Quiz title

1. A number which can be put in the form $\frac{p}{q}$ where $p,q \in z$ and $q\neq0$ is called
   1. a complex number
   2. a rational number
   3. a natural number
   4. an irrational number
2. $\pi$ is ————?
   1. a complex number
   2. a rational number
   3. a natural number
   4. an irrational number
3. $\frac{3}{4}$ is ————-
   1. an odd number
   2. an even number
   3. a natural number
   4. a rational number
4. $\sqrt{16}$ is ————-
   1. a rational number
   2. an irrational number
   3. an odd number
   4. a prime number
5. $\sqrt{3}$ is ————-
   1. a rational number
   2. a natural number
   3. an irrational number
   4. an integer
6. $0$ is ———-
   1. positive integer
   2. a negative integer
   3. a natural number
   4. an integer
7. $\frac{1}{3}$ is ————-
   1. a prime number
   2. an integer
   3. a rational number
   4. an irrational number
8. $\sqrt{35}$
   1. $\frac{11}{36}$
   2. $\frac{7}{12}$
   3. $\frac{35}{36}$
   4. None of these
9. If a vector space is \textbf{V} has a base of n vectors, then every basis of \textbf{V} must consist of exactly …….. vectors.
   1. $n+1$
   2. $n$
   3. $n-1$
   4. None of these
10. The complex matrix A=$\left[\begin{array}{cc}2& 2+i\\ 2-i& 6\end{array}\right]^n$ has which one of the following as an eigenvalue?
    1. $-1$
    2. $3$
    3. $7$
    4. $i$
11. A problem in mathematics is given to three students A,B,C and their respective probability of solving the problem is $\frac{1}{2}$, $\frac{1}{3}$ and $\frac{1}{4}$. Probability that the problem is solved is ?
    1. $\frac{3}{4}$
    2. $\frac{1}{2}$
    3. $\frac{2}{3}$
    4. $\frac{1}{3}$
12. If $\alpha \neq \beta$ and ${\alpha}^2=5 \alpha-3$, $\beta^2 =5 \beta -3$, then the equation having $\frac{\alpha}{\beta}$ and $\frac{\beta}{\alpha}$ as its roots is ?
    1. $3x^2+19x+3=0$
    2. $3x^2-19x+3=0$
    3. $3x^2+19x-3=0$
    4. $3x^2-16x+1=0$
13. The eigenvalues of a matrix $\left[\begin{array}{cc}2& b\\ 3& -1\end{array}\right]^n$ are $-4$ and $b-1$. Find $b$?
    1. $2$
    2. $3$
    3. $4$
    4. $6$
14. How many generators does the graph $(Z_{24}, +)$ have?
    1. $2$
    2. $6$
    3. $8$
    4. $10$
15. The number of conjugacy classes of a symmetric group of degree $3$ is ………. ?
    1. $0$
    2. $2$
    3. $3$
    4. $4$
16. What are Zero divisors in the ring integers modulo $6$?
    1. $\bar{1},\bar{2},\bar{4}$
    2. $\bar{0},\bar{2},\bar{3}$
    3. $\bar{0},\bar{2},\bar{4}$
    4. $\bar{2},\bar{3},\bar{4}$
17. If $1$, $\frac{1}{2}\log_3(3^{1-x}+2)$, $\log_3(4.3^x-1)$ are in A.P. then $x$ is equal to ?
    1. $\log_3 4$
    2. $1-\log_34$
    3. $1-\log_43$
    4. $\log_43$
18. Which of the following group is cyclic?
    1. $Z_2 \times Z_4$
    2. $Z_2 \times Z_6$
    3. $Z_3 \times Z_4$
    4. $Z_3 \times Z_6$
19. $\lim_{n\to\infty}\frac{1+2(10)^n}{5+3(10)^n}$=?
    1. $\frac{1}{5}$
    2. $\frac{2}{3}$
    3. $\frac{3}{8}$
    4. $\infty$
20. $\lim_{n\to\infty}\frac{\sqrt{1-cos2x}}{\sqrt{2}x}$=?
    1. $1$
    2. $-1$
    3. $0$
    4. does not exist
21. Set of square matrices of order $3$ forms a ……….?
    1. groupoid
    2. semi group
    3. momoid
    4. group
22. The dimension of the row space or column space of a matrix is called the …….. of the matrix.
    1. Basis
    2. Null space
    3. Rank
    4. None of these
23. $(\underline{a}\times \underline{b})\times \underline{c}$ is a vector lying in the plane containing vectors.
    1. \underline{a},\underline{b} and \underline{c}
    2. \underline{a} and \underline{c}
    3. \underline{b} and \underline{c}
    4. \underline{b} and \underline{a}
24. $(p\wedge q)\longrightarrow p$ is a
    1. contradiction
    2. tautology
    3. simple proposition
    4. none of these
25. In class of $100$ students, there are $70$ boys whose average marks in the subjects are $75$. If the average marks of the complete class is $72$, then what is the average of the girls?
    1. $73$
    2. $65$
    3. $68$
    4. $74$
26. Let $X$ and $Y$ be a vector space over the field $F$ with $dim X=m$ and $dimY=n$ then the $dim \textbf{H}om(X,Y)$=
    1. $mn$
    2. $n$
    3. $n^m$
    4. $m^2$
27. The order and degree of the differential equation $(1+3\frac{dy}{dx})^{\frac{2}{3}}=4\frac{d^3y}{dx^3}$ are
    1. $1,\frac{2}{3}$
    2. $3,1$
    3. $3,3$
    4. $1,2$
28. Multiplicative identity in complex number is
    1. $(0,0)$
    2. $(0,1)$
    3. $(1,0)$
    4. $(1,1)$
29. $3$ is
    1. An odd integer
    2. Irrational number
    3. Rational number
    4. Imaginary number
30. Factorization of $9a^2+16b^2$ is \correctchoice $(3a-4ib)(3a+4ib)$
    1. $(3a-4b)(3a+4b)$
    2. $(3b-4a)(3b+4a)$
    3. $(3b-4ia)(3b+4ia)$
31. The value of $(a+bi)^3$ is
    1. $a^3+b^3$
    2. $a^3+3ab^2+3a^2b+b^3$
    3. $a^3-b^3-3ab(a+b)$
    4. $a^3-3ab^2+3a^2bi-b^3i$
32. If $n$ is prime then $\sqrt{n}$ is
    1. Rational
    2. Irrational
    3. Natural number
    4. Verbal no
33. $p$ : Islamabad is capital of Pakistan $q$: Lahore is not capital of Pakistan, the conjunction $p\wedge q$ is \correctchoice False
    1. True
    2. Not valid
    3. Unknown
34. $p$ : $4<7$, $q$: 7<11, the conjunction $p\wedge q$ is
    1. False
    2. True
    3. Not valid
    4. Unknown
35. A disjunction of two statements $p$ and $q$ is true if
    1. $p$ is false
    2. Both $p$ and $q$ are false
    3. One of $p$ and $q$ is true
    4. $q$ is false
36. An element $b$ of a set $B$ can be written as
    1. $b\subseteq B$
    2. $b<B$
    3. $b\in B$
    4. $B\in b$
37. If $A=\{1,3,4\}$, $B=\{c,a,f\}$ then $A\cap B=$ ?
    1. $\{0\}$
    2. $\{c,a,f\}$
    3. $\phi$
    4. $\{1,2,3,4,e,d,f\}$
38. If $A$ is matrix of order $m \times n$ and $B$ is a matrix of order $n\times p$ then order of $AB$ is
    1. $p\times n$
    2. $n \times p$
    3. $p \times p$
    4. $m\times p$
39. Let $A=[a_{ij}]_{m\times n}$ If $a_{ij} =0$ $\forall i\neq j$ and $a_{ij}\neq 0$ for some $i=j$ then matrix $A$ is \correctchoice Diagonal matrix
    1. Symmetric matrix
    2. Hermitian matrix
    3. None of these
40. If a system of equation has a unique solution or infinitely many solutions then it is known as \correctchoice Consistent
    1. Inconsistence
    2. None linear
    3. None
41. Minimum number of equation for any system of equations
    1. $|A|\neq 0$
    2. $|A|=0$
    3. $|A|=\infty$
    4. None
42. The leading diagonal or main diagonal of a square matrix known as
    1. The secondary diagonal
    2. The principal diagonal
    3. Both $a$ and $b$
    4. None of these
43. If $n$ is a nonnegative integer, Then $a_nx^n+\ldots+a_1x+a_o$ is a
    1. Polynomial of degree $3$
    2. Polynomial of degree $n$
    3. Polynomial of degree $2$
    4. Polynomial of degree $0$
44. $7y^2+5\sqrt{y}+3$ is a polynomial over
    1. Natural number
    2. Integers
    3. Rational number
    4. None of these
45. Which is the root of the equation $x^4-9x^3+6x^2+2=0$ \correctchoice $1$
    1. $2$
    2. $-2$
    3. $-1$
46. $x^2+4x+4$ is \correctchoice Polynomial
    1. Equaton
    2. Identity
    3. None of these
47. The product of the roots of the equation $9x^2-5x-27=0$ is
    1. $\frac{5}{27}$
    2. $\frac{-5}{9}$
    3. $\frac{-1}{3}$
    4. $-3$
48. A relation in which the equality is true only for a number of unknown is called
    1. Identity
    2. Equation
    3. Algebraic equation
    4. Algebraic relation
49. $x+\frac{3}{x}=4$ is
    1. A transcendental equation
    2. Cubic equation
    3. An identity
    4. An equation
50. The function of the form $f(x)=\frac{p(x)}{q(x)}$ $q(x)\neq 0$ where $p(x)$ and $q(x)$ are polynomial in $x$ is called
    1. Identity
    2. Equation
    3. Fraction
    4. Algebraic equation
51. A plane which pases through the point $(3,2,0)$ and the line $\frac{x-4}{1}=\frac{y-7}{5}=\frac{z-4}{4}$ is
    1. $x-y+z=1$
    2. $x+y+z=5$
    3. $x+2y-z=1$
    4. $2x-y+z=5$
52. The solution of the equation $\frac{d^2y}{dx^2}=e^{-2x}$ is
    1. $\frac{e^{-2x}}{4}$
    2. $\frac{e^{-2x}}{4}+cx+d$
    3. $\frac{e^{2x}}{4}+cx^2+d$
    4. $\frac{e^{-2x}}{4}+cx-d$
53. Fifth term of GP is $2$, then the product of its $9$ term is
    1. $256$
    2. $512$
    3. $1024$
    4. None of these
54. The vectors $v_1=(-1,1,1)$, $v_2=(1,1,1)$, and $v_3=(1,-1,k)$ from a basis for $R^3$ for all real values of $k$ EXCEPT $k=$
    1. $-2$
    2. $-1$
    3. $0$
    4. $1$
55. $\int_{0}^{10\pi}|sinx|dx$
    1. $20$
    2. $8$
    3. $10$
    4. $18$
56. Center of the graph of quaternions $Q_8$ is of order
    1. $1$
    2. $2$
    3. $8$
    4. $4$
57. $\underline{a}.(\underline{b}\times \underline{c})$ is not equal to
    1. $\underline{a}.(\underline{c}\times \underline{b})$
    2. $(\underline{a}\times \underline{b}).\underline{c}$
    3. $\underline{b}.(\underline{c}\times \underline{a})$
    4. $\underline{c}.(\underline{a}\times \underline{b})$
58. Let $G$ be a group. Then the derived group $G`$ is ……………….. subgroup of $G$.
    1. Normal but not fully invariant
    2. Characteristic but not fully invariant
    3. Fully invariant
    4. None of these
59. $\int_{-\pi}^{\pi}\frac{2x(1+sinx)}{1+cos2x}$ is
    1. $\frac{\pi^2}{4}$
    2. $\pi^2$
    3. $0$
    4. $\frac{\pi}{2}$
60. If $siny=xsin(a+y)$, then $\frac{dy}{dx}$ is
    1. $\frac{sina}{sina sin^2(a+y)}$
    2. $\frac{sin^2(a+y)}{sina}$
    3. $sina sin^2(x+y)$
    4. $\frac{sin(a-y)}{sina}$
61. The differential equation $ydx-2xdy=0$ represents
    1. a family of straight lines
    2. a family of parabola
    3. a family of hyperbola
    4. a family of circles
62. The differential equation $ydx-2xdy=0$ represents
    1. a family of straight lines
    2. a family of parabola
    3. a family of hyperbola
    4. a family of circles
63. Two cards are drawn from a well shuffled pack, find the probability that one of them is an ace of heart:
    1. $\frac{1}{25}$
    2. $\frac{1}{26}$
    3. $\frac{1}{52}$
    4. $\frac{1}{13}$
64. Let $A$ and $B$ be two events such that $p(A)=3$, $p(A\bigcup B)=8$, if $A$ and $B$ are independent events, then $p(B)$:
    1. $\frac{5}{7}$
    2. $\frac{5}{13}$
    3. $\frac{1}{13}$
    4. $\frac{1}{2}$
65. The value of $\sqrt{3}sinx+cosx$ will be greatest when $x$ is equal to
    1. $\frac{\pi}{2}$
    2. $\frac{\pi}{4}$
    3. $\frac{\pi}{6}$
    4. $\frac{\pi}{3}$
66. If a particle in equilibrium is subjected to four forces, $F_1=2\hat{i}-5\hat{j}+6\hat{k}$, $F_2=\hat{i}+3\hat{j}-7\hat{k}$, $F_3=2\hat{i}-2\hat{j}-3\hat{k}$ and $F_4$, then $F_4$ is equal to
    1. $-5\hat{i}+4\hat{j}+4\hat{k}$
    2. $5\hat{i}-4\hat{j}-4\hat{k}$
    3. $3\hat{i}-2\hat{j}-\hat{k}$
    4. $3\hat{i}+\hat{j}-10\hat{k}$
67. Find the sum of the roots of equations $\sqrt{x-1}+\sqrt{2x-1}=x$
    1. $1$
    2. $2$
    3. $4$
    4. $6$
68. The equation $3x^2+7xy+2y^2+5x+2=0$ represents
    1. a pair of straight line
    2. en ellipse
    3. a hyperbola
    4. a parabola
69. The equation of the normal to the hyperbola $\frac{x^2}{16}-\frac{y^2}{9}=1$ at $(-4,0)$ is:
    1. $y=0$
    2. $y=x$
    3. $x=0$
    4. $x=-y$
70. Determine the exact value of the sum $Aretan 1+ Aretan 2 + Aretan3$
    1. $\frac{\pi}{2}$
    2. $\pi$
    3. $\frac{3\pi}{2}$
    4. $\frac{\pi}{3}$
71. The value of $\int_{0}^{\pi}\frac{x tanx}{secx+cosx}dx$ is
    1. $\frac{3\pi^2}{4}$
    2. $\frac{\pi^2}{3}$
    3. $\frac{\pi^2}{4}$
    4. $\frac{\pi^2}{2}$
72. The value of $\int_{0}^{\infty}\frac{dx}{1+x^2}$ is
    1. $\frac{\pi}{2}$
    2. $\frac{\pi}{4}$
    3. $0$
    4. $\infty$
73. The value of $\hat{i}\times(\bar{a}\times \hat{i})+\hat{j}\times(\bar{a}\times \hat{j})+\hat{k}\times(\bar{a}\times \hat{k})$
    1. $\bar{a}$
    2. $2\bar{a}$
    3. $3\bar{3}$
    4. $0$
74. $f(z)=\frac{1}{z}$ is not uniformly continuous in the region
    1. $0\leq|z|\leq1$
    2. $0\leq|z|<1$
    3. $0<|z|<1$
    4. $0<|z|\leq1$
75. $f(z)=z^3+3i$ is ……………..
    1. analytic everywhere except $z=3i$
    2. analytic everywhere except $z=0$
    3. analytic everywhere except $z=-3i$
    4. analytic everywhere
76. The projection of vector $\hat{i}-2\hat{j}+\hat{k}$ on the vector $4\hat{i}-4\hat{j}+7\hat{k}$ is
    1. $\frac{5\sqrt{6}}{10}$
    2. $\frac{19}{9}$
    3. $\frac{9}{19}$
    4. $\frac{\sqrt{6}}{19}$
77. If $\bar{a}=2\hat{i}+4\hat{j}-5\hat{k}$ and $\bar{b}=\hat{i}+2\hat{j}+3\hat{k}$ then $|\bar{a} \times \bar{b}|$ is
    1. $11\sqrt{5}$
    2. $11 \sqrt{3}$
    3. $11 \sqrt{7}$
    4. $11 \sqrt{2}$
78. Two parallel like forces $4n$ and $8n$ are acting $18m$ apart, find the position of the resultant from small force:
    1. $12N$
    2. $10N$
    3. $8N$
    4. None of these
79. $-(p\wedge q)$ is logically equivalent to \correctchoice $-p\wedge-q$
    1. $-p\vee -q$
    2. $-p\wedge q$
    3. $p\wedge -q$
80. $\int_{0}^{1}\frac{dx}{x}$ is
    1. $0$
    2. $1$
    3. $2$
    4. None of these
81. A sequence of numbers who's reciprocal from an arithmetic sequence is called ………… sequence
    1. Arithmetic
    2. Geometric
    3. Harmonic
    4. None
82. For $\frac{1}{4},\frac{2}{5},1,\ldots\ldots$ $6th$ term is
    1. $-2$
    2. $\frac{-2}{7}$
    3. $\frac{1}{9}$
    4. $\frac{-5}{6}$
83. $a_{27}$ of $7,\frac{23}{2},\frac{32}{2},\ldots\ldots\ldots.$ is
    1. $117$
    2. $124$
    3. $\frac{119}{2}$
    4. $\frac{146}{2}$
84. The fifth term and nth term of the $(AP.)$ $1,5\ldots.$ are \correctchoice $17,4n-3$
    1. $4n-3,17$
    2. $17,3n-4$
    3. $17,4n$
85. The $A.p.$ whose nth term is $2n-1$ is
    1. $1,3,6,\ldots.$
    2. $2,3,5\ldots.$
    3. $1,3,5,\ldots.$
    4. $5,3,1,\ldots.$
86. Probability theory was introduced by ……….
    1. British mathematician
    2. French mathematician
    3. German mathematician
    4. American mathematician
87. Events $A$, $B$ and $C$ are equally likely when
    1. $p(A)+p(B)=p(C)$
    2. $p(A)=p(B)+p(C)$
    3. $p(B)=p(A)+p(C)$
    4. $p(A)=p(B)=p(C)$
88. The relation between ${c_r}^n$ and ${p_r}^n$
    1. ${c_r}^n=r!{p_r}^n$
    2. ${c_r}^n\times r!={p_r}^n$
    3. ${c_r}^n\times n!={p_r}^n$
    4. None
89. $4!+5!$=
    1. $24$
    2. $144$
    3. $25$
    4. $23$
90. $\frac{6!}{8!}$=
    1. $\frac{1}{56}$
    2. $65$
    3. $56$
    4. $\frac{1}{56}$
91. The number of term in expansion of $(a-b)^17$ is
    1. $2$
    2. $17$
    3. $18$
    4. $20$
92. The coefficient of $21^{st}$ term in the expansion of $(a+b)^{23}$ is \correctchoice $1771$
    1. $2891$
    2. $3421$
    3. $1563$
93. Sum of even coefficient is equal to……. in binomial expression of $(1+x)^n$
    1. $2n$
    2. $2n-1$
    3. $2_{n-1}$
    4. $2^n$
94. If $n$ is an positive integer, then $n!>3^{n-1}$ is true for all
    1. $n>5$
    2. $n\geq5$
    3. $n\geq3$
    4. $n>3$
95. If $n$ is an positive integer, then $\left(\begin{array}{c}5\\ 5\end{array}\right)+\left(\begin{array}{c}6\\ 5\end{array}\right)+\left(\begin{array}{c}7\\ 5\end{array}\right)+\ldots+\left(\begin{array}{c}{n+4}\\ 5\end{array}\right)$ = \correctchoice $\left(\begin{array}{c}{n+5}\\ 6\end{array}\right)$
    1. $\left(\begin{array}{c}{n+5}\\ 5\end{array}\right)$
    2. $\left(\begin{array}{c}{n+4}\\ 4\end{array}\right)$
    3. $\left(\begin{array}{c}{n+6}\\ 6\end{array}\right)$
96. The $3600^{th}$ part of the degree is called ……..
    1. Degree
    2. Minute
    3. Second
    4. None
97. If $sin\phi<0$ and $tan\phi>0$ then terminal side line which quadrant
    1. $I$
    2. $II$
    3. $III$
    4. $IV$
98. $1$ radian = ……………….. degree
    1. $\mathring{57}17'45''$
    2. $\mathring{57}18'48''$
    3. $\mathring{57}18'32''$
    4. $\mathring{57}19'43''$
99. $(cot^2\phi-1)(sin^2\phi+1)$ = ………
    1. $1-sin^2\phi$
    2. $1+sin^2\phi$
    3. $cos2\phi-sin2\phi$
    4. All
100. Measure of the central angle of an arc of a circle whose length is equal to the radius of the circle known as
     1. $1$ Degree
     2. Radian
     3. Minute
     4. Second

1-b, 2-b, 3-c, 4-c, 5-c, 6-c, 7-c, 8-c, 9-c, 10-c, 11-c, 12-c, 13-c, 14-c, 15-c, 16-c, 17-c, 18-c, 19-c, 20-c, 21-c, 22-c, 23-c, 24-c, 25-c, 26-c, 27-c, 28-c, 29-c, 30-a, 31-d, 32-d, 33-a, 34-b, 35-c, 36-c, 37-c, 38-d, 39-a, 40-a, 41-b, 42-b, 43-b, 44-d, 45-a, 46-a, 47-d, 48-b, 49-d, 50-c, 51-c, 52-c, 53-c, 54-c, 55-c, 56-c, 57-b, 58-c, 59-c, 60-c, 61-c, 62-c, 63-c, 64-c, 65-c, 66-c, 67-c, 68-c, 69-c, 70-c, 71-c, 72-c, 73-c, 74-c, 75-c, 76-c, 77-c, 78-c, 79-a, 80-c, 81-c, 82-b, 83-b, 84-a, 85-c, 86-b, 87-d, 88-c, 89-c, 90-d, 91-c, 92-a, 93-c, 94-b, 95-a, 96-c, 97-c, 98-b, 99-c, 100-b