32581 + Interview Questions in Mathematics Page 235 InterviewSolution

11701.	If four numbers in A.P. are such that their sum is 50 and the greatest number is 4 times, the least, then the numbers are(a) 5, 10, 15, 20(b) 4, 101, 16, 22(c) 3, 7, 11, 15(d) none of these
Answer» If four numbers in A.P. are such that their sum is 50 and the greatest number is 4 times, the least, then the numbers are (a) 5, 10, 15, 20 (b) 4, 101, 16, 22 (c) 3, 7, 11, 15 (d) none of these

Discussion

11702.	Question 49 Solve the following: 3x−82x=1
Answer» Question 49 Solve the following: $\frac{3 x - 8}{2 x} = 1$

11702.

Question 49 Solve the following: 3x−82x=1

Answer»

Question 49

Solve the following:

$\frac{3 x - 8}{2 x} = 1$

Discussion

11703.	Natural numbers less than 10,000 and divisible by 4 and consisting of only the digits 0,1,2,3,4 and 5 are formed without repetition. Prove that the number of ways to do this is 103.
Answer» Natural numbers less than 10,000 and divisible by 4 and consisting of only the digits 0,1,2,3,4 and 5 are formed without repetition. Prove that the number of ways to do this is 103.

Discussion

11704.	if a+b+c=1,ab+bc+ca=2,and abc=3 then find 1/a+bc+1/b+ca+1/c+ab
Answer» if a+b+c=1,ab+bc+ca=2,and abc=3 then find 1/a+bc+1/b+ca+1/c+ab

Discussion

11705.	(i) In an A.P., the sum of first n terms is 3n22+13nn. Find its 25th term.(ii) If the sum of first n terms of an A.P. is n2, then find its 10th term.
Answer» (i) In an A.P., the sum of first n terms is $\frac{3 n^{2}}{2} + \frac{13}{n} n .$ Find its 25^thterm. (ii) If the sum of first n terms of an A.P. is n², then find its 10th term.

Discussion

11706.	How many circles can be drawn passing through three definite points when they are non collinear?
Answer» How many circles can be drawn passing through three definite points when they are non collinear?

Discussion

11707.	A chord of a circle subtends an angle of θ at the centre of the circle. The area of the minor segment cut off by the chord is one eighth of the area of the circle. Prove that8 sinθ2cosθ2+π=πθ45.
Answer» A chord of a circle subtends an angle of $θ$ at the centre of the circle. The area of the minor segment cut off by the chord is one eighth of the area of the circle. Prove that $8 \sin \frac{θ}{2} \cos \frac{θ}{2} + π = \frac{πθ}{45} .$

Discussion

11708.	The following is known about an AP: Tm=1n,Tn=1m Find the value of Smn. [4 MARKS]
Answer» The following is known about an AP: $T_{m} = \frac{1}{n}, T_{n} = \frac{1}{m}$ Find the value of $S_{m n}$ . [4 MARKS]

Discussion

11709.	Draw the graphs of the pair of linear equations x − y + 2 = 0 and 4x − y − 4 = 0 . Calculate the area of the triangle formed by the lines so drawn and the x-axis .
Answer» Draw the graphs of the pair of linear equations $x - y + 2 = 0$ and $4 x - y - 4 = 0$ . Calculate the area of the triangle formed by the lines so drawn and the x-axis .

Discussion

11710.	To construct a triangle similar to a given ∆ABC with its side 8/5 of the corresponding side of ∆ABC draw a ray BX such that ∠CBX is an acute angle and X is on the opposite side of A with respect to BC. The minimum number of points to be located at equal distances on ray BX is(a) 5(b) 8(c) 13(d) 3
Answer» To construct a triangle similar to a given ∆ABC with its side 8/5 of the corresponding side of ∆ABC draw a ray BX such that ∠CBX is an acute angle and X is on the opposite side of A with respect to BC. The minimum number of points to be located at equal distances on ray BX is (a) 5 (b) 8 (c) 13 (d) 3

Discussion

11711.	Question 6Is 0.2 a root of the equation x2 – 0.4 = 0? Justify your answer.
Answer» Question 6 Is 0.2 a root of the equation $x^{2}$ – 0.4 = 0? Justify your answer.

Discussion

11712.	If the ratio of the sum of the first n terms of two A.PS is (7n + 1) : (4n + 27), then find the ratio of their 9th terms
Answer» If the ratio of the sum of the first n terms of two A.PS is (7n + 1) : (4n + 27), then find the ratio of their 9th terms

Discussion

11713.	Five persons entered the lift cabin on the ground floor of an 8 floor house. Suppose that each of them independently and with equal probability can leave the cabin at any floor beginning with the first, then the probability of all 5 persons leaving at different floor is(a) P5775(b) 75P57(c) 6P56(d) P5555
Answer» Five persons entered the lift cabin on the ground floor of an 8 floor house. Suppose that each of them independently and with equal probability can leave the cabin at any floor beginning with the first, then the probability of all 5 persons leaving at different floor is (a) $\frac{{}^{7}P_{5}}{7^{5}}$ (b) $\frac{7^{5}}{{}^{7}P_{5}}$ (c) $\frac{6}{{}^{6}P_{5}}$ (d) $\frac{{}^{5}P_{5}}{5^{5}}$

Discussion

11714.	Volume of two spheres are in ratio 64: 27. Find the ratio of their surface areas.
Answer» Volume of two spheres are in ratio 64: 27. Find the ratio of their surface areas.

Discussion

11715.	Solve each of the following quadratic equations: 3√7x2+4x−√7=0
Answer» Solve each of the following quadratic equations: $3 \sqrt{7} x^{2} + 4 x - \sqrt{7} = 0$

Discussion

11716.	The value of limn→∞cos(x2)cos(x4)⋯cos(x2n−1)cos(x2n) is
Answer» The value of $lim n \to \infty cos (\frac{x}{2}) cos (\frac{x}{4}) \dots cos (\frac{x}{2^{n - 1}}) cos (\frac{x}{2^{n}})$ is

Discussion

11717.	Which of the following pairs of lines are parallel?
Answer» Which of the following pairs of lines are parallel?

Discussion

11718.	Two tangents TP and TQ are drawn from an external point T to a circle with centre O as shown in Fig. 10.73. If they are inclined to each other at an angle of 100°, then what is the value of ∠POQ?
Answer» Two tangents TP and TQ are drawn from an external point T to a circle with centre O as shown in Fig. 10.73. If they are inclined to each other at an angle of 100°, then what is the value of ∠POQ?

Discussion

11719.	In an arithmetic sequence, the ratio of the first term to the second is 2 : 3. What is the ratio of the third term to the fifth term?
Answer» In an arithmetic sequence, the ratio of the first term to the second is 2 : 3. What is the ratio of the third term to the fifth term?

Discussion

11720.	Three semicircles each of diameter 3 cm, a circle of diameter 4.5 cm and a semicircle of radius 4.5 cm are drawn in the given figure. Find the area of the shaded region.
Answer» Three semicircles each of diameter 3 cm, a circle of diameter 4.5 cm and a semicircle of radius 4.5 cm are drawn in the given figure. Find the area of the shaded region.

11720.

Three semicircles each of diameter 3 cm, a circle of diameter 4.5 cm and a semicircle of radius 4.5 cm are drawn in the given figure. Find the area of the shaded region.

Answer»

Three semicircles each of diameter 3 cm, a circle of diameter 4.5 cm and a semicircle of radius 4.5 cm are drawn in the given figure. Find the area of the shaded region.

Discussion

11721.	The line joining two points A(2,0) and B(3,1) is rotated about A in anticlockwise direction through an angle of 15∘. find the equation of line in the new position. If b goes to c in the new position what will be the coordinates of C.
Answer» The line joining two points A(2,0) and B(3,1) is rotated about A in anticlockwise direction through an angle of 15∘. find the equation of line in the new position. If b goes to c in the new position what will be the coordinates of C.

Discussion

11722.	The radii of two circles are 8 cm and 6 cm respectively. Find the radius of the circle having area equal to the sum of the areas of the two circles.
Answer» The radii of two circles are 8 cm and 6 cm respectively. Find the radius of the circle having area equal to the sum of the areas of the two circles.

Discussion

11723.	The area enclosed by the circle x2 + y2 = 2 is equal to(a) 4π sq. units(b) 22π sq. units(c) 4π2 sq. units(d) 2π sq. units
Answer» The area enclosed by the circle x² + y² = 2 is equal to (a) 4π sq. units (b) $2 \sqrt{2} π$ sq. units (c) 4π² sq. units (d) 2π sq. units

Discussion

11724.	A chord of a circle is equal to the radius of the circle. Find the angle subtended by the chord at a point on the major arc.
Answer» A chord of a circle is equal to the radius of the circle. Find the angle subtended by the chord at a point on the major arc.

Discussion

11725.	22. If the midpoint of the line segment joining the points A(-k, 5)and B(3,2k) lies on the line 3x+6y=-3 then find the value of 'K
Answer» 22. If the midpoint of the line segment joining the points A(-k, 5)and B(3,2k) lies on the line 3x+6y=-3 then find the value of 'K

Discussion

11726.	A steel box has dimensions of 2 m, 3 m, and 0.5 m. It has to be gold plated using electrolysis. If each square meter of gold plating costs Rs.100, then gold plating the outer surface of the box costs ___.
Answer» A steel box has dimensions of 2 m, 3 m, and 0.5 m. It has to be gold plated using electrolysis. If each square meter of gold plating costs Rs.100, then gold plating the outer surface of the box costs ___.

Discussion

11727.	The probability of happening of an event is p. The maximum and minimum values of pare
Answer» The probability of happening of an event is p. The maximum and minimum values of pare

Discussion

11728.	Question 6The marks obtained (out of 100) by a class of 80 students are given below:MarksNumber of students10−20620−301730−501550−701670−10026Construct a histogram to represent the data above.
Answer» Question 6 The marks obtained (out of 100) by a class of 80 students are given below: $\begin{matrix} Marks & Number of students 10 - 20 & 6 20 - 30 & 17 30 - 50 & 15 50 - 70 & 16 70 - 100 & 26 \end{matrix}$ Construct a histogram to represent the data above.

Discussion

11729.	Find the missing term in the sequence 100, 100, ?, 72, 50.4, 30.24
Answer» Find the missing term in the sequence 100, 100, ?, 72, 50.4, 30.24

11729.

Find the missing term in the sequence 100, 100, ?, 72, 50.4, 30.24

Answer»

Find the missing term in the sequence

100, 100, ?, 72, 50.4, 30.24

Discussion

11730.	Question 7If figure common tangents AB and CD to two circles intersect at E. Prove that AB = CD.
Answer» Question 7 If figure common tangents AB and CD to two circles intersect at E. Prove that AB = CD.

Discussion

11731.	In the given figure, XY and X'Y' are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersects XY at A and X'Y' at B. Then ∠AOB= ___
Answer» In the given figure, XY and X'Y' are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersects XY at A and X'Y' at B. Then $∠ A O B =$ ___

11731.

In the given figure, XY and X'Y' are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersects XY at A and X'Y' at B. Then ∠AOB= ___

Answer»

In the given figure, XY and X'Y' are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersects XY at A and X'Y' at B. Then $∠ A O B =$ ___

Discussion

11732.	What is the distance between two parallel tangents of a circle having radius 4.5 cm ? Justify your answer.
Answer» What is the distance between two parallel tangents of a circle having radius 4.5 cm ? Justify your answer.

Discussion

11733.	The wheels of a car make 2500 revolutions in covering a distance of 4.95 km. Find the diameter of a wheel.
Answer» The wheels of a car make 2500 revolutions in covering a distance of 4.95 km. Find the diameter of a wheel.

Discussion

11734.	How many three-digit numbers are divisible by 9? [CBSE 2013]
Answer» How many three-digit numbers are divisible by 9? [CBSE 2013]

Discussion

11735.	If the circumference of two circles are in the ratio 2 : 3, what is the ratio of their areas?
Answer» If the circumference of two circles are in the ratio 2 : 3, what is the ratio of their areas?

Discussion

11736.	Find the point where 3x + 2y = 8 intersects the Y axis.
Answer» Find the point where 3x + 2y = 8 intersects the Y axis.

Discussion

11737.	the value of a+b+c, if \sqrt{9+2(1+\sqrt3)(1+\sqrt7)}=a+b\sqrt3+c\sqrt7is
Answer» the value of a+b+c, if \sqrt{9+2(1+\sqrt3)(1+\sqrt7)}=a+b\sqrt3+c\sqrt7is

Discussion

11738.	If the volume of a hemisphere is four times its total surface area, what is its radius?
Answer» If the volume of a hemisphere is four times its total surface area, what is its radius?

Discussion

11739.	In a triangle ABC and DE parallel to BC , if AD= 1.5, AE=1cm and DB =3cm, find EC
Answer» In a triangle ABC and DE parallel to BC , if AD= 1.5, AE=1cm and DB =3cm, find EC

Discussion

11740.	the equation 3sin^2x+10cosx-6=0 is satisfied when
Answer» the equation 3sin^2x+10cosx-6=0 is satisfied when

Discussion

11741.	If an AP has 10 terms and an represents the nth term of the AP, then which of the following is incorrect?
Answer» If an AP has 10 terms and $a_{n}$ represents the $n^{t h}$ term of the AP, then which of the following is incorrect?

Discussion

11742.	A chord of a circle is equal to the radius of the circle.Find the angle subtended by the chord at a point on the minor arc and also at a point on the major arc
Answer» A chord of a circle is equal to the radius of the circle.Find the angle subtended by the chord at a point on the minor arc and also at a point on the major arc

Discussion

11743.	Find the quantity of water in a frustum of height 14 cm and radii 3 cm and 9 cm if water is filled upto brim.1716
Answer» Find the quantity of water in a frustum of height 14 cm and radii 3 cm and 9 cm if water is filled upto brim. 1716

Discussion

11744.	Mark the correct alternative in each of the following:The probability that a number selected at random from the numbers 1, 2, 3, ..., 15 is a multiple of 4, is(a) 415 (b) 215 (c) 15 (d) 13 [CBSE 2014]
Answer» Mark the correct alternative in each of the following: The probability that a number selected at random from the numbers 1, 2, 3, ..., 15 is a multiple of 4, is (a) $\frac{4}{15}$ (b) $\frac{2}{15}$ (c) $\frac{1}{5}$ (d) $\frac{1}{3}$ [CBSE 2014]

Discussion

11745.	Which of the following represent(s) the total Surface area of a square pyramid?
Answer» Which of the following represent(s) the total Surface area of a square pyramid?

Discussion

11746.	If the 4th, 7th and 10th terms of a G.P. be a, b, c respectively, then the relation between a, b, c is
Answer» If the 4th, 7th and 10th terms of a G.P. be a, b, c respectively, then the relation between a, b, c is

Discussion

11747.	A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle 30∘ with it. The distance between the foot of the tree to the point where the top touches the ground is 9 m. Find the height of the tree.
Answer» A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle $30^{\circ}$ with it. The distance between the foot of the tree to the point where the top touches the ground is 9 m. Find the height of the tree.

Discussion

11748.	A solid is composed of a cylinder with hemispherical ends. If the whole length of the solid is 104 cm and the radius of each of the hemispherical ends is 7 cm, find the cost of polishing its surface at the rate of Rs 10 per dm2 .
Answer» A solid is composed of a cylinder with hemispherical ends. If the whole length of the solid is 104 cm and the radius of each of the hemispherical ends is 7 cm, find the cost of polishing its surface at the rate of Rs 10 per dm² .

Discussion

11749.	Explain why 7×11×13+13 & 7×6×5×4×3×2×1+5 are composite numbers ?
Answer» Explain why $7 \times 11 \times 13 + 13$ & $7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 + 5$ are composite numbers ?

Discussion

11750.	Question 4A cone of radius 8 cm and height 12 cm is divided into two parts by a plane through the mid-point of its axis parallel to its base. Find the ratio of the volumes of two parts
Answer» Question 4 A cone of radius 8 cm and height 12 cm is divided into two parts by a plane through the mid-point of its axis parallel to its base. Find the ratio of the volumes of two parts

Discussion

Explore topic-wise InterviewSolutions in .

If four numbers in A.P. are such that their sum is 50 and the greatest number is 4 times, the least, then the numbers are(a) 5, 10, 15, 20(b) 4, 101, 16, 22(c) 3, 7, 11, 15(d) none of these

Question 49 Solve the following: 3x−82x=1

Natural numbers less than 10,000 and divisible by 4 and consisting of only the digits 0,1,2,3,4 and 5 are formed without repetition. Prove that the number of ways to do this is 103.

if a+b+c=1,ab+bc+ca=2,and abc=3 then find 1/a+bc+1/b+ca+1/c+ab

(i) In an A.P., the sum of first n terms is 3n22+13nn. Find its 25th term.(ii) If the sum of first n terms of an A.P. is n2, then find its 10th term.

How many circles can be drawn passing through three definite points when they are non collinear?

A chord of a circle subtends an angle of θ at the centre of the circle. The area of the minor segment cut off by the chord is one eighth of the area of the circle. Prove that8 sinθ2cosθ2+π=πθ45.

The following is known about an AP: Tm=1n,Tn=1m Find the value of Smn. [4 MARKS]

Draw the graphs of the pair of linear equations x − y + 2 = 0 and 4x − y − 4 = 0 . Calculate the area of the triangle formed by the lines so drawn and the x-axis .

Question 6Is 0.2 a root of the equation x2 – 0.4 = 0? Justify your answer.

If the ratio of the sum of the first n terms of two A.PS is (7n + 1) : (4n + 27), then find the ratio of their 9th terms

Volume of two spheres are in ratio 64: 27. Find the ratio of their surface areas.

Solve each of the following quadratic equations: 3√7x2+4x−√7=0

The value of limn→∞cos(x2)cos(x4)⋯cos(x2n−1)cos(x2n) is

Which of the following pairs of lines are parallel?

Two tangents TP and TQ are drawn from an external point T to a circle with centre O as shown in Fig. 10.73. If they are inclined to each other at an angle of 100°, then what is the value of ∠POQ?

In an arithmetic sequence, the ratio of the first term to the second is 2 : 3. What is the ratio of the third term to the fifth term?

Three semicircles each of diameter 3 cm, a circle of diameter 4.5 cm and a semicircle of radius 4.5 cm are drawn in the given figure. Find the area of the shaded region.

The line joining two points A(2,0) and B(3,1) is rotated about A in anticlockwise direction through an angle of 15∘. find the equation of line in the new position. If b goes to c in the new position what will be the coordinates of C.

The radii of two circles are 8 cm and 6 cm respectively. Find the radius of the circle having area equal to the sum of the areas of the two circles.

The area enclosed by the circle x2 + y2 = 2 is equal to(a) 4π sq. units(b) 22π sq. units(c) 4π2 sq. units(d) 2π sq. units

A chord of a circle is equal to the radius of the circle. Find the angle subtended by the chord at a point on the major arc.

22. If the midpoint of the line segment joining the points A(-k, 5)and B(3,2k) lies on the line 3x+6y=-3 then find the value of 'K

A steel box has dimensions of 2 m, 3 m, and 0.5 m. It has to be gold plated using electrolysis. If each square meter of gold plating costs Rs.100, then gold plating the outer surface of the box costs ___.

The probability of happening of an event is p. The maximum and minimum values of pare

Question 6The marks obtained (out of 100) by a class of 80 students are given below:MarksNumber of students10−20620−301730−501550−701670−10026Construct a histogram to represent the data above.

Find the missing term in the sequence 100, 100, ?, 72, 50.4, 30.24

Question 7If figure common tangents AB and CD to two circles intersect at E. Prove that AB = CD.

In the given figure, XY and X'Y' are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersects XY at A and X'Y' at B. Then ∠AOB= ___

What is the distance between two parallel tangents of a circle having radius 4.5 cm ? Justify your answer.

The wheels of a car make 2500 revolutions in covering a distance of 4.95 km. Find the diameter of a wheel.

How many three-digit numbers are divisible by 9? [CBSE 2013]

If the circumference of two circles are in the ratio 2 : 3, what is the ratio of their areas?

Find the point where 3x + 2y = 8 intersects the Y axis.

the value of a+b+c, if \sqrt{9+2(1+\sqrt3)(1+\sqrt7)}=a+b\sqrt3+c\sqrt7is

If the volume of a hemisphere is four times its total surface area, what is its radius?

In a triangle ABC and DE parallel to BC , if AD= 1.5, AE=1cm and DB =3cm, find EC

the equation 3sin^2x+10cosx-6=0 is satisfied when

If an AP has 10 terms and an represents the nth term of the AP, then which of the following is incorrect?

A chord of a circle is equal to the radius of the circle.Find the angle subtended by the chord at a point on the minor arc and also at a point on the major arc

Find the quantity of water in a frustum of height 14 cm and radii 3 cm and 9 cm if water is filled upto brim.1716

Mark the correct alternative in each of the following:The probability that a number selected at random from the numbers 1, 2, 3, ..., 15 is a multiple of 4, is(a) 415 (b) 215 (c) 15 (d) 13 [CBSE 2014]

Which of the following represent(s) the total Surface area of a square pyramid?

If the 4th, 7th and 10th terms of a G.P. be a, b, c respectively, then the relation between a, b, c is

A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle 30∘ with it. The distance between the foot of the tree to the point where the top touches the ground is 9 m. Find the height of the tree.

A solid is composed of a cylinder with hemispherical ends. If the whole length of the solid is 104 cm and the radius of each of the hemispherical ends is 7 cm, find the cost of polishing its surface at the rate of Rs 10 per dm2 .

Explain why 7×11×13+13 &amp; 7×6×5×4×3×2×1+5 are composite numbers ?

Question 4A cone of radius 8 cm and height 12 cm is divided into two parts by a plane through the mid-point of its axis parallel to its base. Find the ratio of the volumes of two parts

Explain why 7×11×13+13 & 7×6×5×4×3×2×1+5 are composite numbers ?