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Published on: 04/11/2019
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Questions + Answers key
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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 set builder method, the null set is represented by _____.
{}
ф
{x: x\(\ne\)x}
{x : x = x}
23.
If A = {x : x is a multiple of 3} and B = {x : x is a multiple of 5} then A - B is _____.
\(A\cap B\)
\(A-\bar B\)
\(\bar A\cap\bar B\)
\(\overline {A\cap B}\)
24.
Let A = {x : x ∈ R, x ≥ 4}and B = {x : x ∈ R,x < 5}then A \(\cap\) B is _____.
{4}
{4,5}
{5,5}
{5,4}
25.
If A = {1, 2, 3, 4, 5, 6}then the number of proper sub-sets is _____.
64
36
26
63
26.
Let U be the universal set containing 700 elements. If A and B are sub-sets of U such that n(A) = 200, n(B) = 300 and n(A \(\cap\) B) = 100, then n(A' \(\cap\) B') =___.
400
500
300
800
27.
If A and B are two sets then A \(\cap\) (A \(\cap\) B') =_______.
A
B
A'\(\cap\)B'
ф
28.
For any two sets A and B, A \(\cup\) B = A iff _____.
A ⊂ B
B∈A
A=B
A\(\ne\)B
29.
For any two sets A and B, (A - B) \(\cup\) (B - A)=_____.
(A - B) \(\cup\) A
(B - A) \(\cup\) B
(A \(\cup\) B) - (A \(\cap\) B)
(A \(\cup\) B) \(\cap\) (A \(\cap\) B)
30.
If \(A\cap B=B\) then _____.
B⊂A
A=ф
A⊂B
B=ф
31.
For any two sets A and B, \(A\cap(A\cup B)=\)_____.
B
A
ф
none of these
32.
The number of subsets of a set containing n elements is _____.
2n - 2
n2
2n
n
33.
The sum of infinity of the G.P. a, ar, ar2, ar3, ...... \(\infty\) is ______.
\(\frac{a-1}{1-r}\)
\(\frac{a}{1-r}\)
\(\frac{2a}{1-r}\)
\(\frac{a}{1-r^2}\)
34.
The seen to infinity of the series \(1+2.\frac{1}{2}+3.\frac{1}{2^2}+4.\frac{1}{2^3}+...+\infty\) ______.
4
5
1
None
35.
The sum of the square of (n - 1) natural numbers is ______.
\(\frac{n(n+1)(2n+1)}{6}\)
\(\frac{n(n-1)(2n-1)}{6}\)
\(\frac{(n+1)(n-1)(n-2)}{6}\)
None
36.
The sum to infinity of \(\frac{1}{3}+\frac{3}{9}+\frac{5}{27}+\frac{7}{81}+...+\infty\) is ______.
2
1
0
3
37.
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
38.
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
39.
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
40.
\(\overset{lim}{x\rightarrow \frac{\pi}{2}} \) (sec x-tan x) is equal to ______.
0
1
2
3
41.
\(\overset{lim}{x\rightarrow 0} \frac{\sqrt{1+x}-1}{x}\) is equal to _____.
3
0
\(\frac{1}{2}\)
1
42.
\(\overset{lim}{x\rightarrow 1} \frac{sin\pi x}{x-1}\) is equal to _______.
-\(\pi\)
\(\pi\)
-\( \frac{1}{\pi}\)
\( \frac{1}{\pi}\)
43.
\(\overset{lim}{x\rightarrow 0} \frac{x^{n}-a^{n}}{x-a}\) is equal to ______.
na
n
nan-1
none of these
44.
\(\overset{lim}{x\rightarrow 0} \frac{sin2x}{x}\) is _______.
3
\(\frac{1}{3}\)
2
\(\frac{1}{2}\)
45.
\(\overset{lim}{x\rightarrow 0} \frac{x}{tan x}\) is _______.
0
1
2
3
46.
The latus rectum of the hyperbola \({ 16x }^{ 2 }-{ ay }^{ 2 }=144\quad is\) _______.
323
\(\frac { 15 }{ 4 } \)
\(\frac { 4 }{ 3 } \)
\(\frac { 3 }{ 4 } \)
47.
The difference of the focal distances of any point on the hyperbola is equal to ______.
length of conjugate axis
length of transverse axis
latus rectum
none of these
48.
The eccentricity of the hyperbola whose latus rectum is half of its transverse axis is _______.
\(\frac { 1 }{ 2 } \)
\(\sqrt { \frac { 1 }{ 3 } } \)
\(\sqrt { \frac { 2 }{ 3 } } \)
\(\sqrt { \frac { 3 }{ 2 } } \)
49.
The difference between the lengths of the major axis and the latus rectum of an ellipse is ______.
\({ 2ae }^{ 2 }\)
\(ae\)
\(3ae\)
\(ae^{ 2 }\)
50.
The eccentricity of the ellipse \(\frac { { x }^{ 2 } }{ { a }^{ 2 } } +\frac { { y }^{ 2 } }{ { b }^{ 2 } } =1\) if its latus rectum is equal to one half of its minor axis is _______.
\(\frac { 1 }{ 2 } \)
\(\frac { \sqrt { 3 } }{ 2 } \)
\(\frac { 1 }{ \sqrt { 3 } } \)
None of these
51.
In the parabola y2 = 4ax,the length of the chord passing through the vertex and inclined to the axis at π/4 is ________.
\(4\sqrt { 2 } a\)
\(3\sqrt { 2 } a\)
\(2\sqrt { 2 } a\)
\(\sqrt { 2 } a\)
52.
The locus of the points of trisection of the double ordinates of a parabola is a ______.
pair of lines
parabola
circles
none of these
53.
The four distinct points (0,0), (2,0), (0,−2) and (k,−2) are concyclic if k is equal to ______.
-1
-2
2
0
54.
If the circle x2+y2+2ax+c = 0 and x2+y2+2by+c = 0 touch each other then ______.
\(\frac { 1 }{ { a }^{ 2 } } +\frac { 1 }{ { b }^{ 2 } } =\frac { 1 }{ c } \)
\(\frac { 1 }{ { a }^{ 2 } } +\frac { 1 }{ { b }^{ 2 } } =\frac { 1 }{ { c }^{ 2 } } \)
\(\frac { 1 }{ a } +\frac { 1 }{ b } =\frac { 1 }{ c } \)
None of these
55.
The circle x2+y2+2gx+2fy+c = 0 does not intersect x − axis if ______.
\(g^{ 2 }>c\)
\(g^{ 2 }
\(g^{ 2 }>2c\)
\(g^{ 2 }<2c\)
56.
Constant term in the expansion of \(\left( x-\frac { 1 }{ x } \right) ^{ 14 }\) _____.
3032
3432
5042
-3442
57.
The coefficient of x5y8 in the expansion of (x + y)13 is _____.
13C5
13C8
8C5
None of the these
58.
The total number of terms in the expansion of (x + a)80 + (x - a)80 is _____.
41
31
51
161
59.
If in the expansion of (1 +x)15, the coefficient of (2x + 3)th and (r - 1)th terms are equal then r is equal to _____.
9
5
8
none of the these
60.
The middle term in the expansion of \(\left( \frac { { 2x }^{ 2 } }{ 3 } +\frac { 3 }{ { 2x }^{ 2 } } \right) ^{ 10 }\)is _____.
240
280
262
252
61.
If in the expansion of (1 +x)n, the coefficients of fifth, sixth and seventh terms are inA.P. then n is equal to _____.
5,7
7,16
7,14
8,15
62.
If in the expansion of (a + b)n and (a + b)n + 3, the ratio of the coefficients of second and third terms and third and fourth terms respectively are equal then n is _____.
2
8
5
none of these
63.
If C0 + C1 + C2 +...+Cn = 256 then 2nC2 is equal to ______.
45
105
120
130
64.
If 40Cr+2 = 40Cr-2 then r is equal to ______.
20
18
14
28
65.
The number of arrangements of the letters of the word BHARAT taking 3 at a time is ______.
54
120
62
72
66.
The number of ways to arrange the letters of the word HAPPY are ______.
120
90
40
60
67.
Total number of words formed by 3 vowels and 5 consonants taken from 4 vowels and 7 consonants is equal to ______.
75360
60480
54230
none of these
68.
In the three dimensional space the equation x2 - 7x + 12 = 0 represents ______.
pair of straight lines
curves
planes
none of these
69.
If (3, 4, -1) and (-1, 2, 3) be the endpoints of a diameter of a sphere. Then radius of sphere is equal to ______.
2
4
5
6
70.
The points (3, 3, 3), (0, 6, 3), (1, 7, 7) and (4, 4, 7) are vertices of ______.
a rectangle
a square
a parallelogram
a rhombus
71.
The ratio in which the line joining the points (a, b, c) and (-4, 3, -6) is divided by XY-plane is ______.
c : 6
6 : c
2 : 4
b : 3
72.
The ratio in which the line joining (4, -3, 2) and (6, -5, -1) is divided by YZ-plane is _______.
2 : 3
2 : -3
-2 : 3
none of these
73.
The vertices of a triangle are (6, 0), (0, 6) and (6, 6). The distance between its circumcentre and centriod is ______.
√3
2√3
√2
none of these
74.
The angle between the lines 3x - 2y + 5 = 0 and 2x + 3y - 7 = 0 is ______.
45°
60°
30°
90°
75.
If p be the length of the perpendicular from the origin to the line \({x\over a}+{y\over b}=1\) then ______.
\({1\over p^2}=a^2 + b^2\)
\({1\over p^2}={1\over a^2} +{1\over b^2}\)
p2 = a2 + b2
none of these
76.
The area of a triangle whose vertices are (3, -2), (5, 6) and (-2, -5) is ______.
15 sq. units
16 sq. units
17 sq. units
18 sq. units
77.
A line passes through the point (2, 2) and is perpendicular to the line 3x + y = 3. Its y intercept is ______.
1/3
5
3/4
4/3
78.
Sum of n terms of ,the series \(\sqrt { 2 } +\sqrt { 8 } +\sqrt { 18 } +\sqrt { 32 } +\)..... is ______.
\(\left[ \frac { n(n+1) }{ 2 } \right] ^{ 2 }\)
n2 (n+3)
\(\frac { n(n+1) }{ \sqrt { 2 } } \)
2
79.
If the sum of first n even natural numbers is equal to m times the sum of first n is odd natural numbers then m is equal to ______.
\(\frac { n-1 }{ n } \)
\(\frac { n+1 }{ n } \)
\(\frac { 2n+1 }{ n } \)
None of these
80.
The three geometric means between the numbers 1 and 81 are ______.
3, 6 and 18
3, 9 and 27
3, 6 and 27
None of these
81.
If the first term of an AP. is 5 and common difference is - 3 then sum of its 60 terms is equal to ______.
-1050
-5010
3010
None of these
82.
If the first, 'second and last term of an AP. are a, band 2a respectively then its sum is equal to ______.
\(\frac { b }{ 2(b-a) } \)
\(\frac { a }{ 3(b-a) } \)
\(\frac { 3ab }{ 2(b-a) } \)
\(\frac { 2ab }{ 3(b-a) } \)
83.
If Sn denote the sum of n terms of an AP. whose first term is a and common difference is d given by is d given by d = Sn - kSn-1 + Sn-2 then K is equal to ______.
5
2
3
4
84.
If the S. D. of a set of observation is 8 and if each observation is divided by- 2 then S.D. of new set of observation is ______.
-4
4
8
-8
85.
The mean deviation of the series a, a + d, a + 2d, .... a + nd from its mean is ______.
\({(n+1)d\over (n+2)}\)
\(nd\over 2n+1\)
\(n(n+1)d\over 2n+1\)
\((2n+1)d\over n\)
86.
If ⋋is the variance and o is the S.D. then ______.
\(⋋={1\over σ^2}\)
⋋ = σ2
\(σ={1\over ⋋}\)
\(σ={1\over ⋋^2}\)
87.
Standard deviation of a data is given by ______.
\(σ=\sqrt{{1\over N}\sum fd^2-\left({1\over N}\sum fd\right)^2}\)
\(σ=\sqrt{\left({1\over N}\sum fd\right)^2-{1\over N}\sum fd^2}\)
\(σ=\sqrt{{1\over N}\sum fd^2-{1\over N}\sum fd^2}\)
None of these
88.
Two die are thrown simultaneously. The probability of getting a pair of aces is _______.
\(\frac { 1 }{ 36 } \)
\(\frac { 1 }{ 26 } \)
\(\frac { 1 }{ 6 } \)
None of these
89.
The probability that a leap year will have 53 Sundays is _______.
\(\frac { 3 }{ 7 } \)
\(\frac { 1 }{ 7 } \)
\(\frac { 4 }{ 7 } \)
\(\frac { 2 }{ 7 } \)
90.
Six boys and six girls sit in a row. The probability that all girls sit together is _______.
\(\frac { 1 }{ 132 } \)
\(\frac { 1 }{ 105 } \)
\(\frac { 1 }{ 142 } \)
\(\frac { 1 }{ 165 } \)
91.
Two die are thrown simulatneously. The probability of getting a total of 5 is _______.
\(\frac { 1 }{ 16 } \)
\(\frac { 1 }{ 10 } \)
\(\frac { 1 }{ 9 } \)
\(\frac { 1 }{ 6 } \)
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)
{x: x\(\ne\)x}
23.
(b)
\(A-\bar B\)
24.
(a)
{4}
25.
(d)
63
26.
(c)
300
27.
(c)
A'\(\cap\)B'
28.
(b)
B∈A
29.
(c)
(A \(\cup\) B) - (A \(\cap\) B)
30.
(a)
B⊂A
31.
(b)
A
32.
(c)
2n
33.
(b)
\(\frac{a}{1-r}\)
34.
(d)
None
35.
(b)
\(\frac{n(n-1)(2n-1)}{6}\)
36.
(a)
2
37.
(c)
30o
38.
(b)
cos-1\(\left( \frac { 7 }{ 25 } \right) \)
39.
40.
(a)
0
41.
(c)
\(\frac{1}{2}\)
42.
(c)
-\( \frac{1}{\pi}\)
43.
(c)
nan-1
44.
(c)
2
45.
(b)
1
46.
(a)
323
47.
(b)
length of transverse axis
48.
(d)
\(\sqrt { \frac { 3 }{ 2 } } \)
49.
(a)
\({ 2ae }^{ 2 }\)
50.
(b)
\(\frac { \sqrt { 3 } }{ 2 } \)
51.
(a)
\(4\sqrt { 2 } a\)
52.
(b)
parabola
53.
(c)
2
54.
(a)
\(\frac { 1 }{ { a }^{ 2 } } +\frac { 1 }{ { b }^{ 2 } } =\frac { 1 }{ c } \)
55.
(a)
\(g^{ 2 }>c\)
56.
(d)
-3442
57.
(a)
13C5
58.
(a)
41
59.
(b)
5
60.
(d)
252
61.
(b)
7,16
62.
(c)
5
63.
(c)
120
64.
(a)
20
65.
(d)
72
66.
(d)
60
67.
(b)
60480
68.
(c)
planes
69.
(d)
6
70.
(b)
a square
71.
(a)
c : 6
72.
(c)
-2 : 3
73.
(c)
√2
74.
(d)
90°
75.
(b)
\({1\over p^2}={1\over a^2} +{1\over b^2}\)
76.
(c)
17 sq. units
77.
(d)
4/3
78.
(c)
\(\frac { n(n+1) }{ \sqrt { 2 } } \)
79.
(b)
\(\frac { n+1 }{ n } \)
80.
(b)
3, 9 and 27
81.
(b)
-5010
82.
(c)
\(\frac { 3ab }{ 2(b-a) } \)
83.
(b)
2
84.
(b)
4
85.
(b)
\(nd\over 2n+1\)
86.
(b)
⋋ = σ2
87.
88.
(a)
\(\frac { 1 }{ 36 } \)
89.
(d)
\(\frac { 2 }{ 7 } \)
90.
(a)
\(\frac { 1 }{ 132 } \)
91.
(c)
\(\frac { 1 }{ 9 } \)
11th Standard CBSE Syllabus & Materials
11th Standard CBSE
CBSE 11th Business Studies Forms of Business Organisation Sample Question Papers Study Material - QB365 Set A
NEW11th Standard CBSE
CBSE 11th Business Studies Business, Trade and Commerce Sample Question Papers Study Material - QB365 Set A
NEW11th Standard CBSE
CBSE 11th Physics Waves Sample Question Papers Study Material - QB365 Set A
NEW11th Standard CBSE
CBSE 11th Physics Kinetic Theory Sample Question Papers Study Material - QB365 Set A
CBSE 11th Standard CBSE Subjects
CBSE Standards
