Explore topic-wise InterviewSolutions in Current Affairs.

Splitting the middle term,x^2-15x-2x+30=0 x(x-15)-2(x-15)=0 (x-2)(x-15)=0 x=2 x=15

thanos

thank u very much

√7, √28, √63

√7, 2√7, 3√7 common difference = 2√7 - √7 = √7

Comman difference will not be thereas

No,They are not in AP because for being in AP the differences between two consecutive numbers should be same.But here, they are different.√6 - √3 = 0.717√9 - √6 = 0.551

hit like if you find it useful

Find the common difference a1,a2,a3hence difference =a2-a1

🙏

Hence 25th term is 3 times of 11th term

Let one number be xand other number be 9-x

a/q

1/x + 1/9-x = 1/2

9-x+x/x(9-x) = 1/29/x(9-x) = 1/2x(9-x)=18x^2-9x+18=0x^2-6x-3x+18=0x(x-6)-3(x-6)=0(x-6)(x-3)=0x=6,3when one=6, other=3

Given a^4 = 0

That is (a + 3d) = 0

⇒ a = - 3d ........... (1)

nth term of AP is given by an = a + (n – 1)d

a^11 = a + 10d = – 3d + 10d = 7d [From (1)]

a^25 = a+ 24d = – 3d + 24d = 21d [From (1)]

= 3 x 7d

Hence a^25 = 3 x a^11

You need to Proof the congruence of Triangle ABC and triangle BDC to Make AO AND OD equal

Thankyou

Since, ABCD is a quadrilateral and ∠A+∠D= 180°.

From the figure, we can see that ∠A and ∠D form the adjacent angle pair and it is already known that the two adjacent angles always add to give their angle sum equal to 180°.

Also, adjacent angles are formed if the two lines are parallel which means that if two adjacent angles are given then the two ,lines must be parallel, therefore AB is parallel to CD.

If the two lines are parallel and also, the angle sum of two adjacent angles equal to 180°, then this type of quadrilateral is known as "Trapezium".

4 is the correct answer

Yes. If Angle A + Angle D = 180°,then definitely AB || DC.With this information, we can conclude that only one pair of opposite sides are parallel. Hence, a special name for this quadrilateral will be trapezium.See picture for the proof.

ABCD is a quadrilateral with four equal sidesIf the sides are equal they will produce four equal anglesHence each angle will be 90 degree (Sum of interior angles is 360 degree)Hence ABCD is considered as a SQUAREAC and BD are joined which meet at OAC and BD are diagonals , which bisect interior angles.Angle BAD is bisected by ACAngles BAC = DACAngle BCD is bisected by ACAngles ACD = BCASince, BAD = BCD = 90°Angles BAC = DAC = Angles ACD = BCABAC = ACDThey are also interiorly alternate to each other.So by converse theorem,AB is parallel to CDSimilarlyAngles ABD = CBD = ADB = CDB (when BD is the bisector)CBD = ADBThey are also interiorly alternate to each other.So by converse theorem,AD is parallel to BCHence opposite pairs of sides are parallel to each other.

a=10,s15=675,Sn=n/2(2a+(n-1)d)675=15/2(2×10+(15-1) d) 675 ×2/15=(20+14d)45×2=20+14d90-20=14d70=14d d=70/14d=5an=a +(n-1) dan=10+(25-1) 5an=10+24×5an=10+120an=130

The number of form 2n + 1 , where n is any natural number

Sn = 3n²/2 + 5n/2

We know that ,

nth term = (sum of nth term) - (sum of (n-1)th term)

So , according to the question ,

25th term = (sum of 25th term) - (sum of (25-1)th term)= (sum of 25th term) - (sum of 24th term)= [3(25)²/2 + 5(25)/2] - [3(24)²/2 + 5(24)/2]= [1875/2 + 125/2] - [1728/2 + 120/2]= (2000/2) - (864 + 60)= 1000 - 924= 76

So , the 25th term of the AP is 76.

2352

/ \2 1176

/ \2588

/ \2294

/ \2147

/ \349

/ \77

/ \71

1)The prime factors are: 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3

or also written as { 2, 2, 2, 2, 2, 2, 3, 3 }

Written in exponential form: 26x 32

2) The prime factors are: 5 x 5 x 7 x 7

or also written as { 5, 5, 7, 7 }

Written in exponential form: 52x 72

2*2*2*3*32*2*3*7common is 3*2*2= 12

2×2×2×3×32×2×3×7HCF= 2×2×3HCF= 12 is the correct answer

336 = 2x2x2x2x3x7

54 = 2x3x3x3

LCM= 2x2x2x2x3x3x3x7 = 3024