(Time: 2 Hrs.\( ) \)
First 1 arin Exam
(Page-2)
Std. \( 10^{\text {th }} \)
Sub. : Mathematics (I) (71) (Semi)
Marks : 40
Q. 1 (A) Choose correct alternative for each of the following questions.
(4)
1) For simultaneous equations in variables \( x \) and \( y \), if \( D=4 \) and \( D_{x}=12 \) then what is \( x \) ?
a) \( -\frac{1}{3} \)
b) -2
e) 3
d) \( \frac{1}{3} \)
2) Which one is the quadratic equation ?
a) \( x(x+5)=2 \)
b) \( \frac{5}{y}-4=y^{2} \)
c) \( b-1=2 b \)
d) \( \frac{1}{x}(x+5)=x^{3} \)
3) For an given A.P. \( t_{7}=4, d=-4 \) then find a
a) 6
b) 7
c) 20
\( 1 d 28 \)
4) In the format of GSTIN there are \( \qquad \) alpha numerals.
a) 15
b) 10
c) 16
d) 9
(B) Solve the following subquestions.
1) For the equation \( x+y=6 \), if the value of \( x \) is 4 then find the value of \( y \)
2) Determine the linear and quadratic equation
4 then find the value of
i) quadratic ean
ii) Linew eq
i) \( 5 a^{2}-3 a+7=0 \)
ii) \( 5 b+4=0 \)
\( 4+y=6 \)
- (4)ke=h
\[
\left\{\begin{array}{l}
=6 \quad \text { (4) } \\
4+y=6 \\
y=6-4 \\
y=?
\end{array}\right.
\]
3) What is the sum of the first 30 natural numbers? \( X \)
4) \( \mathrm{FV}=? 100 \), premium \( =? 65 \) then \( \mathrm{MV}= \) ? \( \times \) Dif Cound
Q. 2
A) Complete any two activities.
(4)
1) Find the value of \( A=\left|\begin{array}{ll}5 & 3 \\ 7 & 9\end{array}\right| \)
\[
\begin{array}{l}
\text { Solution: } A=\left|\begin{array}{ll}
5 & 3 \\
7 & 9
\end{array}\right| \\
=5 \times \square-3 \times \square \\
=45-21=24
\end{array}
\]
4
2) One root of the equation \( x^{2}-7 x+k=0 \) is 4 . Complete the following activity to find the value of \( k \).
Solution: One root of the equation \( x^{2}-7 x+k=0 \) is 4
\( \therefore x=4 \), Put the value of \( x \) in the equation
\[
(4)^{2}-7 \times 4+k=0, \quad 16-28+k=0, k=12
\]
3) Find the sum of first 50 terms of the A.P. 14, 16, 18, 20, \( \qquad \)
Solution: \( a=14 \),
\[
\begin{aligned}
d & =16-14=2, n=50 \\
S_{n} & =\frac{n}{2}[2 a+(n-1) d] \\
S_{50} & =\frac{50}{2}[2 \times 14+(50-1) \times \square] \\
& =25[2 \times 14+98] \\
& =25 \times \square \times 26 \\
& =3150
\end{aligned}
\]
\( \begin{array}{r}10 \\ 9 \\ 2 \\ \hline 2\end{array} \)
(PTO 2)
