HSC State board/Matriculation objective type Maths questions from 34 to 40 are provided in this post. These questions are very important to score 100% in the public examination.
34) A spherical snowball is melting in such a way that its volume is decreasing at a rate of 1 $ cm^3 $/min. The rate at which the diameter is diameter when the diameter is 10 cms is:
a) $ -\frac{1}{50\pi} \; cm/min $
b) $ \frac{1}{50\pi} \; cm/min $
c) $ -\frac{11}{75\pi} \; cm/min $
d) $ -\frac{2}{75\pi} \; cm/min $
35) The surface area of a sphere when the volume is increasing at the same rate as its radius, is:
a) 1
b) $ \frac{1}{2\pi} $
c) $ 4\pi $
d) $ \frac{4\pi}{3} $
36) If $ [\overrightarrow{a}+\overrightarrow{b}, \overrightarrow{b}+\overrightarrow{c}, \overrightarrow{c}+\overrightarrow{a}] $, then $ [\overrightarrow{a}, \overrightarrow{b}, \overrightarrow{c}] $ is:
a) 4
b) 16
c) 32
d) –4
37) The equation of the plane passing through the point (2, 1, –1) and the line of intersection of the planes $ \overrightarrow{r}.(\overrightarrow{i}+3\overrightarrow{j}-\overrightarrow{k})=0 $ and $ \overrightarrow{r}.(\overrightarrow{j}+2\overrightarrow{k})=0 $ is:
a) x + 4y – z = 0
b) x + 9y + 11z = 0
c) 2x + y – z + 5 = 0
d) 2x – y + z = 0
38) The two lines $ \frac{x-1}{2}=\frac{y-1}{-1}=\frac{z}{1} $ and $ \frac{x-2}{3}=\frac{y-1}{-5}=\frac{z-1}{2} $ are:
a) parallel
b) intersecting
c) skew
d) perpendicular
39) The angle between the two vectors $ \overrightarrow{a} $ and $ \overrightarrow{b} $ if $ |\overrightarrow{a} \times \overrightarrow{b}|=\overrightarrow{a}.\overrightarrow{b} $, is:
a) $ \frac{\pi}{4} $
b) $ \frac{\pi}{3} $
c) $ \frac{\pi}{6} $
d) $ \frac{\pi}{2} $
40) Chord AB is a diameter of the sphere $ |\overrightarrow{r}-(2\overrightarrow{i}+\overrightarrow{j}-6\overrightarrow{k})|=\sqrt18 $ with coordinate of A as (3, 2, –2). The coordinate of B is:
a) (1, 0, 10)
b) (-1, 0, –10)
c) (-1, 0, 10)
d) (1, 0, –10)
Refer to the previous question range in Set 1 here for 1-6 , 7-12 , 13-19 , 20-26 , and 27-33 .
HSC Maths Objective Questions
SSLC Maths - Objective type Questions
Refer to this post for questions 27 to 33. These questions are of multiple choice type (choose the best answer).
27) The curved surface area of a sphere of radius 5, intercepted between two parallel planes of distance 2 and 4 on the same side from the centre is:
a) $ 20\pi $
b) $ 40\pi $
c) $ 10\pi $
d) $ 30\pi $
28) The arc length of the curve y = f(x) from x = a to x = b is:
a) $ \int_{a}^{b}\sqrt{(1+(\frac{\mathrm{d}y }{\mathrm{d} x})^2}\;\;dx $
b) $ \int_{a}^{b}\sqrt{(1+(\frac{\mathrm{d}x }{\mathrm{d} y})^2}\;\;dx $
c) $ 2\pi\int_{a}^{b}y\sqrt{(1+(\frac{\mathrm{d}y }{\mathrm{d} x})^2}\;\;dx $
d) $ 2\pi\int_{a}^{b}y\sqrt{(1+(\frac{\mathrm{d}x }{\mathrm{d} y})^2}\;\;dx $
29) Solution of $ \frac{\mathrm{d}y }{\mathrm{d} x} + mx=0 $, where m<0 is:
a) $ x=ce^{my} $
b) $ x=ce^{-my} $
c) $ x=my+c $
d) $ x=c $
30) The differential equation $ (\frac{\mathrm{d}y }{\mathrm{d} x})^2\;+\;5y^\frac{1}{3} = x $ is:
a) of order 2 and degree 1
b) of order 1 and degree 2
c) of order 1 and degree 6
d) of order 1 and degree 3
31) The equations of the latus rectum of $ \frac{x^2}{16}+\frac{y^2}{9}=1 $, are:
a) $ y=\pm \sqrt{7} $
b) $ x=\pm \sqrt{7} $
c) $ x=\pm \;7 $
d) $ y=\pm\; 7 $
32) The eccentricity of the hyperbola $ 12y^2-4x^2-24x+48y-127=0 $ is:
a) 4
b) 3
c) 2
d) 6
33) The length of the latus rectum of the rectangular hyperbola xy = 32 is :
a) $ 8\sqrt{2} $
b) $ 32 $
c) $ 8 $
d) $ 16 $
Refer to the question ranges here 1-6 , 7-12 , 13-19 and 20-26 .
+2 HSC Maths - Practice Questions
Question series from 20 to 26 are provided below. For more questions, refer to 'Related Post' section.
20) The are of the parallelogram having a diagonal $ 3\overrightarrow{i}+\overrightarrow{j}-\overrightarrow{k} $ and a side $ \overrightarrow{i}-3\overrightarrow{j}+4\overrightarrow{k} $ is:
a) $ 10\sqrt{3} $
b) $ 6\sqrt{30} $
c) $ \frac{3}{2}\sqrt{30} $
d) $ 3\sqrt{30} $
21) In the set of integers under the operation * defined by $ a*b=a+b-1 $, the identity element is
a) 0
b) 1
c) a
d) b
22) $ \mu_{2}=20 $, $ \mu_{2}=276 $ for a discrete random variable X. Then, the mean of the random variable X is:
a) 16
b) 5
c) 3
d) 1
23) The random variable X follows normal distribution, $ f(x)=ce^{-\frac{1}{2}\frac{(x-100)^2}{25}} $. Then the value of ‘c’ is:
a) $ \sqrt{2\pi} $
b) $ \frac{1}{\sqrt{2\pi}} $
c) $ 5\sqrt{2\pi} $
d) $ \frac{1}{5\sqrt{2\pi}} $
24) A discrete random variable X has probability mass function p(x), then
a) $ 0\leq p(x)\leq1 $
b) $ p(x)\geq 0 $
c) $ p(x)\leq1 $
d) 0< p(x)<1
25) In 16 throws of a die, getting an even number is considered a success. Then the variance of the success is:
a) 4
b) 6
c) 2
d) 256
26) The area of the region bounded by the graph of $ y = sin x $ and $ y = cos \;x $ between $ x = 0 $ and $ x = \frac{\pi}{4} $ is :
a) $ \sqrt2\;+\;1 $
b) $ \sqrt2\;-\;1 $
c) $ 2\sqrt2\;-\;2 $
d) $ 2\sqrt2\;+\;2 $
Refer to questions 1-6 , 7-12 and 13-19 here.
Plus 2 - Mathematics Important Questions
Questions 13-19 are provided in this post for practice. If you want more +2 sample one mark questions, refer to the 'Related Post' section below.
13) If $ -i + 2 $ is one root of the equation $ ax^{2}-bx+c=0 $, then the other root is
a) $ –i - 2 $
b) $ i - 2 $
c) $ 2 + i $
d) $ 2i + i $
14) Polynomial equation P(x) = 0 admits conjugate pairs of imaginary roots only if the coefficients are
a) imaginary
b) complex
c) real
d) either real or complex
15) The line $ 4x+2y=c $ is a tangent to the parabola $ y^{2} = 16x $ then c is:
a) -1
b) –2
c) 4
d) -4.
16) The rank of the diagonal matrix
$ \begin{bmatrix} -1 & & & & \\ & 2 & & & \\ & & 0 & & \\ & & & -4 & \\ & & & & 0 \\ \end{bmatrix} $ is:
a) 0
b) 2
c) 3
d) 5
17) If A is scalar matrix with scalar k $ \neq $, of order 3, then $ A^{-1} $is:
a) $ \frac{1}{k^2}I $
b) $ \frac{1}{k^3}I $
c) $ \frac{1}{k}I $
d) $ KI $
18) In a system of three linear non-homogenous equations with three unknowns, if $ \Delta \; = \; 0 $ and $ \Delta_{x} \; = \; 0 $, $ \Delta_{y} \; \neq \; 0 $ and $ \Delta_{z} \; = \; 0 $ then the system has:
a) unique solution
b) two solutions
c) infinitely many solutions
d) no solution.
19) In the system of three linear equations with three unknowns, in the non-homogenous system, $ \rho (A) \; = \; \rho (A,B) \;= \; 2$ ; then the system
a) has unique solution
b) reduces to two equations and has infinitely many solutions
c) reduces to a single equation and has infinitely many solutions
d) is inconsistent.
Check here for questions 1-6 and 7-12 .
FTP Data Directly to SQL Loader
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name varchar2(15),
rollno number
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Model One Mark Questions - SSLC Mathematics
+2 Maths one mark question collection for Practice - Part2:
7) If ‘f' has a local extremum at ‘a’ and if $ f^{'}(a) $ exists then
a) $ f^{'}(a) < 0 $
b) $ f^{'}(a) > 0 $
c) $ f^{'}(a) = 0 $
d) $ f^{''}(a) = 0 $
8) If $ u = log[\frac{(x^{2}+y^{2})}{xy}] $ then $ x\frac{\partial u}{\partial x} + y\frac{\partial u}{\partial y} $ is
a) 0
b) u
c) 2u
d) $ u^{-1} $
9) The curve $ a^{2}y^{2} = x^{2} (a^{2}-x^{2}) $ has
a) only one loop between x = 0 and x = a
b) two loops between x = 0 and x = a
c) two loops between x = -a and x = a
d) no loop.
10) The value of $ \int_{0}^{\frac{\pi }{4}} cos^{3}\; 2x\; dx $ is:
a) $ \frac{2}{3} $
b) $ \frac{1}{3} $
c) 0
d) $ \frac{2\pi}{3} $
11) The modulus and amplitude of the complex number $ [e^{(3-\frac{i\pi}{4})}]^{3} $ are respectively:
a) $ e^9 $, $ \frac{\pi }{2} $
b) $ e^9 $, $ -\frac{\pi }{2} $
c) $ e^6 $, $ -\frac{3\pi }{4} $
d) $ e^9 $, $ -\frac{3\pi }{4} $
12) If P represents the variable complex number ‘z’, and if $ \mid 2z-1\mid \; = \; 2\mid z \mid $, then the locus of P is:
a) the straight line $ x \; = \; \frac{1}{4} $
b) the straight line $ y \; = \; \frac{1}{4} $
c) the straight line $ z \; = \; \frac{1}{2} $
d) the circle $ x^{2}+y^{2}-4x-1=0 $.
Refer here for question range 1-7 .
Discrete Mathematics–Important Points for Review
Some important points / Questions in +2 Discrete Mathematics from an SSLC examination angle.
1) N = set of all Natural numbers = { 1,2,3,……..}
2) W = set of all whole numbers = {0,1,2,3,……}
3) Z = set of integers = {0,+1,-1,+2,-2,…….}
4) Z+ = N
5) Q = the set of all rationals
6) Q* = the set of all non zero rationals
7) R = the set of all reals
8) R* = the set of all non zero reals
9) R+ = the set of all positive reals
10) C = the set of all complex numbers
11) C+ = the set of all non zero complex numbers
12) Closure Axiom : Binary operation on G is a map from G x G into G. If * is a binary operation then
$\forall \; a, b \; \epsilon \; G, a * b \; \epsilon \; G$
This axiom can also be called as the closure property of G w.r.t. *.
13) Associative Axiom: $(a*b)*c=a*(b*c)\; \forall \; a,b,c \; \epsilon \; G$
14) Identity Axiom: If there exists an element of the form $e \; \epsilon \; G$ such that $a*e=e*a \; \forall \; a \; \epsilon \; G$ then e is called the identity.
15) Commutative Axiom: * is commutative if $a*b=b*a \; \forall \; a,b \; \epsilon \; G$
Important One Mark Questions - HSC Mathematics
SSLC Maths one mark question collection for Practice - Part1:
These questions will be very useful for +2 State board examination.
1) If $f^{'}(x)=\sqrt{x}$ and $f(1)$=2, then $f(x)$ is:
1) $-\frac{2}{3}(x\sqrt{x}+2)$
2) $\frac{3}{2}(x\sqrt{x}+2)$
3) $\frac{2}{3}(x\sqrt{x}+2)$
4) $-\frac{2}{3}x(x\sqrt{x}+2)$
2) The differential equations corresponding to $xy=c^{2}$ , where ‘c’ is an arbitrary constant, is:
1) $xy^{''}+x=0$
2) $y^{''}=0$
3) $xy^{'}+y=0$
4) $xy^{''}-x=0$
3) if ‘p’ is true and ‘q’ is false then which of the following is not true?
1) $p \to \ q$ is false
2) $p \vee q$ is ture
3) $p \wedge q$ is false
4) $p \leftrightarrow q$ is true
4) If truth values of ‘p’ is T and ‘q’ is F, then which of the following are having the truth value T?
a) $p \vee q$
b) ~$p \vee q$
c) $p \vee$~$q$
d) $p \wedge$~$q$
1) a, b, c only
2) a, b, d only
3) a, c, d only
4) b, c, d only
5) Which of the following is not a binary operation on R?
1) $a\ast b=ab$
2) $a\ast b=a-b$
3) $a\ast b=\sqrt{ab}$
4) $(a\ast b)=\sqrt({a^{2}}+{b^{2}})$
6) The curve $y=-e^{-x}$ is:
1) concave upward for $x > 0$
2) concave downward for $x > 0$
3) everywhere concave upward
4) everywhere concave downward
Refer here for questions 7 - 12.
India Vs England–Live Streaming -World Cup ODI
India v England, ICC Cricket World Cup 2011, Group B, Bangalore, (14:30 local time | 09:00 GMT).
Aloo Palak–Recipe
Item | Measurement |
Chopped Spinach | 3 Cups |
Large Onions | 2, Chopped fine |
Potato | 2, boiled and peeled |
Tomato | 1, grated |
Green Chillies | 2 |
Ginger | 1 small piece |
Lemon Juice | 1 tea spoon |
Flour | 1/2 tsp, wheat or other flour |
Red Chilli Powder | 1 tea spoon |
Cinnamon-Clove Powder | 1 tea spoon |
Turmeric Powder | 1/4 tsp |
cumin seeds | 1/2 tsp |
asafoetida | 2 pinches |
Garam Masala | 1/2 tsp |
Butter | 1/2 tsp |
Ghee | 4 tsp |
Salt | to taste |
Preparation Method:
SQL Loader - Load XML data into XMLTYPE column
SQL Loader - Load Multiple Input Files Into Multiple Tables - Conditionally
(
COUNTRY VARCHAR2(10),
REFID VARCHAR2(10)
)
CREATE TABLE TB_SA
(
COUNTRY VARCHAR2(10),
REFID VARCHAR2(10)
)
CREATE TABLE TB_REST
(
COUNTRY VARCHAR2(10),
REFID VARCHAR2(10)
)
SQL Loader Keyword Options
userid -- ORACLE username/password for the database on which the extract needs to be loaded
control -- Name of the control file
log -- Name of the log file
bad -- bad file details
data -- data file name
discard -- discard file name
discardmax -- number of discards to allow (Default all)
skip -- number of logical records to skip (Default 0)
load -- number of logical records to load (Default all)
errors -- number of errors to allow (Default 50)
rows -- number of rows in conventional path bind array or between direct path data saves (Default: Conventional path 64, Direct path all)
bindsize -- size of conventional path bind array in bytes (Default 256000)
silent -- suppress messages during run (header,feedback,errors,discards,partitions)
direct -- use direct path (Default FALSE)
parfile -- parameter file: name of file that contains parameter specifications
parallel -- do parallel load (Default FALSE)
file -- file to allocate extents from
skip_unusable_indexes -- disallow/allow unusable indexes or index partitions (Default FALSE)
skip_index_maintenance -- do not maintain indexes, mark affected indexes as unusable (Default FALSE)
commit_discontinued -- commit loaded rows when load is discontinued (Default FALSE)
readsize -- size of read buffer (Default 1048576)
external_table -- use external table for load; NOT_USED, GENERATE_ONLY, EXECUTE (Default NOT_USED)
columnarrayrows -- number of rows for direct path column array (Default 5000)
streamsize -- size of direct path stream buffer in bytes (Default 256000)
multithreading -- use multithreading in direct path
resumable -- enable or disable resumable for current session (Default FALSE)
resumable_name -- text string to help identify resumable statement
resumable_timeout -- wait time (in seconds) for RESUMABLE (Default 7200)
date_cache -- size (in entries) of date conversion cache (Default 1000)
SQL Loader - Direct Path Loading-Example
India Vs Bangladesh - 2011 World Cup - watch live
ICC Cricket World Cup, 1st Match, Group B: Bangladesh v India at Dhaka, Feb 19, 2011