100525 + Interview Questions in GENERAL QA IN GENERAL AWARENESS Page 446 InterviewSolution

22251.	An allosteric inhibitor of adenylosuccinate synthetase is (A) AMP (B) ADP (C) GMP (D) GDP
Answer» An allosteric inhibitor of adenylosuccinate synthetase is AMP.

Discussion

22252.	The cofactors required for synthesis of adenylosuccinate are (A) ATP, Mg++ (B) ADP (C) GTP, Mg++ (D) GDP
Answer» (C) GTP, Mg⁺⁺

Discussion

22253.	According to the transpiration – cohesion theory, water is pulled upward through the xylem. The cause of the pull is (A) Guttation (B) Root pressure (C) Transpiration (D) Condensation
Answer» According to the transpiration – cohesion theory, water is pulled upward through the xylem. The cause of the pull is Transpiration.

Discussion

22254.	Enlist different types of transpiration
Answer» Stomatal transpiration. Lenticular transpiration. Cuticular transpiration.

Discussion

22255.	In the following figure numbers are written with a specific rule. Find the rule and decide which alternative will be in place of question mark.1)(1) 140 (2) 220 (3) 320 (4) 5002) (1) 19 (2) 23 (3) 31 (4) 25
Answer» 1) (4) 500 Multiply the corner elements with each other i.e., 15 x 6 x 4 = 360 then ∴ divided it by 10 ∴ 360 ÷ 10 = 36 is the middle no. Q 50 x 10 x 10 = 5000 ÷ 10 = 500 2) (3) 31 Addition of square [3] not of adjacent Number. 25 = 5 64 = 8 is 144 = 12 96 = 6 = 31

22255.

In the following figure numbers are written with a specific rule. Find the rule and decide which alternative will be in place of question mark.1)(1) 140 (2) 220 (3) 320 (4) 5002) (1) 19 (2) 23 (3) 31 (4) 25

Answer»

1) (4) 500

Multiply the corner elements with each other i.e., 15 x 6 x 4 = 360 then ∴ divided it by 10

∴ 360 ÷ 10 = 36 is the middle no.

Q 50 x 10 x 10 = 5000 ÷ 10 = 500

2) (3) 31

Addition of square [3] not of adjacent Number.

25 = 5

64 = 8

is 144 = 12

96 = 6

= 31

Discussion

22256.	7) Three cardb are drawen from an ordin ry 52 dech of cards ui thout replaremant (drawn cards are not plaed in to thedeck). Find probobility that1) nene of 3 cards is heartii) the 3 cards are non-heate-, heart, heart (in thatorder)iii) first 2 cards are non-heart and third in heart.iv) cthe cards contain one heart and 2 -non-heart.
Answer» H=hearts, O=other (non-hearts) "HHH", "HOH","OHH","HHO" For "HHH", there are 131211=1716 ways. For "HOH" there are 133912=6084 ways. For "OHH" there are 391312 =6084 ways For "HHO" there are 131239 = 6084 ways. So we have 1716+(3*6084)=19968 ways in total. As mentioned, out of those, 1716 are of type "HHH", so the probability amounts to 1716/19968.

Discussion

22257.	Q.6 Which of the following vectors is perpendicular to vector \( (\hat{\imath} Q \sin \theta-\hat{\jmath} \operatorname{Pcos} \theta) \)(a) \( \hat{\imath} P \cos \theta+\hat{\jmath} Q \sin \theta \)4b) \( \hat{\imath} \operatorname{Qcos} \theta-\hat{\jmath} P \sin \theta \)(c) \( \hat{\imath} P \sin \theta+\hat{\jmath} Q \cos \theta \)(d) \( \hat{\imath} Q \sin \theta-\hat{\jmath} P \cos \theta \)
Answer» Given vector \(\vec A\) = (\(\hat i\) θ sin θ - \(\hat j\) P cos θ) option (a) (\(\hat i\) P cos θ + \(\hat j\) θ sin θ) Let \(\vec B\) = (\(\hat i\) P cos θ + \(\hat j\) θ sin θ) Perpendicular condition \(\vec A.\vec B=0\) = (\(\hat i\) θ sin θ - \(\hat j\) P cos θ) . (\(\hat i\) P cos θ + \(\hat j\) θ sin θ) = P θ sin θ cos θ - P θ sin θ cos θ \(\vec A.\vec B=0\) option (a) is correct.

22257.

Q.6 Which of the following vectors is perpendicular to vector \( (\hat{\imath} Q \sin \theta-\hat{\jmath} \operatorname{Pcos} \theta) \)(a) \( \hat{\imath} P \cos \theta+\hat{\jmath} Q \sin \theta \)4b) \( \hat{\imath} \operatorname{Qcos} \theta-\hat{\jmath} P \sin \theta \)(c) \( \hat{\imath} P \sin \theta+\hat{\jmath} Q \cos \theta \)(d) \( \hat{\imath} Q \sin \theta-\hat{\jmath} P \cos \theta \)

Answer»

Given vector \(\vec A\) = (\(\hat i\) θ sin θ - \(\hat j\) P cos θ)

option (a) (\(\hat i\) P cos θ + \(\hat j\) θ sin θ)

Let \(\vec B\) = (\(\hat i\) P cos θ + \(\hat j\) θ sin θ)

Perpendicular condition

\(\vec A.\vec B=0\)

= (\(\hat i\) θ sin θ - \(\hat j\) P cos θ) . (\(\hat i\) P cos θ + \(\hat j\) θ sin θ)

= P θ sin θ cos θ - P θ sin θ cos θ

\(\vec A.\vec B=0\)

option (a) is correct.

Discussion

22258.	Find:d/dx cot-1((1 - x)/(1 + x))\(\frac{d}{dx}cot^{-1}(\frac{1-x}{1+x})\)
Answer» \(\frac{d}{dx}cot^{-1}(\frac{1-x}{1+x})\) = \(\cfrac{-1}{1+(\frac{1-x}{1+x})^2}\) \(\frac{d}{dx}(\frac{1-x}{1+x})\) = \(\frac{-(1+x)^2}{(1+x)^2+(1-x)^2}\)\(\times\) \(\frac{(1+x)\times-1-(1-x)\times1}{(1+x)^2}\) = \(\frac{-(1+x)^2}{(1+x)^2+(1-x)^2}\) \(\times\)\(\frac{-1-x-1+x}{(1+x)^2}\) = \(\frac1{1+x^2}\) ∴ \(\frac{d}{dx}\)cot ^-1(\(\frac{1-x}{1+x}\)) = \(\frac1{1+x^2}\)

22258.

Find:d/dx cot-1((1 - x)/(1 + x))\(\frac{d}{dx}cot^{-1}(\frac{1-x}{1+x})\)

Answer»

\(\frac{d}{dx}cot^{-1}(\frac{1-x}{1+x})\)

= \(\cfrac{-1}{1+(\frac{1-x}{1+x})^2}\) \(\frac{d}{dx}(\frac{1-x}{1+x})\)

= \(\frac{-(1+x)^2}{(1+x)^2+(1-x)^2}\)\(\times\) \(\frac{(1+x)\times-1-(1-x)\times1}{(1+x)^2}\)

= \(\frac{-(1+x)^2}{(1+x)^2+(1-x)^2}\) \(\times\)\(\frac{-1-x-1+x}{(1+x)^2}\)

= \(\frac1{1+x^2}\)

∴ \(\frac{d}{dx}\)cot ^-1(\(\frac{1-x}{1+x}\)) = \(\frac1{1+x^2}\)

Discussion

22259.	9. Find \( \frac{d y}{d x} \), if \( y=e-x{-x} \)\( ( U ) \)
Answer» solution:-- y=e^-x dy/dx=d(e^-x)/dx dy/dx=e^-x y=e^-x dy/dx = d(e^-x)/d(-x)* d(-x)/dx BY CHAIN RULE dy/dx = - e^-x

22259.

9. Find \( \frac{d y}{d x} \), if \( y=e-x{-x} \)\( ( U ) \)

Answer»

solution:--

y=e^-x

dy/dx=d(e^-x)/dx

dy/dx=e^-x

y=e^-x

dy/dx = d(e^-x)/d(-x)* d(-x)/dx

BY CHAIN RULE

dy/dx = - e^-x

Discussion

22260.	If \( v=\frac{c}{\sqrt{t}} e^{-x^{2} / 4 a^{2} t} \) then show that \( \frac{\partial v}{\partial t}=a^{2} \frac{\partial^{2} v}{\partial x^{2}} \)
Answer» v = \(\frac{c}{\sqrt t}e^{\frac{-x^2}{4a^2t}}\) \(\frac{\partial v}{\partial x}=\frac{-2x}{4a^2t}\frac{c}{\sqrt t}e^{\frac{-x^2}{4a^2t}}\) \(=\frac{-2x}{4a^2t}v\) \(\frac{\partial^2v}{\partial x^2}=\frac{-2v}{4a^2t}-\frac{-2x}{4a^2t}.\frac{\partial v}{\partial x}\) \(=\frac{-2v}{4a^2t}+\frac{2x}{4a^2t}.\frac{2x}{4a^2t}v\) \(=\frac{-2v}{4a^2t}(1-\frac{2x^2}{4a^2t})\) \(a^2\frac{d^2v}{dx^2}=\frac{-v}{2t}(1-\frac{x^2}{2a^2t})\)-----(i) \(\frac{\partial v}{\partial t}=\frac{c}{\sqrt t}e^{-\frac{x^2}{4a^2t}}\) x \(\frac{x^2}{4a^2t^2}-\frac{c}{2t^{3/2}}e^{-\frac{x^2}{4a^2t}}\) \(=\frac{x^2v}{4a^2t^2}-\frac{v}{2t}\) \(= -\frac{v}{2t}(1-\frac{x^2}{2a^2t})\) \(=a^2\frac{\partial^2v}{\partial x^2}\) (From (i))

22260.

If \( v=\frac{c}{\sqrt{t}} e^{-x^{2} / 4 a^{2} t} \) then show that \( \frac{\partial v}{\partial t}=a^{2} \frac{\partial^{2} v}{\partial x^{2}} \)

Answer»

v = \(\frac{c}{\sqrt t}e^{\frac{-x^2}{4a^2t}}\)

\(\frac{\partial v}{\partial x}=\frac{-2x}{4a^2t}\frac{c}{\sqrt t}e^{\frac{-x^2}{4a^2t}}\)

\(=\frac{-2x}{4a^2t}v\)

\(\frac{\partial^2v}{\partial x^2}=\frac{-2v}{4a^2t}-\frac{-2x}{4a^2t}.\frac{\partial v}{\partial x}\)

\(=\frac{-2v}{4a^2t}+\frac{2x}{4a^2t}.\frac{2x}{4a^2t}v\)

\(=\frac{-2v}{4a^2t}(1-\frac{2x^2}{4a^2t})\)

\(a^2\frac{d^2v}{dx^2}=\frac{-v}{2t}(1-\frac{x^2}{2a^2t})\)-----(i)

\(\frac{\partial v}{\partial t}=\frac{c}{\sqrt t}e^{-\frac{x^2}{4a^2t}}\) x \(\frac{x^2}{4a^2t^2}-\frac{c}{2t^{3/2}}e^{-\frac{x^2}{4a^2t}}\)

\(=\frac{x^2v}{4a^2t^2}-\frac{v}{2t}\)

\(= -\frac{v}{2t}(1-\frac{x^2}{2a^2t})\)

\(=a^2\frac{\partial^2v}{\partial x^2}\) (From (i))

Discussion

22261.	If a,b,c,d,e are five positive numbers, thenA. `(a/b+b/c) (c/d+d/e) ge 4 sqrt(a/e)`B. `b/a+c/b+d/c+e/d+a/ege5`C. `a/b+b/c+c/d+d/e+e/a lt 5`D. None of these
Answer» Correct Answer - A

Discussion

22262.	If `S_(n) = 1 + 3 + 7 + 13 + 21 + "….."` upto n terms, thenA. `S_(10) = 340`B. `T_(10) = 91`C. `S_(10) = 430`D. `T_(6) = 31`
Answer» Correct Answer - A

Discussion

22263.	If `b+c+,c+a,a+b` are in H.P. then which of the following hold(s) good ?A. `(b+c)/(a),(c+a)/(b), (a+b)/(c )` are in A.P.B. `(b+c)/(a), (c+a)/(b) , (a+b)/(c )` are in H.P.C. `a^(2) , b^(2), c^(2)` are in A.P.D. `a^(2), b^(2), c^(2)` are in H.P.
Answer» Correct Answer - A

Discussion

22264.	If `s_n=(1-4/1)(1-4/9)(1-4/25)......(1-4/((2n-1)^2)),` where `n in N,` thenA. `S_(n) = (1+2n)/(1-2n)`B. `S_(n) = (1-2n)/(1+2n)`C. `S_(oo) = - 1`D. `S_(oo) = - 2`
Answer» Correct Answer - A

Discussion

22265.	If `y = f(x)`,has following graph Match the column by filling following `4 xx 4` matrix
Answer» Correct Answer - `(A) rarr (r ),(B) rarr (p), (C ) rarr (q), (D) rarr (s)`

Discussion

22266.	The friends whose ages from a G.P. divide a certain sum of money in proportion to their ages. If they do that three years later, when the youngest is halfg the age of the oldest, then he will receive 105 rupees more that the he gets now and the middle friends will get 15 reupees more that he gets now, then ages of the friends areA. `12,18,27`B. `6,12,24`C. `8,18,36`D. divisible by 3
Answer» Correct Answer - A

Discussion

22267.	If `sin(6/5x) = 0` and `cos (x/5) = 0` , thenA. `x = (n-5)pi`B. `x = 6(n-1)pi`C. `x = 5(n-1/2)pi`D. `x = 5(n+1/2)pi`
Answer» Correct Answer - A

Discussion

22268.	Sum of all the 4-digit numbers which can be formed using the digits 0,3, 6, 9 (without repetition of digits) is119988 (b) 115992 (c)3996 (d)None of theseA. 119988B. 115992C. 3996D. None of these
Answer» Correct Answer - A

Discussion

22269.	Number of ways in which 3 tickets can be selected from a set of 500tickets numbered 1,2,3..., 500 so that the number on them are in arithmeticprogression is500 (b) `^500 C_3`(c) 62250(d) None of theseA. 500B. `.^(500)C_(3)`C. `3996`D. None of these
Answer» Correct Answer - A

Discussion

22270.	If the `r^(th)` term of a series is `1 + x + x^2 + .......+ x^(r-1)` , then the sum of the first n terms isA. `(n+(n+1)x+x^(n+1))/((1-x)^(2))`B. `(n-(n+1)x-x^(n+1))/((1-x)^(2))`C. `(n-(n+1)x+x^(n+1))/((1-x)^(2))`D. `(n+(n+1)x-x^(n))/((1-x)^(2))`
Answer» Correct Answer - A

Discussion

22271.	Study carefully the graph of a certain function The graph corresponds toA. `y = \|\|x\|^(2)-\|x\|-6\|`B. `\|y\| = \|\|x\|^(2)-2\|x\|-3\|`C. `y=\|\|x\|^(2) - 2\|x\| - 3\|`D. `\|y\| = \|\|x\|^(2) - \|x\|-6\|`
Answer» Correct Answer - A

Discussion

22272.	Number of roots of equation `3^(\|x\|)-\|2-\|x\|\|=1`isa. 0 b. 2 c. 4 d. 7
Answer» Correct Answer - A

Discussion

22273.	`sum_(k=1)^(360)((1)/(ksqrt(k+1)+(k+1)sqrt(k)))` is the ratio of two relative prime positive integers m and n. The value of `(m+n)` is equal toA. 43B. 41C. 39D. 37
Answer» Correct Answer - A

Discussion

22274.	Solve : (i) `-2 le \|\|x^(2) +1\| -3 \| le 7` (ii) `\|x^(2) - 4x\| le 5`
Answer» Correct Answer - (i) `[-3,5]` (ii) `[-1,3]`

Discussion

22275.	Let `S = sqrt(2) - sin sqrt(3)` and `C = cossqrt(2) - cossqrt(3)` then which one of the following is correct ?A. `S gt 0` and `C lt 0`B. `S gt 0` and `C lt 0`C. `S lt 0` and `C gt 0`D. `S lt 0` and `C lt 0`
Answer» Correct Answer - A

Discussion

22276.	The sum of the series `sum_(r=1)^(n) (-1)^(r-1).""^(n)C_(r)(a-r), n gt 1` is equal to :A. `n.2^(n+1)+a`B. 0C. aD. None of these
Answer» Correct Answer - A

Discussion

22277.	If `2tan""(alpha)/(2) = tan ""(beta)/(2)`, then `(3+5cosbeta)/(5+3cosbeta)` is equal to :A. `cos alpha`B. `cos beta`C. `sin alpha`D. `sin beta`
Answer» Correct Answer - A

Discussion

22278.	If `sum_(r=1)^(n) r(r+1) = ((n+a)(n+b)(n+c))/(3)`, where `a gt b gt c`, thenA. `2b = c`B. `a^(3)-8b^(3)+c^(3) = 8abc`C. a is prime numberD. `(a-2b)^(2) = 0`
Answer» Correct Answer - A

Discussion

22279.	If `2^x = cos(y/2)` and `a^x = sin y` , then `sin(y/2)` is equal toA. `1/2(a/2)^(x)`B. `(a/2)^(x)`C. `(a^(x))/(2)`D. `2^(pi//2)`
Answer» Correct Answer - A

Discussion

22280.	The scale in a graph is given 1 : 50000. In the graph, distance between A and B is 12 cm, then find the actual distance between them1. 8 km2. 7 km3. 6 km4. 9 km
Answer» Correct Answer - Option 3 : 6 km Given: Scale = 1 : 50000 Distance between A and B on the graph = 12 cm Calculation: Actual distance = (50000 × 12) cm ⇒ 600000 cm = 6 km ∴ The actual distance between them is 6 km

22280.

The scale in a graph is given 1 : 50000. In the graph, distance between A and B is 12 cm, then find the actual distance between them1. 8 km2. 7 km3. 6 km4. 9 km

Answer» Correct Answer - Option 3 : 6 km

Given:

Scale = 1 : 50000

Distance between A and B on the graph = 12 cm

Calculation:

Actual distance = (50000 × 12) cm

⇒ 600000 cm = 6 km

∴ The actual distance between them is 6 km

Discussion

22281.	Consider an `A.P. a_(1), a_(2), "……"a_(n), "……."` and the G.P. `b_(1),b_(2)"…..", b_(n),"….."` such that `a_(1) = b_(1)= 1, a_(9) = b_(9)` and `sum_(r=1)^(9) a_(r) = 369`, thenA. `b_(c) = 27`B. `b_(r) = 27`C. `b_(B) = 81`D. `b_(g) = 81`
Answer» Correct Answer - A

Discussion

22282.	The number of integral value(s) of `x`satisfying the equation `\|x^2 .3^(\|x-2\|). 5^(x-1)\|=-x^4 .3^(\|x-2\|). 5^(x-1)`is`2`b. `3`c. `1`d. infiniteA. 2B. 3C. 1D. infinite
Answer» Correct Answer - A

Discussion

22283.	Find the H.C.F. of 108, 288 and 360.
Answer» 108 = 2² x 3³ , 288 = 2⁵ x 3² and 360 = 2³ x 5 x 3² . H.C.F. = 2² x 3² = 36.

22283.

Find the H.C.F. of 108, 288 and 360.

Answer»

108 = 2² x 3³ ,

288 = 2⁵ x 3² and

360 = 2³ x 5 x 3² .

H.C.F. = 2² x 3² = 36.

Discussion

22284.	Which of the following numbers are non-terminating rational numbers1. 36/1252. 18/53. 22/74. 55/8
Answer» Correct Answer - Option 3 : 22/7 Concept: A non-terminating but recurring decimal is defined as a decimal that never ends, but repeats one or more numbers after the decimal point. Calculation: Option 1: 36/125 = 0.288 36/125 is terminating Option 2: 18/5 = 3.6 18/5 is terminating Option 3: 22/7 = 3.1428571429.... 22/7 is non-terminating Option 4: 55/8 = 6.875 55/8 is terminating ∴ 22/7 is non-terminating

22284.

Which of the following numbers are non-terminating rational numbers1. 36/1252. 18/53. 22/74. 55/8

Answer» Correct Answer - Option 3 : 22/7

Concept:

A non-terminating but recurring decimal is defined as a decimal that never ends, but repeats one or more numbers after the decimal point.

Calculation:

Option 1:

36/125 = 0.288

36/125 is terminating

Option 2:

18/5 = 3.6

18/5 is terminating

Option 3:

22/7 = 3.1428571429....

22/7 is non-terminating

Option 4:

55/8 = 6.875

55/8 is terminating

∴ 22/7 is non-terminating

Discussion

22285.	For `x>0` the sum of the series `1/(1+x)-(1-x)/(1+x)^2+(1-x)^2/(1+x)^3-....oo` is equal toA. `1/4`B. `1/2`C. `3/4`D. `1`
Answer» Correct Answer - A

Discussion

22286.	(4√6) × (6√24) what type of expression is this1. Imaginary 2. Rational 3. Irrational4. None of these
Answer» Correct Answer - Option 2 : Rational Concept used: Rational numbers are those numbers that can be expressed in p/q form where p and q are integers and q ≠ 0, example:- 2/3, 15, 0 etc. Irrational numbers cannot be expressed in p/q form (i.e. they are no rational), example:- √2, √5 etc. An imaginary number is a complex number that can be written as a real number multiplied by the imaginary unit i (iota) Calculation: (4√6) × (6√24) = 6 × 4 × √6 × √24 ⇒ 24√144 ⇒ 24 × 12 = 288 288 can be expressed as 288/1 ⇒ 288 is a rational number ∴ The given expression is a rational number

22286.

(4√6) × (6√24) what type of expression is this1. Imaginary 2. Rational 3. Irrational4. None of these

Answer» Correct Answer - Option 2 : Rational

Concept used:

Rational numbers are those numbers that can be expressed in p/q form where p and q are integers and q ≠ 0, example:- 2/3, 15, 0 etc.

Irrational numbers cannot be expressed in p/q form (i.e. they are no rational), example:- √2, √5 etc.

An imaginary number is a complex number that can be written as a real number multiplied by the imaginary unit i (iota)

Calculation:

(4√6) × (6√24) = 6 × 4 × √6 × √24

⇒ 24√144

⇒ 24 × 12 = 288

288 can be expressed as 288/1

⇒ 288 is a rational number

∴ The given expression is a rational number

Discussion

22287.	Let `a_(1),a_(2),a_(3)"……."` be an arithmetic progression and `b_(1), b_(2), b_(3), "……."` be a geometric progression sequence `c_(1),c_(2),c_(3,"…."` is such that `c_(n)= a_(n) + b_(n) AA n in N`. Suppose `c_(1) = 1, c_(2) = 4, c_(3) = 15` and `c_(4) = 2`. The value of sum of `sum_(i = 1)^(20) a_(i)` is equal toA. 480B. 770C. 960D. 1040
Answer» Correct Answer - A

Discussion

22288.	The equation `x-8/(\|x-3\|)=3-8/(\|x-3\|)`hasonly one solution (b) infinite solutionsno solution (d) none of theseA. only one solutionB. infinite solutionsC. no solutionD. two solutions
Answer» Correct Answer - A

Discussion

22289.	The graph of linear polynomial p(x) = 5x + 3, x ∈ R is ______(A) Ray(B) Line(C) Parabola open downward(D) Parabola open upward
Answer» Correct option (B) Line Explanation: ∴ P(x) = 5x + 3 It is a linear polynomial graph will be a line.

22289.

The graph of linear polynomial p(x) = 5x + 3, x ∈ R is ______(A) Ray(B) Line(C) Parabola open downward(D) Parabola open upward

Answer»

Correct option (B) Line

Explanation:

∴ P(x) = 5x + 3

It is a linear polynomial

graph will be a line.

Discussion

22290.	The solution set of the equation `\|2x+3\| -\|x-1\|=6` is :A. `x in (-10 , 2)`B. `x in [-10,2)`C. `x in [-10,2]`D. `x in {-10,2}`
Answer» Correct Answer - A

Discussion

22291.	The formula to find the root of a quadratic equation ax2 + bx + c = 0, a ≠ 0, by method of completing square was given by mathematician _____(A) Pythagoras (B) Sridhar Acharya (C) Hilbert (D) Uclid
Answer» (B) Sridhar Acharya

Discussion

22292.	The minimum value of the function `y = \|2x+1\| + 2\|x-2\|`, isA. `4x - 3`B. `3x - 1`C. 5D. 1
Answer» Correct Answer - A

Discussion

22293.	Solve the following equations : (i) `\|x^(2)-2\| = 2 \|x-3\|` (ii) `\|x^(2)-4\|+\|x^(2)-9\|=0` (iii) `\|x-1\|+\|x+5\| = 6`
Answer» Correct Answer - (i) `x = - 4,2` (ii) No solution (iii) `x in [-5,1]`

Discussion

22294.	Solve `\|(x^2-5x+4)/(x^2-4)\|
Answer» Correct Answer - `[0,8//5]uu[5//2,oo]`

Discussion

22295.	In a certain time, the ration of a certain principal and interest obtained from tit are in the ration 10:3 at 10% interest per annum. The number of years for which the money was invested is(10 % वार्षिक बियाज की दर से किसी निश्तित समय के बाद एक निश्तित मूलधन और साधरण बियाज का अनुपात 10 :3 था। निवेश किये गए धन की अवधि कितने वर्ष थी )A. 1yearsB. 3yearsC. 5yearsD. 7years
Answer» (b) According to the question, `{:("Principle","Interest"),(10,3):}` Rate%=10% Time=`(3)/(10)xx(100)/(10)=3years`

Discussion

22296.	For a fixed amount, 5 years at an annual rate of 12% on regular interest. The interest received later was Rs.7,440. Find the amount invested.
Answer» Let the amount invested or principal amount be Rs. P Given rate of interest = R = 12% Time = T = 5 years S. I. = Rs. 7440 \(\because\) S. I. = \(\frac{PRT}{100}\) ⇒ 7440 = \(\frac{P\times12\times5}{100}\) ⇒ P = \(\frac{74400}{12\times5}\) = \(\frac{744000}{60}=\frac{74400}6\) = 12400 Hence, the invested amount is Rs. 12400.

22296.

For a fixed amount, 5 years at an annual rate of 12% on regular interest. The interest received later was Rs.7,440. Find the amount invested.

Answer»

Let the amount invested or principal amount be Rs. P

Given rate of interest = R = 12%

Time = T = 5 years

S. I. = Rs. 7440

\(\because\) S. I. = \(\frac{PRT}{100}\)

⇒ 7440 = \(\frac{P\times12\times5}{100}\)

⇒ P = \(\frac{74400}{12\times5}\) = \(\frac{744000}{60}=\frac{74400}6\) = 12400

Hence, the invested amount is Rs. 12400.

Discussion

22297.	John invested a sum of money at an annual simple interest arte of 10%. At the end of four years the amont invested plys interest earned was 770. The amount =invested was:(जॉन ने एक धनराशि को 10 % वार्षिक साधारण बियाज की दर से निवेशित किया। चार वर्षो बाद राशि, बियाज सहित रुपया 770 हो जाता है तदनुसार वह कितने थी )A. 650B. 3.5C. 550D. 500
Answer» (c ) Let the amount invested(माना की निवेश की शेष राशि) =Rs P Accordingt to the question, `P+(Pxx10xx4)/(100)=770` `P+(4P)/(10)=770` `(14P)/(10)=770 Rightarrow P =(770xx10)/(14)=550` Hence Required invested amount(तक)=550 Alterante (वैकल्पिक विधि ) `10%=(1to "Interest")/(10to"Principal")` Interest in 4 years=`1xx4=4` `"Amount"=("interest"+"principal")=4+10=14` According to the question, 14units=770 `1 "units"=(770)/(14)xx10=550` The amount invested =550

Discussion

22298.	If a, b, c are in G.P., prove that log a, log b, log c are in A.P.
Answer» If a, b, c are in GP ⇒ \(\frac{b}{a} = \frac{c}{b}\) common ratio .....(i) We know, log a – log b = log \(\frac{b}{a}\) {property of logarithm} and according to equation (i) ⇒ log \(\frac{b}{a}\) = log \(\frac{c}{b}\) ⇒ log b – log a = log c – log b ⇒ 2 log b = log a + log c {property of arithmetic mean} Hence they are in AP. …proved

22298.

If a, b, c are in G.P., prove that log a, log b, log c are in A.P.

Answer»

If a, b, c are in GP

⇒ \(\frac{b}{a} = \frac{c}{b}\) common ratio .....(i)

We know,

log a – log b = log \(\frac{b}{a}\) {property of logarithm}

and according to equation (i)

⇒ log \(\frac{b}{a}\) = log \(\frac{c}{b}\)

⇒ log b – log a = log c – log b

⇒ 2 log b = log a + log c {property of arithmetic mean}

Hence they are in AP. …proved

Discussion

22299.	A charge particle is projected in a region of magnetic field and electric field if mass if mass of charged particle is m a its speed charges from `V_(0)` to `2V_(0) [W_(E)=` work done by electric field `W_(B)=` work done by magnetic field] which statement is incorrect.?A. `W_(B)=(1)/(2)mv_(0)^(2)`B. `W_(B)+W_(E)=(3)/(2)mv_(0)^(2)`C. `W_(E)=(3)/(2)mv_(0)^(2)`D. `W_(E)-W_(B)=(3)/(2)mv_(0)^(2)`
Answer» Correct Answer - A `W_(B)=0` `W_(E)=DeltaKE,W_(B)+W_(E)=DeltaKE`

Discussion

22300.	The unit digit of 4756 × 6483 × 2674 × 998 is – 1. 62. 43. 84. 2
Answer» Correct Answer - Option 1 : 6 GIVEN: N = 4756 × 6483 × 2674 × 998 CONCEPT: Unit digit of a number is the digit in the one's place of the number. i.e It is the rightmost digit of the number. For example, the unit digit of 458 is 8, the unit digit of 7859 is 9. CALCULATION: N = 4756 × 6483 × 2674 × 998 The unit digit of N is – ⇒ 6 × 3 × 4 × 8 ⇒ (18) × (32) ⇒ 8 × 2 ⇒ 16 ⇒ 6 ∴ The unit digit of the given number N is 6.

22300.

The unit digit of 4756 × 6483 × 2674 × 998 is – 1. 62. 43. 84. 2

Answer» Correct Answer - Option 1 : 6

GIVEN:

N = 4756 × 6483 × 2674 × 998

CONCEPT:

Unit digit of a number is the digit in the one's place of the number. i.e It is the rightmost digit of the number. For example, the unit digit of 458 is 8, the unit digit of 7859 is 9.

CALCULATION:

N = 4756 × 6483 × 2674 × 998

The unit digit of N is –

⇒ 6 × 3 × 4 × 8

⇒ (18) × (32)

⇒ 8 × 2

⇒ 16

⇒ 6

∴ The unit digit of the given number N is 6.

Discussion

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