+\cos ^{2} \gamma=1 \)
\(\left(\frac{1}{2}\right)^{2}+\left(\frac{1}{\sqrt{2}}\right)^{2}+\cos ^{2} \gamma=1 \Rightarrow \cos ^{2} \gamma=1-\frac{1}{4}-\frac{1}{2} \)
\(\cos ^{2} \gamma=\frac{4-1-2}{4}=\frac{1}{4} \Rightarrow \cos \gamma=\frac{1}{2} \Rightarrow \gamma=60^{\circ} \)
\(\text { Angle between } \overrightarrow{O P} \text { and } z \text { axis is } 60^{\circ}\)
7.
\(\vec{a}+\vec{b} =2 \hat{i}-\hat{j} \)
\(|\vec{a}+\vec{b}| =\sqrt{4+1}=\sqrt{5} \)
\(\text { Unit vector }=\frac{2 \hat{i}-\hat{j}}{\sqrt{5}}\)
8.
(b)
R \ {4};{-1,1}
9.
(d)
2mn
10.
(a)
A x C ⊂ B x D
11.
(b)
an odd function
12.
(a)
2b2 = 9ac
13.
(d)
128
14.
(c)
\({x+3\over 2}\)
15.
(c)
16.
(a)
symmetric
17.
(a)
reflexive
18.
It is not a function since it has two images
19.
It is onto not one-one
\(\text { Since } \sin 30^{\circ}=\frac{1}{2}\)
\(\sin 150^{\circ}=\frac{1}{2}\)
20.
(c)
n
11th Standard Syllabus & Materials
11th Standard
Tamilnadu 11th Standard Tamil பீடு பெற நில் - செய்யுள் - காவடிச்சிந்து Important Questions And Answers Study Material - QB365 Set A
NEW11th Standard
Tamilnadu 11th Standard Tamil பீடு பெற நில் - உரைநடை - மலை இடப்பெயர்கள் : ஓர் ஆய்வு Important Questions And Answers Study Material - QB365 Set B
NEW11th Standard
Tamilnadu 11th Standard Tamil பீடு பெற நில் - உரைநடை - மலை இடப்பெயர்கள் : ஓர் ஆய்வு Important Questions And Answers Study Material - QB365 Set A
NEW11th Standard
Tamilnadu 11th Standard Tamil மாமழை போற்றுதும் - செய்யுள் - ஐங்குறுநூறு Important Questions And Answers Study Material - QB365 Set B
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
