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Published on: 15/09/2018
Model Paper 2
Download CBSE Class 11th Standard CBSE Mathematics question papers, sample papers, important questions, and previous year solved papers in PDF format. Get free study materials, NCERT solutions, and exam preparation resources for Class 11th Standard CBSE Mathematics
Questions + Answers key
Take MCQ Mathematics Test
1.
The domain of the function \(f(x)=\sqrt{x-1}+\sqrt{3-x}\) is ______.
(1,\(\infty\))
(\(\infty\),5)
(1, 3)
[1, 3]
2.
If f: R\(\rightarrow\) R be given by f(x) =\({4^x\over 4^x+2}\) for all x \(\in\) R, then ______.
f(x) = f(1 + x)
f(x) + f(1 + x) = 0
f(x) + f(1 - x) = 1
none of these
3.
If f(x) =\({x+1\over x-1}\) is a real function,\(\neq\) 1, then \(f[f\{f(2)\}]\) is ______.
-1
-3
3
4
4.
If \(f(x)={2^x+2^{-x}\over 2}\) then f(x+y) f(x-y)is equal to ______.
\({1\over2}[f(2x)+f(2y)]\)
\({1\over2}[f(2x)-f(2y)]\)
\({1\over3}[f(2x)+f(2y)]\)
\({1\over3}[f(2x)-f(2y)]\)
5.
If f(x) = log\({1+x\over 1-x}\) and g(x) = \({3x+x^3\over 1+3x^2}\) then f(g(x)) is equal to ______.
f(2x)
\([f(x)]^2\)
3f(x)
- f(3x)
6.
Let f(x) = Ix-1I then ______.
f(x2) = [f(x)]2
f(x +y) = f(x) f(y)
f(IxI) = I f(x) I
none of these
7.
Which one of the following is not a function
{(x, y) (:) x, y \(\in\) R, x2 = y}
{(x, y) (:) x, y \(\in\) R, y2 = x}
{(x, y) (:) x, y \(\in\) R, x = y3}
{(x, y) (:) x, y \(\in\) R, y = x3}
8.
If R is a relation from a finite set A having m elements to a finite set B having n elemen.ts, then the number of relations from A to B is ______.
2mn
2mn-1
2mn
mn
9.
Let R be a relation from a set A to B, then ______.
R=A\(\cup\)B
R =A\(\cap\)B
R\(\subset\)A x B
R \(\subset\) B x A
10.
If the set A has m elements, B has n elements then the number of elements in A x B is ______.
m + n
m + n + 1
mn
n2
11.
Find the general solutions of\(\sqrt{3}\) sin x-cos x =2 ______.
X = n\(\pi +{\pi\over 6}+(-1)^n{\pi\over2}\)
X = n\(\pi -{\pi\over 6}+(-1)^n{\pi\over2}\)
X = n\(\pi +{\pi\over 6}+(-1)^{n+1}{\pi\over2}\)
None
12.
The solution of the equation cos2 \(\theta\) -+sin\(\theta\)+ 1=0lies in the interval ______.
\(({\pi\over 4},{3\pi\over4})\)
\((-{\pi\over 4},{3\pi\over4})\)
\(({3\pi\over 4},{5\pi\over4})\)
\(({5\pi\over 4},{7\pi\over4})\)
13.
If 4 sin2\(\theta=1\) then the values of \(\theta\) are ______.
\(2n\pi\pm{\pi\over3},n\in Z\)
\(n\pi\pm{\pi\over3},n\in Z\)
\(n\pi\pm{\pi\over6},n\in Z\)
\(2n\pi\pm{\pi\over6},n\in Z\)
14.
If A, B, C are in A.P. then \({sinA-sinC\over cosC-cosA}\) is equal to ______.
sin B
cot B
sin 2B
cot 2B
15.
If sin \(\theta\) + sin \(\phi\)= \(\alpha\) and cos\(\theta\) - cos\(\phi\)= b then tan\({\theta -\phi\over 2}\) is equal to ______.
\(\sqrt{a^2+b^2}\)
\(-{a\over b}\)
\(-{b\over a}\)
\(1\over \sqrt{a^2-b^2}\)
16.
In a\(\triangle\) ABC, if tan A +tanB+ tan C = o then cot A cot B cot C is equal to______.
6
3
\(1\over6\)
\(1\over3\)
17.
If tan \(\theta={\alpha\over \alpha+1}\) and tan \(\phi ={1\over 2\alpha+1}\) , then (A+ B) is equal to ______.
0
\(\pi\over4\)
\(\pi\over6\)
\(\pi\over2\)
18.
If tan \(\theta\) + sec \(\theta\) = ex then cos\(\theta\) is equal to ______.
\({e^x+e^{-x}\over 2}\)
\({e^x-e^{-x}\over 2}\)
\({e^x-e^{-x}\over e^x+e^x}\)
\({2\over e^x+e^{-x}}\)
19.
If tan\(\theta\) + cot \(\theta\) = 5 then tan3 \(\theta\) + cot3 \(\theta\) is equal to ______.
135
140
110
90
20.
sin6\(\theta\) + cos6\(\theta\) + 3 sin2\(\theta\) cos2\(\theta\) is equal to ______.
0
1
4
2
21.
If x = r sin\(\alpha\) cos \(\beta\), y = r sin\(\alpha\) sin \(\beta\)and z = r cos\(\alpha\), then X2 + y2 + Z2 is independent of ______.
\(\alpha , \beta\)
\(\gamma , \alpha\)
\(\gamma , \beta\)
none of these
22.
In a ΔABC, if the sides are 7cm, 4\(\sqrt { 3 } \) cm and .\(\sqrt { 13 } \) cm, then the smallest angle is ______.
45o
60o
30o
90o
23.
In a ΔABC if a = 5, b = 6 and c = 5, then ∠B is ______.
cos-1 \(\left( \frac { 7 }{ 24 } \right) \)
cos-1\(\left( \frac { 7 }{ 25 } \right) \)
cos-1 \(\left( \frac { 7 }{30 } \right) \)
None
24.
In a ∆ABC, if ∠A = 45o, ∠B = 60o and ∠C = 75o, then the ratio of sides is ______.
2 : \(\sqrt { 6 } :(\sqrt { 3 } +1)\)
\(\sqrt { 2 } :6:(\sqrt { 3 } +1)\)
\(2:\sqrt { 6 } :(\sqrt { 3 } -1)\)
None
1.
(d)
[1, 3]
2.
(c)
f(x) + f(1 - x) = 1
3.
(c)
3
4.
(a)
\({1\over2}[f(2x)+f(2y)]\)
5.
(c)
3f(x)
6.
(d)
none of these
7.
(b)
{(x, y) (:) x, y \(\in\) R, y2 = x}
8.
(a)
2mn
9.
(c)
R\(\subset\)A x B
10.
(c)
mn
11.
(a)
X = n\(\pi +{\pi\over 6}+(-1)^n{\pi\over2}\)
12.
(d)
\(({5\pi\over 4},{7\pi\over4})\)
13.
(c)
\(n\pi\pm{\pi\over6},n\in Z\)
14.
(b)
cot B
15.
(c)
\(-{b\over a}\)
16.
(c)
\(1\over6\)
17.
(b)
\(\pi\over4\)
18.
(d)
\({2\over e^x+e^{-x}}\)
19.
(c)
110
20.
(b)
1
21.
(a)
\(\alpha , \beta\)
22.
(c)
30o
23.
(b)
cos-1\(\left( \frac { 7 }{ 25 } \right) \)
24.
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