1. (i) Find the next term of the list of numbers \[\mathbf{1}/\mathbf{6},\text{ }\mathbf{1}/\mathbf{3},\text{ }\mathbf{2}/\mathbf{3},\text{ }\ldots \] (ii) Find the next term of the list of numbers \[\mathbf{3}/\mathbf{16},\text{ }-\mathbf{3}/\mathbf{8},\text{ }{\scriptscriptstyle 3\!/\!{ }_4},\text{ }-\mathbf{3}/\mathbf{2},\ldots \]

1. (i) Find the next term of the list of numbers

$\mathbf{1}/\mathbf{6},\text{ }\mathbf{1}/\mathbf{3},\text{ }\mathbf{2}/\mathbf{3},\text{ }\ldots$

(ii) Find the next term of the list of numbers

$\mathbf{3}/\mathbf{16},\text{ }-\mathbf{3}/\mathbf{8},\text{ }{\scriptscriptstyle 3\!/\!{ }_4},\text{ }-\mathbf{3}/\mathbf{2},\ldots$

1. (i) Find the next term of the list of numbers

$\mathbf{1}/\mathbf{6},\text{ }\mathbf{1}/\mathbf{3},\text{ }\mathbf{2}/\mathbf{3},\text{ }\ldots$

(ii) Find the next term of the list of numbers

$\mathbf{3}/\mathbf{16},\text{ }-\mathbf{3}/\mathbf{8},\text{ }{\scriptscriptstyle 3\!/\!{ }_4},\text{ }-\mathbf{3}/\mathbf{2},\ldots$

From the question,

First term a =

$1/6$

Then,

$\begin{array}{*{35}{l}} ~r\text{ }=\text{ }\left( 1/3 \right)\text{ }\div \text{ }\left( 1/6 \right) \\ r\text{ }=\text{ }\left( 1/3 \right)\text{ }\times \text{ }\left( 6/1 \right) \\ r\text{ }=\text{ }6/3 \\ r\text{ }=\text{ }2 \\ \end{array}$

Therefore, next term =

$~2/3\text{ }\times \text{ }2\text{ }=\text{ }4/3$

(ii) Find the next term of the list of numbers

$\mathbf{3}/\mathbf{16},\text{ }-\mathbf{3}/\mathbf{8},\text{ }{\scriptscriptstyle 3\!/\!{ }_4},\text{ }-\mathbf{3}/\mathbf{2},\ldots$

Solution:-

From the question,

First term a = 3/16

Then,

$\begin{array}{*{35}{l}} r\text{ }=\text{ }\left( -3/8 \right)\text{ }\div \text{ }\left( 3/16 \right) \\ r\text{ }=\text{ }\left( -3/8 \right)\text{ }\times \text{ }\left( 16/3 \right) \\ r\text{ }=\text{ }\left( -3\text{ }\times \text{ }16 \right)/\left( 8\text{ }\times \text{ }3 \right) \\ r\text{ }=\text{ }\left( -1\text{ }\times \text{ }2 \right)/\text{ }\left( 1\text{ }\times \text{ }1 \right) \\ r\text{ }=\text{ }-2 \\ \end{array}$

Therefore, next term =

$~-3/2\text{ }\times \text{ }\left( -2 \right)\text{ }=\text{ }6/2\text{ }=\text{ }3$

More Material

A …… lens is used to correct myopia and a ….. lens is used to correct hypermetropia.
A Concave, concave
B Convex, convex
C Convex, concave
D Concave, convex

Rate of reaction of any substance depends on
(A) active mass
(B) molecular weight
(C) atomic weight
(D) equivalent weight

Formula of oleum is
(A) $\mathrm{H}_{2} \mathrm{~S}_{2} \mathrm{O}_{7}$
(B) $\mathrm{H}_{2} \mathrm{SO}_{4}$
(C) $\mathrm{H}_{2} \mathrm{SO}_{3}$
(D) $\mathrm{H}_{2} \mathrm{SO}_{5}$

A line passes through the point (2, 1, -3) and is parallel to the vector Find the equations of the line in vector and Cartesian forms.

Two cells of emf $\varepsilon_{1}$ and $\varepsilon_{2}$ , internal resistance $r_{1}$ and $r_{2}$ , connected in parallel. The equivalent emf of the combination is- (A) $\frac{\varepsilon_{1} r_{1}+\varepsilon_{1} r_{1}}{r_{1}+r_{2}}$ (B) $\frac{\varepsilon_{1} r_{2}+\varepsilon_{2} r_{1}}{r_{1}+r_{2}}$ (C) $\sqrt{\varepsilon_{1} \times \varepsilon_{2}}$ (D) $\frac{\varepsilon_{1}+\varepsilon_{2}}{2}$

More Material

A …… lens is used to correct myopia and a ….. lens is used to correct hypermetropia.
A Concave, concave
B Convex, convex
C Convex, concave
D Concave, convex

Rate of reaction of any substance depends on
(A) active mass
(B) molecular weight
(C) atomic weight
(D) equivalent weight

Formula of oleum is
(A) $\mathrm{H}_{2} \mathrm{~S}_{2} \mathrm{O}_{7}$
(B) $\mathrm{H}_{2} \mathrm{SO}_{4}$
(C) $\mathrm{H}_{2} \mathrm{SO}_{3}$
(D) $\mathrm{H}_{2} \mathrm{SO}_{5}$

A line passes through the point (2, 1, -3) and is parallel to the vector Find the equations of the line in vector and Cartesian forms.

If the points $A(a, 0), B(0, b)$ and $C(1,1)$ are collinear, prove that $\frac{1}{a}+\frac{1}{b}=1$

If $A(-2,0), B(0,4)$ and $C(0, k)$ be three points such that area of a $A B C$ is 4 sq units, find the value of $k$ .

Find the value of $k$ for which the area of a ABC having vertices $A(2,-6), B(5,4)$ and $C(k, 4)$ is 35 sq units.

Find the value of $k$ for which the points $A(1,-1), B(2, k)$ and $C(4,5)$ are collinear.

Find the value of $k$ for which the points $P(5,5), Q(k, 1)$ and $R(11,7)$ are collinear.

Find the value of $k$ for which the points $A(3,-2), B(k, 2)$ and $C(8,8)$ are collinear.

Use determinants to show that the following points are collinear. $P(-2,5), Q(-6,-7)$ and $R(-5,-4)$

Sign up now and study all subjects for free

Class

Syllabus

Question Papers

Social Media

Apps