algebra class exshort

8/10/2019 Algebra Class Exshort

1/7

Algebra class ex

Q In a 4- digit number, the sum of the first two digits is equal to that of the last two digits. The

sum of the first and last digits is equal to the third digit. Finally, the sum of the second and fourthdigits is twice the sum of the other two digits. hat is the third digit of the number!

". # $. % &. " 4. 4

Q. 'y ne(hew adores chocolates. )e li*es biscuits but he hates a((les. I told him that he can buy

as many chocolates he wishes but then he must ha+e biscuits twice the number of chocolates and

a((les more than biscuits and chocolates together. ach chocolate cost e. ". The cost of a((le is

twice of the chocolate and four biscuits are worth of one a((le. Then which of the following canbe the amount that I s(ent on that e+ening on my ne(hew!

a s. &4 b s. && c s. % d /one of

these

Q 0, Q, , 1 ha+e s.$23 between them. 0 has twice as much as , and Q has three

times as much as 1. and 1 together ha+e s.#3 less than 0. Find the share of

each.

Q. A man has a number of one ru(ee and fi+e-(aise coins. )e obser+es that if the

ru(ees were turned into fi+e-(aise coins and the fi+e-(aise coins into ru(ees, hewould ha+e s.#.3 more. If the ru(ees were turned into fifty-(aise coins and the

fi+e-(aise coins into ten-(aise coins, he would ha+e s.".2# less. )ow much

amount does he ha+e!

Q A merchant bought certain metres of cloth for s.#3. )e *e(t # m for himself and

sold the rest at e." (er metre more than he ga+e, and made a (rofit of s."3.

)ow many metres did he buy!Q 56a*ar and 7esha+ attem(ted to sol+e a quadratic equation. 56a*ar made a mista*e in writing

down the constant term. )e ended u( with the roots 84,&. 7esha+ made a mista*e in writing

down the coefficient of x. )e got the roots as 8&,$. hat will be the exact roots of the original

quadratic equation!

". 89," $. 8-&, -4 &. 84,& 4. 8-4, -&

Q. x and y are real numbers satisfying the conditions $: x : & and -% : y : -. hich of the

following ex(ressions will ha+e the least +alue!

". x$y $. xy$ &. #xy 4. /one of

these

DIRECTIONS for questions The batting a+erage 8;A of a test batsman is com(uted from runsscored and innings (layed-com(leted innings and incom(lete innings 8not out in the following

manner max B3, 8r$? n$ - r"? n"C

';A$= 8r"> r$? 8n"> n$

Q. ;ased on the information (ro+ided which of the following is true!

". ';A";A ';A$ $. ;A ';A$';A"

&. ';A$;A ';A" 4. /one of these

Q. An ex(erienced cric*eter with no incom(lete innings has a ;A of #3. The next time he bats,

the innings is incom(lete and he scores 4# runs. In can be inferred that

". ;A and ';A"will both increase

$. ;A well increase and ';A$will decrease

&. ;A will increase and not enough data is a+ailable to assess change in ';A"and ';A$

4. /one of these

Q. Find the common root of the equations x$D #x > 9 = 3 and x$D x > "3 = 3.

Q. 1ol+e for x< 8&x > ?8$x D # E &, where x is a whole number.Q. 1ol+e for x< x E #.

Q. 1ol+e< $x > # : 2..

Q. 1ol+e for x & > $ = " 8b &x D "& > "$ =

Q. Find the +alue of x< x > # : $x D > "#

Q. $x > 4 E x D 2

Q. If x E # and y : -", then which of the following statements is true!

". 8x > 4y E " $. x E - 4y &. - 4x : #y 4. /one

of these

Q. If a, b, c and d are four (ositi+e real numbers such that abcd = ", what is the minimum +alue

of 8l>a 8l>b 8l>c 8l>d

". 4 $. " &. "9 4. "%

Q If& 4

&%

x < # and x > y = 4.

Find the solution set for y.

$


3/7

Q Ifx

yE4, x > y : 3, x :&,

find the solution set for y.

Q. Gi+en x, y, H are integers xEyEH. hich is the minimum among the choices!

a. xy8" D H b. xH8" D y c. yH8" D xd. annot be determined

Q In Q.2 if x, y, H : 3 then which of the choices is the largest!a. xy8" D H b. xH8" D y c. yH8" D x

d. annot be determined

Q. 1ol+e for x &x D "% 8&x$D x D 9 3 sol+e for x.

Q. The "thterm of an arithmetic (rogression is #. If the total number of terms of the

(rogression is && find the sum of all the terms of the (rogression

Q. A blac* mon*ey is climbing a $33m tall building. It starts from the ground, climbs 4m in

the"st second, sli(s $m in the $ndsecond, climbs 9m in the &rdsecond, then sli(s $m in thefourth, climbs %m in the #thsecond, sli(s in the next and so on. Find when would it reach

the to( of the building!

a. $#thsec b. $9thsec c. $thsec d. &3thsec

Q If f8t = $t$> $?t$> #?t > #t, what is f8"?t!

Q If f8x = xx, find, in terms of f8x, the +alue of Bf8-xC$

Q. hat is f8$, if f 8x = x&> x$> x > "!

Q f83, y > $ = y > #f8x > #, y = f 8x, y-" find the +alue of f 8#, 9

Q f8a, b = a$> b&, g 8a, b = a > b Then what is the +alue of f 8&, g 8&, 4

Q f8x = x? 8x > "

fn8x = 8n D " fn-"8x n E "

find the +alue of f48".

&


4/7

Q. 0a*istan is (lanning to conduct a missile defense test. The (ath of the missile,

which has to be targeted, is a second-degree (olynomial function of time, in

which constant term is negligible. The (ath of the interce(tor, which is su((osedto hit the missile, is also gi+en by the same (olynomial, with constant term ha+ing

considerable +alue. ill this test be successful!

Q If F8x, y, H = x > y > H, for all real +alues of x

G 8x, y, H = x > y > H, for all real +ales of x, then what will be the relation

between these two functions!

Directions for QThe following o(erations are defined for real numbers b if a and b both are (ositi+e else a J b = ".

a b = 8aba > bif ab is (ositi+e else a b = ".

Q. 8$ J "?8" $ =

a "?% b " c &?% d &

Q. K88" J " J $ - 8"3".&log"33."L?8" $ =

a &?% b 4log"33."?% c 84 > "3".&?% d /one of these

Q. 88M J - N?8- M N = &?%, then which of the following must be true!

a M = $, N = " b x E 3, N : 3 c M, N both (ositi+e d M, N both negati+e

Directions for Q. : These questions are based on the situation gien be!o":

Oet x and y be real numbers and let

f8x,y = x> y, F8f8x,y = - f8x,y and G8f8x,y = - F8f8x,y

Q. hich of the following statement is true!

a F8f8x,y . G8f8x, y = - F8f8x, y. G8f8x, y

b F8f8x, y. G8f8x, y E - F8f8x, y. G8f8x, y

c F8f8x, y. G8f8x, y G8f8x, y . F8f8x, y

d F8f8x, y > G8f8x, y > f8x, y = f8- x, - y

Q. hat is the +alue of f8G8f8", 3, f8F8f8" $ , G8f8", $!a & b $ c " d 3

Q. hich of the following ex(ressions yields x$as its result!

a F8f8x, - x . G8f8x, - x b F8f8x, x . G8f8x, x. 4

c - F8f8x, x . G8f8x, x P log$"9 d f8x, x. f8x, x

Directions for Q. #or three distinct rea! nu$bers x% y and &% !et

f8x, y, H = min 8max8x, y, max 8y, H, max 8H, x

g8x, y, H = max 8min8x, y, min 8y, H, max 8H, x

h8x, y, H = max 8max8x, y, max8y, H, max 8H, x

68x, y, H = min 8min 8x, y, min8y, H, min 8H, x

m8x, y, H = max 8x, y, H

n8x, y, H = min 8x, y, H

4


5/7

Q. hich of the following is necessarily greater than "!

a 8h8x, y, H - f8x, y, H ? 68x, y, H b 68x, y, H?h8x, y, H

c f8x, y, H?g8x, y, H d 8f8x, y, H > h8x, y, H - g8x, y, H?68x, y, H

Q. hich of the following ex(ressions is necessarily equal to "!

a 8f8x, y, H - m8x, y, H?8g8x, y, H - h8x, y, Hb 8m8x, y, H - f8x, y, H?8g8x, y, H - n8x, y, H

c 868x, y, H - g8x, y, H ?h8x, y, H

d 8f8x, y, H - h8x, y, H ?f8x, y, H

Q hich of the following ex(ressions is indeterminate!

a 8f8x, y, H - h8x, y, H?8g8x, y, H - 68x, y, H

b 8f8x, y, H > h8x, y, H > g8x, y, H > 68x, y, H?868x, y, H > h8x, y, H - m8x, y, H - n8x, y,

H

c 8g8x, y, H - 68x, y, H?8f8x, y, H - h8x, y, H

d 8h8x, y, H - f8x, y, H?8n8x, y, H - g8x, y, H

If x is (ositi+e what is the greatest +alue of 8#-x 8x > &!.

Find all +alues of x which satisfy x$> 9x D $ E 3 and 4 > &x D x$E

1ol+e the inequality $x$> 2x D E 3.

1ol+e the inequality &x$D $3x > " 3.

1ol+e the inequality x?$ : $.

Oet y = min K8x > 9, 84 D xL. If x, what is the maximum +alue of y!

Directions for Q.: These questions are based on the situation gien be!o":

In each of the questions %2 to 2$ a (air of gra(hs F8x and F"8x is gi+en. These are com(osed of

straight-line segments, shown as solid lines, in the domain x 8- $, $.

If F"8x = - F8x choose the answer as a

If F"8x = F8- x choose the answer as bIf F"8x = - F8- x choose the answer as c

And if none of the abo+e is true, choose the answer as d.

#


6/7

Q F8M F"8M

$ $

-$ $ M - $ $ M

3 3

- $ - $

a a b b c c d d

23. F8x F"8x

$ $

- $ 3 $ x - $ 3 $

x

- $ - $

a a b b c c d d

9


7/7

2". F8x F" 8x$ $

- $ $ x - $ 3 $

x

- $ - $a a b b c c d d

2$. F8x F"8x

"

" "

- $ 3 " $ x - $ 3 $

x

- " - "

- $

- $

a a b b c c d d

algebra class exshort

Documents