Explore topic-wise InterviewSolutions in Current Affairs.

This section includes 7 InterviewSolutions, each offering curated multiple-choice questions to sharpen your Current Affairs knowledge and support exam preparation. Choose a topic below to get started.

1.

3. One root of the quadratic equation+ (3-2a)x-6a0 is-3, find its other root.

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2.

1. Find the value of k, for which one root of thFind the value of k, for which one root of the quadratic equation ko -14other.= 0 is six times the

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3.

Prove the faliowing by using the principie of mathematical induction1+3+3^{2}+\ldots+3^{-1}=\frac{\left(3^{x}-1\right)}{2}

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4.

Find the value ofk, for whichch one root of the quadratic equation kx'-14x+8 0 is 2.root

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As x = 2

kx²-14x+8 = 0

k(2)²-14(2)+8 = 0

4k = 28-8

4k = 20

k = 5

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5.

7. If one root of 2x2 + kx - 6 = 0 is 2, find the valueof k and the other root.(3)

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bro I am not sure hi 😄 for

2*2*2+2k-6=2+2k=02k=-2k=-1

2x^2+kx-6=0; 2(2)^2+k(2)+6=0 2(4)+2k-6=8+2k-6=0; 2k=6-8=-2; k=-2/2=-1

6.

Q7. Show that 5V2 + 3 is an irrational number.

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7.

टु)- बिद०७०- Fot सील्ख . 92७, मौन S pidbe पेले=q oall o जहर e (‘d’\/\ S Q,\'\O’{c;\ q-

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Given that : AB and CD are two equal chords. And, M, N are mid point of chord AB and CD respectively.

To prove : ∠AMN=∠CNM and ∠BMN=∠DNM

Construction : Join OM and ON

Proof :Since the line segment joining the centre of a circle to the midpoint of a chord is perpendicular to the chord.

Since AB and CD are equal chords, they are equidistant from the other. i.e., OM =ON

In ΔOMN,OM=ON (Proved)∠OMN=∠ONM (Angles opposite to equal sides) .....1∠OMA=∠ONC (each 90°) .....2 ∠OMB=∠OND (each 90°) .....3Subtracting 2 from 1, we have,∠OMA-∠OMN=∠ONC-∠ONM⇒∠AMN=∠CNMAdding 1 and 3, we have,∠OMB+∠OMN=∠OND+∠ONM⇒∠BMN=∠DNMHence Proved.

8.

22. Prove that 3+5V2 is an irrational number.

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9.

7. Show that 5V2 + 3 is an irrational number.

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hope it helps u

10.

Find the area of a square whose diagonal is 5v2 cm.

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11.

u If one root of equation5r" +13x+に0 is reciprocal of theother root, then the value of k is

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12.

If one root of 5x2 + 13 x + k = 0 is the reciprocal of the other root, then find value of k.

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13.

EXAMPLE 3.13Differentiate v by first principle

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14.

ple 2.34Using mathematical induction method, Prove thatmin+1), nEN

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Let the statement P (n) be1 + 2 + 3 + ... + n = n (n + 1) / 2STEP 1: We first show that p (1) is true.Left Side = 1Right Side = 1 (1 + 1) / 2 = 1Both sides of the statement are equal hence p (1) is true.STEP 2: We now assume that p (k) is true1 + 2 + 3 + ... + k = k (k + 1) / 2and show that p (k + 1) is true by adding k + 1 to both sides of the above statement1 + 2 + 3 + ... + k + (k + 1) = k (k + 1) / 2 + (k + 1)= (k + 1)(k / 2 + 1)= (k + 1)(k + 2) / 2The last statement may be written as1 + 2 + 3 + ... + k + (k + 1) = (k + 1)(k + 2) / 2Which is the statement p(k + 1)

15.

Prove by the principle of mathematical induction, for all n e N.1)(2人

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16.

b)Prove by the method of mathematical induction21 35 7++ 2n

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17.

Q. 18. The sum of the 4th and 8th term of an A.P. is 24 and thesum of the 6th and 10th terms is 44. Find the first three terms of theА.Р.nnd d' he the first term and common difference of

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thanks sir

18.

Lubricant Formulation

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Theformulationof alubricantis made up of base oils and additives that combine to determine behaviour when in use, both in terms of performance and in terms of duration.

Theformulationof alubricantis made up of base oils and additives that combine to determine behaviour when in use, both in terms of performance and in terms of duration.

Thanku Pandey JEE.

19.

Divide 30x4 + 11.13-82x2-12x+ 18 by (322 2x - 4) and verify the result by divisionalgorithm.5.

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20.

4v3 +5v2V4818

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please like my answer if you find it useful

21.

The value of 2V3-V3+4V3 is

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22.

tetwinelleHallรณwingas a quadratic equation in x and then solve for x2x + 3(AI CBSE2A two digit number is such that the product of ite diaite i 1e un

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23.

1. Find the square root of 1+4v3

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24.

The polynomial f(x) -x*-2x3 +3x2-ax+b when divided by (x-1) and (x +1) leavesthe remainder 5 and 19 respectively. Find the values of a and b. Hence, find the remainderwhen f(x) is divided by (x-2).

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25.

A number, when divided by 119,leaves a remainder of 19. If itis divided by 17, it will leave aremainder of

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On dividing the given number by 119, let k be the quotient and 19 as remainder. Then, number = 119k + 19

17*7k+17*1+217(7k+1)+2 Hence, the given number when divided by 17,

26.

(b) Form the differential equation from thefollowingy=Asin (nt + α).

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27.

A number when divided by 53, gives 33 as quotient and19 as remainder. Then, the number is(i)

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Solution :-

Given - Divisor = 53, Quotient = 33 and Remainder = 19

We know that

Dividend = (Divisor× Quotient) + Remainder

⇒ (53 × 33) + 19

⇒ 1749 + 19

= 1768

So, the number is 1768.

28.

EXAMPLE 3.13Differentiate V by frst principle

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29.

河t;135 322

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30.

frsta,... form an AP where a is defined as below:0 a, 3+4n(ii) an = 9-5n

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31.

113terms of the AP:9, 17,25,... must be taken to give a sum of 636frst term of an APis 5, the last term is45 nnd

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a=9d=17-9=8S=(n/2)(2a+(n-1)d)636*2=n(18+(n-1)8)1272=n(8n+10)1272=8n^2+10n8n^2+10n-1272=0n=12

32.

1. Fill the grid on the basis of the pattern followed10203012251510

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answer for the first column element of each row is the sum of the 2nd column element and the 3rd column element of that row

for the 1st row:30 = 10+20

for the 3rd row:25=15+10

thus for the 2nd row:12=x+7x=5

33.

4& 3222x + 8

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Thanx bro!

34.

Simplify by rationalising the denominator

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35.

The rationalising factor of 2 - 1 is :

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36.

16-4 36+4v3Simplifyby rationalising the denominator.

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37.

What denominator do we obtain after rationalising the denominator of?

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38.

l, Write the rationalising factor of the denominator inV2+3 12014

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1/√2+√3*√2-√3/√2-√3=√2-√3/2-3=√3-√2

39.

If x=12 then find (X square +1/x square)

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Please hit the like if you find the answer useful

Please solve my other problems

40.

8.(i)Show that a-b, a and a + b form consecutive terms of A.P

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If sum of first and third digit is twice of second digit then the three numbers are in AP.This is true here so the given three terms are consecutive terms of an AP

41.

18. The area of a square is given by A = x2 + 4x + 4,then the diagonal of the square is(a) (x - 2)(b) (x + 2)(c) JZ (x-2)(d) 12 (x + 2)

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Let side of square be S

Then,Area of square = S^2

Hence,S^2 = x^2 + 4x + 4S^2 = (x + 2)^2S = (x + 2)

Diagonal of square = side*root(2)= (x + 2)*root(2)= root(2)(x + 2)

(d) is correct option

42.

Find the square root of121(x-a)^{4}(x-b)^{6}(x-c)^{12}

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43.

109 A square dais is of area 92.16 m² What isthe measure of its side? If tiles measuring12 cm x 12 cm are laid on the dais, find thenumber of tiles needed to pave it.

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44.

(D) The perimeter of a trinngle in 14 cm. The second aide is b em loss than thü HPsL HIau iHa lne URPd i more than the second sido. The firat side of the triangle is unknown.(a) W

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45.

126Theorem 6.2 Ifa line divides any two sides of atriangle in the same ratio, then the line is parallelto the third side

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46.

A square dais is of area 92.16 m2. What ismeasure of its side? If tiles measuring12 cm x 12 cm are laid on the dais, find thember of tiles needed to pave it.

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47.

Theom 6.2 : Ifa line divides anv two sides of aretriangle in the same ratio, then the line is pto the third side.line DE such

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48.

Express the following expression in the form of a + ib:34i.5)(3-1.5

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49.

Theorem 6.2lf a line divides any two sides of atriangle in the same ratio, then the line is parallelto the third side.

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50.

Theorem 6.2 lf a line divides any two sides of atriangle in the same ratio, then the line is parallelto the third side.

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