The four arithmetic means between 3 and 23 are - Vidyadip

MCQ

The four arithmetic means between $3$ and $23$ are

A
$5, 9, 11, 13$
✓
$7, 11, 15, 19$
C
$5, 11, 15, 22$
D
$7, 15, 19, 21$

✓

Answer

Correct option: B.

$7, 11, 15, 19$

b
(b) Let four arithmetic means are ${A_1},{A_2},\;{A_3}$ and ${A_4}$.

So $3,\;{A_1},\;{A_2},\;{A_3},\;{A_4},\;23$

$ \Rightarrow $ ${T_6} = 23 = a + 5d$

$ \Rightarrow $ $d = 4$

Thus ${A_1} = 3 + 4 = 7,\;{A_2} = 7 + 4 = 11,\;$

$A_3 = 11+4 =15 ,\, A_4 = 15+ 4=19$

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

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

The area of the rectangle formed by the perpendiculars from the centre of the standard ellipse to the tangent and normal at its point whose eccentric angle is $\pi /4$ is :

Let $f :[0,1] \rightarrow R$ be a twice differentiable function in $(0,1)$ such that $f (0)=3$ and $f (1)=5$. If the line $y=2 x+3$ intersects the graph of $f$ at only two distinct points in $(0,1)$, then the least number of points $x \in(0,1)$, at which $f ^{\prime \prime}( x )=0$, is$......$

The number of distinct real values of $\lambda$, for which the vectors $-\lambda^2 \hat{i}+\hat{j}+\hat{k}, \hat{i}-\lambda^2 \hat{j}+\hat{k}$ and $\hat{i}+\hat{j}-\lambda^2 \hat{k}$ are coplanar, is

$\int_{}^{} {(1 - {x^2})\log x\;dx = } $

A fair die is tossed repeatedly until a six is obtained. Let $\mathrm{X}$ denote the number of tosses required and let $\mathrm{a}=\mathrm{P}(\mathrm{X}=3), \mathrm{b}=\mathrm{P}(\mathrm{X} \geq 3)$ and $\mathrm{c}=$ $\mathrm{P}(\mathrm{X} \geq 6 \mid \mathrm{X}>3)$. Then $\frac{\mathrm{b}+\mathrm{c}}{\mathrm{a}}$ is equal to

If sum of infinite terms of a $G.P.$ is $3$ and sum of squares of its terms is $3$, then its first term and common ratio are

Let $A B C D$ be a quadrilateral such that there exists a point $E$ inside the quadrilateral satisfying $A E=B E=C E=D E$. Suppose $\angle D A B, \angle A B C, \angle B C D$ is an arithmetic progression. Then the median of the set $\{\angle D A B, \angle A B C, \angle B C D\}$ is

Let $V_{\mathrm{r}}$ denote the sum of the first $\mathrm{r}$ terms of an arithmetic progression $(A.P.)$ whose first term is $\mathrm{r}$ and the common difference is $(2 \mathrm{r}-1)$. Let

$T_{\mathrm{I}}=V_{\mathrm{r}+1}-V_{\mathrm{I}}-2 \text { and } \mathrm{Q}_{\mathrm{I}}=T_{\mathrm{r}+1}-\mathrm{T}_{\mathrm{r}} \text { for } \mathrm{r}=1,2, \ldots$

$1.$ The sum $V_1+V_2+\ldots+V_n$ is

$(A)$ $\frac{1}{12} n(n+1)\left(3 n^2-n+1\right)$

$(B)$ $\frac{1}{12} n(n+1)\left(3 n^2+n+2\right)$

$(C)$ $\frac{1}{2} n\left(2 n^2-n+1\right)$

$(D)$ $\frac{1}{3}\left(2 n^3-2 n+3\right)$

$2.$ $\mathrm{T}_{\mathrm{T}}$ is always

$(A)$ an odd number $(B)$ an even number

$(C)$ a prime number $(D)$ a composite number

$3.$ Which one of the following is a correct statement?

$(A)$ $Q_1, Q_2, Q_3, \ldots$ are in $A.P.$ with common difference $5$

$(B)$ $\mathrm{Q}_1, \mathrm{Q}_2, \mathrm{Q}_3, \ldots$ are in $A.P.$ with common difference $6$

$(C)$ $\mathrm{Q}_1, \mathrm{Q}_2, \mathrm{Q}_3, \ldots$ are in $A.P.$ with common difference $11$

$(D)$ $Q_1=Q_2=Q_3=\ldots$

Give the answer question $1,2$ and $3.$

If $\hat{a}, \hat{b}, \hat{c}$ are unit vectors, then least value of $\left | \hat{a}+\hat{b} \right |^2+\left | \hat{b}+\hat{c} \right |^2+\left | \hat{c}+\hat{a} \right |^2$ will be-

The integral $\int_{\pi /6}^{\pi /4} {\frac{{dx}}{{\sin \,2x\,\left( {{{\tan }^5}\,x + {{\cot }^5}\,x} \right)}}} $ equals