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This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.
| 4501. |
If x=-2 , y=6 is a solution of equation 3ax+2ay=6 then find value of \'b\' from 2(a-1)+2(3b-4)=4. |
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Answer» Given, x = -2 and y = 63ax+2ay=63a(-2) + 2a(6)=6-6a+12a=66a=6a=6/6=1=>2(a-1)+2(3b-4)=42(1-1)+2(3b-4)=40+(3b-4)=4/23b=2+4b=6/3=2 3a(2)+2a(6)=66a+12a=618a=6a=32(3-1)+2(3b-4)=42(2)+6b-8=44-8+6b=4-4+6b=46b=4+46b=8b=8÷6b=1.3 Please answer the questions |
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| 4502. |
Show that diagonal of a square are equal and bisect each other at right angle |
| Answer» Consider a square ABCD whose diagonals AC and BD intersect each other at a point O.We have to prove that AC = BD, OA = OC, OB = OD, and ∠AOB = 90º.Consider ΔABC and ΔDCB,AB = DC∠ABC = ∠DCB = 90°BC = CB (Common side)∴ ΔABC ≅ ΔDCB (By SAS congruency)∴ AC = DB (By CPCT)Hence, the diagonals of the square ABCD are equal in length.Now, consider ΔAOB and ΔCOD,∠AOB = ∠COD (Vertically opposite angles)∠ABO = ∠CDO (Alternate interior angles)AB = CD (Sides of a square are equal)∴ ΔAOB ≅ ΔCOD (By AAS congruence rule)∴ AO = CO and OB = OD (By CPCT)Hence, the diagonals of the square bisect each other.Similarly, in ΔAOB and ΔCOB,AO = COAB = CBBO = BO∴ ΔAOB ≅ ΔCOB (By SSS congruency)∴ ∠AOB = ∠COB (By CPCT)∠AOB + ∠COB = 180º (Linear pair)or, 2∠AOB = 180ºor, ∠AOB = 90ºHence, the diagonals of a square bisect each other at right angles. | |
| 4503. |
Construct a ∆ ABc in which Bc = 4.5 cm ∆ B = 45° and Ab + Ac = 8 cm justify your construction |
| Answer» draw a line segment bc 4.5cm construct an angle of 45 degree at point b increase the length of the line till 8cm name the point D join cd draw the perpendicular bisector of cd at the point of intersection of the perpendicular bisector and the line bd name the point a join ac abc is the required triangle | |
| 4504. |
In a llgram ABCD show that angle bisector ao angle A and B intersect at 90° |
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Answer» Given: ABCD is a llgm.Ao is the bisector of angle A\xa0BO is the bisector of angle BTo prove : angle o= 90°Proof: Angle A+ Angle B=180°(co interior angles )Now,1/2A+1/2B =90°Now in triangle AOB,angle ABO + angle BAO + angle OAB = 180° ( ANGLE SUM PROPERTY )Angle OAB= 180°- (angle BAO + angle ABO )Angle OAB= 180° -(90°) [above proved]Angle OAB= 90°\xa0 HENCE, PROVED A=BA=90Then B=90 Solved |
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| 4505. |
Write four solution for the equation: 6x+y=12 |
| Answer» 1). X=16x+y=126(1)+y=126+y=12y=12-6y=62).x=2 6x+y=126(2)+y=1212+y=12y=12-12y=0x=36x+y=126(3)+y=1218+y=12y=12-18y= -6x=46x+y=126(4)+y=1224+y=12y=12-24y= -12 | |
| 4506. |
Prove angleBOC= 90 - 1/2 angle A |
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Answer» Its ncert example?? In triangle ABC where angle bisectors of angle b and c meet at point o In which condition ??????? In which condition ???????? |
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| 4507. |
If two triangle are given ABC and PQR and no no. are show how to find SAS, sss |
| Answer» If sides and one angle b/w them is equal then the congruency will be sas.Qhen all the three sides are equal with each other of the 2 triangles then it is sss congruency. | |
| 4508. |
Find the irrational number between 1.76 and 3.02 |
| Answer» 2.7897534234756211987----------------------------- | |
| 4509. |
√a+√b+√c=0 then prove that a+b-c=3 |
| Answer» The formula of a+b+c=3abc3×1×1×1=3As every integer caontains 1 | |
| 4510. |
If (x-3) is a factor of p(x)=xcube-kxsquare+(k+1)x-12,find the value of k? |
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Answer» Niharika yadav you wrote the wrong answere K=3 p(x) = x3 - kx2 + (k + 1)x - 12x - 3 is a factor So, put x = 333 - k(3)2 + (k +1)3- 12 = 027 - 9k +3k + 3 - 12 = 0-6k + 18 = 0-6k = -18k = 18/6k =3\xa0 K equals to minus 2 |
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| 4511. |
A circle quardilateral is a rectangle |
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| 4512. |
If the area of equilateral triangle is 16cm then find perimeter |
| Answer» 32 | |
| 4513. |
sides of a quadrilateral are extended in order to form |
| Answer» A diagonal of a parallelogram divides it into 2 congruent trianhles | |
| 4514. |
Find median, 41,39,48,52,46,62,54,40,96,52,98,40,42,52,60 |
| Answer» Median:1) Arrange data in ascending order39,40,40,41,42,46,48,52,52,52,54,60,62,96,982) Total numbers of observation= 15Odd: (n+1)/2=(15+1)/2 = 8 th element is medianMedian = 52 | |
| 4515. |
What is total surface area of hemisphere |
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Answer» 3pei r square 3pie r sq. Hemisphere :Curved surface area(CSA) = 2 π r2Total surface area = TSA = 3 π r2 |
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| 4516. |
Between two rational no there is |
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| 4517. |
45×54 |
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Answer» By using (x plus a ) (x plus b) 2430 |
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| 4518. |
Abcd is parallelogram e and f points on diagonal ac ae = cf show befd is llgm |
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| 4519. |
If p=2_a,then prove that a3+6ap+p3-8=0 |
| Answer» A=2 divided by 15 | |
| 4520. |
Find the area of an equilateral triangle with side 10 cm |
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Answer» 3route25 43.3 is the area |
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| 4521. |
I if 5 raise to power 2 x minus 1 minus 25 x minus 1 is equal to 2500 then find the value of x |
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| 4522. |
Find value of k , if x=2,y=1 is a solution of the equation 2x+3y=k. |
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Answer» 2x + 3y = kPut x = 2 and y = 12(2) + 3(1) = k4 + 3 = kk = 7 2 (2)+3 (1)=k4+3=kK=7 |
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| 4523. |
The mean of the following no is 37 find the value of X.28,35,25,32,X,40,45,50. |
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Answer» 71 Mean=Sum of all observations / total number of observations37 = 28 + 35 + 25 + 32 + x + 40 + 45 + 50 / 837 × 8 = 225 + x296 = 225 + xx = 296-225x = 71 X into 28 + 35 + 25 + 32 + X + 40 + 45 + 50 / it that is equal to 37 and from that you can find the value of x |
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| 4524. |
Most IMP formula of mathe |
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| 4525. |
If the mean of the data 3,6,m ,7, 10 is 7 find the value of m |
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Answer» 3+6+m+7+10/5=726+m/526+m=7×526+m=35m=35-26m=9 9 9 |
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| 4526. |
{9^n×3^2×(3^-n/2)^-2-(27)^n}/(3)^3m×2^3 |
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| 4527. |
What is opposite angle are sum 180 of cyclic quadrilateral |
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Answer» Saalo tamiz se bolo 180 sum kyu hota hai Pagal 180 sun kyu hota hai 180 |
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| 4528. |
3 root over 2 by root over 3 + root 6 |
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| 4529. |
Show that in a right angle triangle, the hypotenuse is a longest side |
| Answer» Let ABC be a triangle in which angle A=90 degree which is the greatest angle in the triangle. We know that in a triangle side opposite to the greatest angle is longest. Hence,BC which is hypotenuse is the longest side. | |
| 4530. |
Find the area of a quadrilateral ABCD in which AB= 3cm BC=4cm CD=4cm DA=5cm andAC=5cm |
| Answer» 2√21+6. Or. 2•8+6=8•8cm2 | |
| 4531. |
Factories xsquare plus 3root3 plus |
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| 4532. |
Have a corcle have a chord |
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| 4533. |
Find the perimeter of regular hexagon with each side measuring 8 metre |
| Answer» Perimeter of regular hexagon = 6 (side) = 6(8) = 48 meter | |
| 4534. |
Prove of 1+1=2 |
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Answer» Let 1 + 1 be x + xSo now x + x = 2 2x = 2 X = 2 ÷ 2 X = 1 Therefore we get x as 1now we have x + x so put value of x we get 1 + 1 that is 2. 1+1" 2 |
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| 4535. |
If 125x*25/5= find x |
| Answer» 125x = 5/25X= 5/25*125X= 5 25*125X= 1 125*5X= 1 625X=1/625 ans | |
| 4536. |
Find the remainder when 3x³-6x²-7/9 is divided by 3x-4 |
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| 4537. |
The sides of an equilateral triangle are 2 x minus 3 Y + 1 ,X + Y - 1 and 3x minusy |
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| 4538. |
If p(x)= x3 -3x2 + 2x then find the value of p(1) |
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Answer» G(x)=1P(1)=1^3-3*1^2+2*1P(1)=1-3+2P(1)=3-3P(1)=0 -1 |
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| 4539. |
AB and CD are two parallel lines and a transversal l intersect AB at x and CD at Y. Prove that |
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| 4540. |
The height of sphere is 10cm and 1cm decrease find the volume of sphere 33.1% |
| Answer» No | |
| 4541. |
What is the proper blueprint of cbse for class 10 maths exam |
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| 4542. |
What are the property s of an altitude |
| Answer» An altitude fall 90°at the base of the triangle | |
| 4543. |
Cyclic quadrilateral prove |
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Answer» ABCD is a cyclic quadilateral so, A+C=180° Prove its opposite angle sum =180 |
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| 4544. |
What is method of finding root values |
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| 4545. |
What do you mean by construction |
| Answer» To draw the lines to solve the question | |
| 4546. |
:(p-q)^3+(q-r)^3+(r-p)^3 |
| Answer» 3(p-q)(q-r)(r-p) | |
| 4547. |
H, C, V are hight, csa and volume of cone then prove that 3πvh3-c2h2+qv2=0 |
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| 4548. |
Sum angle at a point? |
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| 4549. |
Factorise x6 - 7x3- 8 |
| Answer» (x*3+1)(x*3-8) | |
| 4550. |
Solve the equation graphically 2x + 3y = 7 |
| Answer» x - 2 , 5.y - 1, (-1) | |