logarithm Model Questions & Answers, Practice Test for ibps clerk prelims 2023
ibps clerk prelims 2023 SYLLABUS WISE SUBJECTS MCQs
Ratio & Proportion
Percentages
Profit & Loss
Time & Work
Time & Distance
Simple Interest & Compound Interest
Mensuration: Area & Volumes
Algebraic Expressions
Trigonometric Ratios & Identity
Linear Equations
Quadratic Equations
Logarithm
Let P, Q, R be the mid-points of sides AB, BC, CA respectively of a triangle ABC. If the area of the triangle ABC is 5 square units, then the area of the triangle PQR is
Answer: (a)
$PQ = 1/2 AC, QR = 1/2 AB, PR = 1/2 BC$
${AB}/{QR} = {BC}/{PR} = {CA}/{PQ} = 2/1$
${\text"area of ABC"}/{\text"area of PQR"} = (2/1)^2 = 4/1$
= in Δ ABC = 5 $cm^2$
as Δ PQR = $5/4 cm^2$
What is the value of $(1/3 log_{10} 125 - 2 log_{10} 4 + log_{10} 32 + log_{10}1)$ ?
Answer: (a)
$1/3 log_{10} 125 – 2log_{10} 4 + log_{10}32 + log_{10}1$
= $1/3 log_{10}(5)^3 – 2log_{10}(2)^2 + log_{10}(2)^5$ + 0
= $log_{10}5 – 4log_{10}2 + 5log_{10}2$
= $log_{10}5 + log_{10}2 = log_{10} 5 × 2 = log_{10}$10 = 1
If ${\text"log"_8} x + {\text"log"_8} = {1/6} = {1/3}$, then the value of x is
Answer: (c)
$\text"log"_8 x + \text"log"_8$ = $1/6 = 1/3$
⇒${\text"log"_8 }(x × {1/6}) = {1/3}⇒{\text"log"_8}(x/6) = 1/3$
⇒$(8)^{1/3} = x/6$ [∵ if $\text"log"_a$ y = x, then $(a)^x$ = y]
⇒$(2^3)^{1/3} = x/6$⇒x = 12
If $log_{10} a = p and log_{10} b = q,$ then what is the value of $log_{10}(a^p p ^q)$?
Answer: (b)
Given that,
$log_{10} a = \text"p and" log_{10}$ b = q
$log_{10} (a^p b^q) = log_{10} a^p + log_{10} b^q$
= $p log_{10} a + q log_{10} b$
= p × p + q × q = $p^2 + q^2$
How many digits are there in $(54)^{10}$ ? (Given that $log_{10}2 = 0.301$ and $log_{10}3 = 0.477$)
Answer: (c)
$log(54)^{10}$ = 10 log 54 =10[3log3 + log2]
= 10[1.431 + 0.301] = 17.32
∴ Number of digits = 17 + 1 = 18
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