Download App

SEQUENCES AND SERIES — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSSEQUENCES AND SERIES1 Mark
MCQ
Choose the correct answer. The lengths of three unequal edges of a rectangular solid block are in G.P. If the volume of the block is $216cm^3$ and the total surface area is $252cm^2$, then the length of the longest edge is:
  • ✓
    12cm
  • B
    6cm
  • C
    18cm
  • D
    3cm
✓

Answer

Correct option: A.
12cm
  1. 12cm.
Solution:
Let the length, breadth and height of rectangular solid block be$\frac{\text{a}}{\text{r}},$ a and ar, respectively.
$\therefore\ \text{Volume}=\frac{\text{a}}{\text{r}}\times\text{a}\times\text{ar}=216\text{cm}^3$
$\Rightarrow\text{a}^3=216=6^3\Rightarrow\text{a}=6$
Also, Surface area $=2\Big(\frac{\text{a}}{\text{r}}.\text{a}+\text{a}.\text{ar}+\frac{\text{a}}{\text{r}}.\text{ar}\Big)=252$
$\Rightarrow2\text{a}^2\Big(\frac{1}{\text{r}}+\text{r}+1\Big)=252$
$\Rightarrow2\times36\Big(\frac{1+\text{r}^2+\text{r}}{\text{r}}\Big)=252$
$\Rightarrow2(1+\text{r}^2+\text{r})=7\text{r}$
$\Rightarrow2\text{r}^2-5\text{r}+2=0$
$\Rightarrow(2\text{r}-1)(\text{r}-2)=0$
$\therefore\ \text{r}=\frac{1}{2},2$
For $\text{r}=\frac{1}{2}:$ Length $=\frac{\text{a}}{\text{r}}=\frac{6\times2}{1}=12,$ Breadth = a = 6
Height $=\text{ar}=6\times\frac{1}{2}=3$
For r = 2: Length $=\frac{\text{a}}{\text{r}}=\frac{6}{2}=3,$ Breadth = a = 6
Height = ar = 6 × 2 = 12

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "MCQ" from SEQUENCES AND SERIES→SEQUENCES AND SERIES — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

If ${\tan ^2}\theta = 2{\tan ^2}\phi + 1,$ then $\cos 2\theta + {\sin ^2}\phi $ equals
→
The triangle $PQR$ is inscribed in the circle ${x^2} + {y^2} = 25$. If $Q$ and $R$ have co-ordinates $(3,4)$ and $(-4, 3)$ respectively, then $\angle QPR$ is equal to
→
If ${x^2} + 2x + 2xy + my - 3$ has two rational factors, then the value of $m$ will be
→
The line $2x + 3y = 12$ meets the $x -$ axis at $A$ and the $y -$ axis at $B$ . The line through $(5, 5)$ perpendicular to $AB$ meets the $x -$ axis, $y -$ axis $\&$ the line $AB$ at $C, D, E$ respectively. If $O$ is the origin, then the area of the $OCEB$ is :
→
The value of $\mathop {\lim }\limits_{x \to \infty } \frac{{{x^2}\sin \frac{1}{x} - x}}{{1 - |x|}}$ is
→
The number of ways in which 10 different diamonds can be arranged to form a necklace, is:
→
The length of the axes of the conic $9{x^2} + 4{y^2} - 6x + 4y + 1 = 0$, are
→
How many numbers between $5000$ and $10,000$ can be formed using the digits $1, 2, 3, 4, 5, 6, 7, 8, 9$ each digit appearing not more than once in each number
→
Let $T_1$ and $T_2$ be two distinct common tangents to the ellipse $E: \frac{x^2}{6}+\frac{y^2}{3}=1$ and the parabola $P: y^2=12 x$. Suppose that the tangent $T_1$ touches $P$ and $E$ at the point $A_1$ and $A_2$, respectively and the tangent $T_2$ touches $P$ and $E$ at the points $A_4$ and $A_3$, respectively. Then which of the following statements is(are) true?

($A$) The area of the quadrilateral $A_1 A _2  A _3 A _4$ is $35$ square units

($B$) The area of the quadrilateral $A_1 A_2 A_3 A_4$ is $36$ square units

($C$) The tangents $T_1$ and $T_2$ meet the $x$-axis at the point $(-3,0)$

($D$) The tangents $T_1$ and $T_2$ meet the $x$-axis at the point $(-6,0)$

→
The number of solution of ${\log _2}(x + 5) = 6 - x$ is
→