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20 questions · timed · auto-graded

MCQ 11 Mark
Find the value of $\lim _{x \rightarrow-6}(10-3 x)^{\frac{-1}{2}}$.
  • A
    $5$
  • B
    $\frac{1}{25}$
  • C
    $-\frac{1}{5}$
  • $\frac{1}{5}$
Answer
Correct option: D.
$\frac{1}{5}$
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MCQ 21 Mark
Find the value of $a$, if $\lim _{x \rightarrow 0} \frac{2}{3 x-5}=\frac{1}{a}$.
  • $5$
  • B
    $1$
  • C
    $-1$
  • D
    $10$
Answer
Correct option: A.
$5$
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MCQ 31 Mark
$\lim _{x \rightarrow 0} \frac{x^2-5 x+6}{x+1}=6$ What is the value of $\lim _{x \rightarrow 0} f(x)$, if $f(x)=3\left(\frac{x^2-5 x+6}{x+1}\right) ?$
  • $18$
  • B
    $2$
  • C
    $6$
  • D
    $0$
Answer
Correct option: A.
$18$
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MCQ 51 Mark
If $x=2+t$ and $x \rightarrow 0$ then $t$ tends to which value ?
  • A
    $0$
  • $-2$
  • C
    $2$
  • D
    $4$
Answer
Correct option: B.
$-2$
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MCQ 61 Mark
What is the value of $\lim _{x \rightarrow 1} \frac{x^2-1}{x-1}$ ?
  • $\frac{9}{2}$
  • B
    $0$
  • C
    $1$
  • D
    $\frac{5}{2}$
Answer
Correct option: A.
$\frac{9}{2}$
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MCQ 71 Mark
What is the value of $\lim _{x \rightarrow 2} \frac{x^4-16}{x-2}$ ?
  • A
    $80$
  • B
    $16$
  • $32$
  • D
    $10$
Answer
Correct option: C.
$32$
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MCQ 91 Mark
What is the value of $\lim _{x \rightarrow 2} \frac{x^2-5 x+6}{x+2} ?$
  • A
    Indeterminate
  • B
    $4$
  • $0$
  • D
    $\frac{1}{4}$
Answer
Correct option: C.
$0$
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MCQ 111 Mark
What is the value of $a$, if the modulus form of $N(a, 1.5)$ is $|x - 5 |$
  • A
    $1.5$
  • B
    $K$
  • $5$
  • D
    $3.5$
Answer
Correct option: C.
$5$
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MCQ 121 Mark
State the modulus form for $N(-1,0.1)$.
  • A
    $|x-1|<0.1$
  • B
    $|x-1|<-0.1$
  • $|x+1|<0.1$
  • D
    $|x+1|>0.1$
Answer
Correct option: C.
$|x+1|<0.1$
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MCQ 131 Mark
What is the interval form for $N(-3,0.033)$ ?
  • A
    $(-2.967,3.033)$
  • $(-3.033,-2.967)$
  • C
    $(-3.33,3.033)$
  • D
    $(3.033,-2.967)$
Answer
Correct option: B.
$(-3.033,-2.967)$
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MCQ 141 Mark
State the interval form for $|2 x+5|<\frac{1}{2}$.
  • $\left(\frac{-11}{4}, \frac{-9}{4}\right)$
  • B
    $\left(\frac{9}{4}, \frac{11}{4}\right)$
  • C
    $\left(\frac{-11}{2}, \frac{-1}{2}\right)$
  • D
    $\left(\frac{-11}{4}, \frac{9}{4}\right)$
Answer
Correct option: A.
$\left(\frac{-11}{4}, \frac{-9}{4}\right)$
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MCQ 151 Mark
What is the an interval form for $|x-2|<0.02 ?$
  • A
    $(1.98,2.2)$
  • B
    $(0,4)$
  • C
    $(-2.2,2.2)$
  • $(1.98,2.02)$
Answer
Correct option: D.
$(1.98,2.02)$
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MCQ 161 Mark
What is the modulus form for $1.05$ neighbourhood of $10 ?$
  • A
    $|x-8.95|<1.05$
  • $|x-10|<1.05$
  • C
    $|x-1.05|<10$
  • D
    $|x+10|<1.05$
Answer
Correct option: B.
$|x-10|<1.05$
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MCQ 171 Mark
If the limits of functions $f(x)$ and $g(x)$ as $x \rightarrow 5$ are $12$ and $3$ respectively, what are the respective limits of $[f(x)-g(x)]$ and $[f(x)+g(x)]$ functions as $x \rightarrow 5 ?$
  • $9$ and $4$
  • B
    $4$ and $9$
  • C
    $15$ and $9$
  • D
    $15$ and $36$
Answer
Correct option: A.
$9$ and $4$
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MCQ 181 Mark
What is an interval known as, when an element ' $a$ ' is included to the open interval $(a, b)$ ?
  • A
    Open interval
  • B
    Closed interval
  • Closed-open interval
  • D
    Open-closed interval
Answer
Correct option: C.
Closed-open interval
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MCQ 191 Mark
In usual notations, what kind of interval is $(a, b]$ ?
  • A
    Open interval
  • B
    Closed interval
  • C
    Closed-open interval
  • Open-closed interval
Answer
Correct option: D.
Open-closed interval
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MCQ 201 Mark
In usual notations, what kind of interval is $[a, b]$ ?
  • A
    Open interval
  • Closed interval
  • C
    Closed-open interval
  • D
    Open-closed interval
Answer
Correct option: B.
Closed interval
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MCQ - Statistics STD 12 Commerce Questions - Vidyadip