HSC Maths Objective Questions

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 .

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

This post describes how to minimize the data load time when using FTP to load large amount of data. It takes considerable amount of time, when we FTP the data first to a target location and invoke SQL Loader to load the FTPed data. Instead of doing this, we will attempt to save time and some amount of disk space by making the FTP operation to feed the data directly to SQL Loader. This essentially means, every time we invoke the FTP operation, SQL Loader would automatically insert the data into Oracle for us. Let us see how to accomplish this.

1) As the first step, it is required to create a named pipe in the box where SQL Loader will run. The name of the pipe should be the name of the control file. As an example to create named pipe, run the command below

bash-2.03$ mknod test.ctl p
prw-r--r--   1 UserID   0 Mar  1 10:00 test.ctl

2) We can now invoke SQL Loader which reads the data from the PIPE that we created.

sqlldr userID/password@DB control=test

Note that the name of the control file is the pipe that we created just now. When this is executed, SQL Loader will wait, as it has not received any input for processing.  If you attempt to terminate the job at this point, you will receive the following error on the screen

SQL*Loader-500: Unable to open file (test.ctl)
SQL*Loader-554: error opening file
SQL*Loader-509: System error: Interrupted system call

3) We now create a simple control file  in the source machine. (from where you want to do the FTP)

load data 
infile * 
into table test_load 
fields terminated by ',' 
name,rollno 
BEGINDATA 
Ramu,100
Anitha,101
Arun,102
Dave,103
Antony,104
Peter,105
Sam,106

test_load is the name of our table..Name this file as "topush.ctl". Make sure that the table test_load is available in the target database. If not, you can create it with the following statement

create table test_load
(
name varchar2(15),
rollno number
)

4) Invoke FTP from the source machine and push this control file. As an example;

ftp> put topush.ctl test.ctl
200 PORT command successful.
150 ASCII data connection for test.ctl.
226 Transfer complete.
local: topush.ctl remote: test.ctl
191 bytes sent in 0.0003 seconds (623.82 Kbytes/s)

5) And that is it..if you have done these steps correctly, you can find SQL loader automatically pushing this into the table test_load. In my case, when I executed the put command, my SQL Loader window processed it as expected..

Commit point reached - logical record count 8

6) The result when the table test_load is queried from the database;

Ramu    100
Anitha   101
Arun      102
Dave      103
Antony 104
Peter     105
Sam       106

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 take on England in Group A world cup ODI Cricket match today in Bengaluru.(Banglore)..Some free live streaming links to watch the match online is provided below

India v England, ICC Cricket World Cup 2011, Group B, Bangalore, (14:30 local time | 09:00 GMT).

Aloo Palak–Recipe

The Ingredients that are required to make delicious Aloo Palak item are as below


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:

Put the washed spinach in a pan. Then add a small amount of water (just a sprinkle) and a pinch of salt.Cover and boil over a high flame for 2 minutes. Cool quickly, or hold under running water in a colander.

Put in a mixie, add green chilli and run for a minute. Keep slightly coarse, do not make very smooth.Keep aside.Cut the potatoes into big pieces. Heat ghee and fry potatoes till light brown.Drain the potatoes, keep aside.In the same hot ghee add the cumin seeds.Add the ginger, onions and fry till very tender.Add the tomato and further fry for two minutes.Add all the dry masalas and fry till ghee separates.

Add spinach and potatoes.When it resumes a boil sprinkle the flour and stir well. Boil for 2-3 minutes. Add lemon juice. Just before serving heat butter in a tiny saucepan and add the asafoetida.Pour over the vegetable and mix gently.Serve hot with naan or parathas or even rice.

SQL Loader - Load XML data into XMLTYPE column

In this example, we will see how to load XML data into XMLTYPE column in an Oracle table.

In one of my earlier posts, I'd described how to load BLOB type data into an Oracle table using SQL Loader. The link for that post is available here. To load XMLTYPE data, just assume that the column image_data is of XMLTYPE and not BLOB.

The rest of the process is the same. Prepare your XML data in separate xml files. You can reuse the same control file as given in the post and make sure that file has a valid path. When this control file is executed, SQL Loader will automatically push XML data into XMLTYPE field.  If you are stuck or you are getting any errors in this process, post it on this blog and let us have a look..

SQL Loader - Load Multiple Input Files Into Multiple Tables - Conditionally

So, what problem you are facing now?

I have three data files. Order1.csv, Order2.csv, Order3.csv. Each of these csv files contain order information from four different countries and order reference number. And I want to load them into multiple tables in Oracle using SQL Loader..

Order1.csv
IND,REF1101
AUS,REF1102
BRZ,REF1103
NZL,REF1104
SAF,REF1105

Order2.csv
IND,REF2101
AUS,REF2102
BRZ,REF2103
NZL,REF2104
SAF,REF2105

Order3.csv
IND,REF3101
AUS,REF3102
BRZ,REF3103
NZL,REF3104
SAF,REF3105

What are the tables into which you want to load this data?

I have three tables, IND, SA and rest of world. Using SQL Loader, I want all records with "IND" to get into the table TB_IND.Similarly, TB_SA for "SAF" and TB_REST for rest..

Do you have some simulation scripts?

Oh yes, I have them handy..here they are:

CREATE TABLE TB_IND
(
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)
)

What version of Oracle you are using?

Oracle Database 10g Express Edition Release 10.2.0.1.0 - Product

Here is your Control file..Note that we have made use of WHEN clause in control file, to get the result

LOAD DATA
INFILE 'C:\ sqlldr\order1.csv'
INFILE 'C:\ sqlldr\order2.csv'
INFILE 'C:\ sqlldr\order3.csv'

  INTO TABLE TB_IND         
  WHEN COUNTRY = 'IND'
  (
                COUNTRY POSITION(1:3)  CHAR,
                REFID POSITION(5:11)  CHAR           
  )

  INTO TABLE TB_SA
  WHEN COUNTRY = 'SAF'
  (
                COUNTRY POSITION(1:3)  CHAR,
                REFID POSITION(5:11)  CHAR           
  )

  INTO TABLE TB_REST 
  WHEN COUNTRY != 'SAF'  AND COUNTRY != 'IND' 
  (
                COUNTRY POSITION(1:3)  CHAR,
                REFID POSITION(5:11)  CHAR           
  )

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

I was experimenting between direct path loading and conventional loading abilities of Oracle SQL Loader and whoop, what a difference direct path loading makes..It loaded 23K odd rows into a table in Oracle in less than 1 second..

Amazing, the speed of loading data in direct path loading is incredibly fast..my logs below

SQL*Loader: Release 10.2.0.1.0 - Production on Wed Feb 23 11:24:01 2011

Copyright (c) 1982, 2005, Oracle.  All rights reserved.

Control File:   load.ctl
Data File:      C:\load.csv
Bad File:     load.bad
Discard File:  none specified

 (Allow all discards)

Number to load: ALL
Number to skip: 0
Errors allowed: 50
Continuation:    none specified
Path used:      Direct

Table SOURCE_DATA, loaded from every logical record.
Insert option in effect for this table: INSERT

   Column Name                  Position   Len  Term Encl Datatype
------------------------------ ---------- ----- ---- ---- ---------------------
INPUT_DATA                             FIRST     *   ,  O(") CHARACTER           


Table SOURCE_DATA:
  23000 Rows successfully loaded.
  0 Rows not loaded due to data errors.
  0 Rows not loaded because all WHEN clauses were failed.
  0 Rows not loaded because all fields were null.

Bind array size not used in direct path.
Column array  rows :    5000
Stream buffer bytes:  256000
Read   buffer bytes: 1048576

Total logical records skipped:          0
Total logical records read:         23000
Total logical records rejected:         0
Total logical records discarded:        0
Total stream buffers loaded by SQL*Loader main thread:        6
Total stream buffers loaded by SQL*Loader load thread:        0

Run began on Wed Feb 23 11:24:01 2011
Run ended on Wed Feb 23 11:24:01 2011

Elapsed time was:     00:00:00.36
CPU time was:         00:00:00.14

For comparison, the same with conventional loading was nearly three times as this one..

Sample control file:
load data
infile 'C:\load.csv'
into table source_data
fields terminated by "," optionally enclosed by '"'                              
(input_data)

India Vs Bangladesh - 2011 World Cup - watch live

Links to watch the match between India and Bangladesh live..watch online at the link below

ICC Cricket World Cup, 1st Match, Group B: Bangladesh v India at Dhaka, Feb 19, 2011