32581 + Interview Questions in Mathematics Page 255 InterviewSolution

12701.	When constructing a histogram with non-uniform (unequal) class widths, we must ensure that the areas of the rectangles are proportional to the ___________.
Answer» When constructing a histogram with non-uniform (unequal) class widths, we must ensure that the areas of the rectangles are proportional to the ___________.

Discussion

12702.	If the sum of the roots of the equation x2 − x = λ(2x − 1) is zero, then λ =(a) −2(b) 2(c) -12(d) 12
Answer» If the sum of the roots of the equation x² − x = λ(2x − 1) is zero, then λ = (a) −2 (b) 2 (c) $- \frac{1}{2}$ (d) $\frac{1}{2}$

Discussion

12703.	A contract on construction job specifies a penalty for delay of completion beyond a certain date as follows: ₹ 200 for the first day, ₹ 250 for the second day, ₹ 300 for the third day, etc., the penalty for each succeeding day being ₹ 50 more than for the preceding day. How much money the contractor has to pay as penalty if he has delayed the work by 30 days?
Answer» A contract on construction job specifies a penalty for delay of completion beyond a certain date as follows: ₹ 200 for the first day, ₹ 250 for the second day, ₹ 300 for the third day, etc., the penalty for each succeeding day being ₹ 50 more than for the preceding day. How much money the contractor has to pay as penalty if he has delayed the work by 30 days?

Discussion

12704.	Which of the following debts is an example of a ‘Treasury bill’?
Answer» Which of the following debts is an example of a ‘Treasury bill’?

Discussion

12705.

The given distribution shows the number of runs scored by some top batsmen of the world in one-day international cricket matches. Runs scored Number of batsmen 3000 − 4000 4 4000 − 5000 18 5000 − 6000 9 6000 − 7000 7 7000 − 8000 6 8000 − 9000 3 9000 − 10000 1 10000 − 11000 1 Find the mode of the data.

Answer»

The given distribution shows the number of runs scored by some top batsmen of the world in one-day international cricket matches.

Runs scored	Number of batsmen
3000 − 4000	4
4000 − 5000	18
5000 − 6000	9
6000 − 7000	7
7000 − 8000	6
8000 − 9000	3
9000 − 10000	1
10000 − 11000	1

Find the mode of the data.

Discussion

12706.	Suppose P,Q are two points on the same side of the line AB, R is a point on the segment PQ such that PR = (lambda) * PQ. Prove that Area of ABR = Area of ABP * (1-lambda) + (lambda) * Area of ABQ.
Answer» Suppose P,Q are two points on the same side of the line AB, R is a point on the segment PQ such that PR = (lambda) * PQ. Prove that Area of ABR = Area of ABP * (1-lambda) + (lambda) * Area of ABQ.

Discussion

12707.	Michael's meeting with Sebastian Shultz had been a chance meeting. Where had it taken place and how?
Answer» Michael's meeting with Sebastian Shultz had been a chance meeting. Where had it taken place and how?

Discussion

12708.	Question 5If we subtract −3x2y2 from x2y2, then we geta) −4x2y2b) −2x2y2c) 2x2y2d) 4x2y2
Answer» Question 5 If we subtract $- 3 x^{2} y^{2}$ from $x^{2} y^{2}$ , then we get a) $- 4 x^{2} y^{2}$ b) $- 2 x^{2} y^{2}$ c) $2 x^{2} y^{2}$ d) $4 x^{2} y^{2}$

Discussion

12709.	In the figure AB & CD are 2 \|\| chords & O is the centre. If the radius of the circle is 15 cm, find the distance MN between the two chords of length 24cm & 18cm respectively.
Answer» In the figure AB & CD are 2 \|\| chords & O is the centre. If the radius of the circle is 15 cm, find the distance MN between the two chords of length 24cm & 18cm respectively.

12709.

In the figure AB & CD are 2 || chords & O is the centre. If the radius of the circle is 15 cm, find the distance MN between the two chords of length 24cm & 18cm respectively.

Answer»

In the figure AB & CD are 2 || chords & O is the centre. If the radius of the circle is 15 cm, find the distance MN between the two chords of length 24cm & 18cm respectively.

Discussion

12710.	16. In the given figure triangle PQRis revolved about PR and a solid in the shape of a cone is formed . The volume of cone is?(see the figure in the picture)
Answer» 16. In the given figure triangle PQRis revolved about PR and a solid in the shape of a cone is formed . The volume of cone is?(see the figure in the picture)

Discussion

12711.	In the given figure, AB and CD are two diameters of a circle (with centre O) perpendicular to each other and OD is the diameter of the smaller circle. If OA = 7 cm, find the area of the shaded region.
Answer» In the given figure, AB and CD are two diameters of a circle (with centre O) perpendicular to each other and OD is the diameter of the smaller circle. If OA = 7 cm, find the area of the shaded region.

12711.

In the given figure, AB and CD are two diameters of a circle (with centre O) perpendicular to each other and OD is the diameter of the smaller circle. If OA = 7 cm, find the area of the shaded region.

Answer»

In the given figure, AB and CD are two diameters of a circle (with centre O) perpendicular to each other and OD is the diameter of the smaller circle. If OA = 7 cm, find the area of the shaded region.

Discussion

12712.	In ∆ABC, a line XY parallel to BC cuts AB at X and AC at Y. If BY bisects ∠XYC, then(a) BC = CY(b) BC = BY(c) BC ≠ CY(d) BC ≠ BY
Answer» In ∆ABC, a line XY parallel to BC cuts AB at X and AC at Y. If BY bisects ∠XYC, then (a) BC = CY (b) BC = BY (c) BC ≠ CY (d) BC ≠ BY

Discussion

12713.	A chord AB of a circle is equal to the radius of the circle. Find the angles subtended by the chord at points on the major arc and the minor arc.
Answer» A chord AB of a circle is equal to the radius of the circle. Find the angles subtended by the chord at points on the major arc and the minor arc.

Discussion

12714.	Question 30Find the sum of last ten terms of the AP 8, 10, 12,…., 126.
Answer» Question 30 Find the sum of last ten terms of the AP 8, 10, 12,…., 126.

Discussion

12715.	If A and B are square matrices of order n such that \|A\|=1 and \|B\|=2, then the value of \|\|3A\|B\| is
Answer» If $A$ and $B$ are square matrices of order $n$ such that $\| A \| = 1$ and $\| B \| = 2,$ then the value of $\| \| 3 A \| B \|$ is

Discussion

12716.	Whether following sequences are APs or not?(i) 2, 4, 8, 16…….. (ii) 2, 3, 5, 7, 11…….. (iii) -1, -1.25, -1.5, -1.75……. (iv) 1, -1, -3, -5, -7…………
Answer» Whether following sequences are APs or not? (i) 2, 4, 8, 16…….. (ii) 2, 3, 5, 7, 11…….. (iii) -1, -1.25, -1.5, -1.75……. (iv) 1, -1, -3, -5, -7…………

12716.

Whether following sequences are APs or not?(i) 2, 4, 8, 16…….. (ii) 2, 3, 5, 7, 11…….. (iii) -1, -1.25, -1.5, -1.75……. (iv) 1, -1, -3, -5, -7…………

Answer»

Whether following sequences are APs or not?

(i) 2, 4, 8, 16……..

(ii) 2, 3, 5, 7, 11……..

(iii) -1, -1.25, -1.5, -1.75…….

(iv) 1, -1, -3, -5, -7…………

Discussion

12717.	The time complexity of an efficient algorithm to merge two binary heaps each of size n into a single heap is
Answer» The time complexity of an efficient algorithm to merge two binary heaps each of size n into a single heap is

Discussion

12718.	What are angles in alternate segments?
Answer» What are angles in alternate segments?

Discussion

12719.	A card is chosen from a well-shuffled deck of 52 cards. Calculate the probability that a card randomly picked will not be an ace.0.923
Answer» A card is chosen from a well-shuffled deck of 52 cards. Calculate the probability that a card randomly picked will not be an ace. 0.923

Discussion

12720.	The following table records the number of books read by fifteen year old kids. Find the median of the data.No. of booksFrequency021427344250617881397102
Answer» The following table records the number of books read by fifteen year old kids. Find the median of the data. $\begin{matrix} No. of books & Frequency 0 & 2 1 & 4 2 & 7 3 & 4 4 & 2 5 & 0 6 & 1 7 & 8 8 & 13 9 & 7 10 & 2 \end{matrix}$

12720.

The following table records the number of books read by fifteen year old kids. Find the median of the data.No. of booksFrequency021427344250617881397102

Answer»

The following table records the number of books read by fifteen year old kids. Find the median of the data.

$\begin{matrix} No. of books & Frequency 0 & 2 1 & 4 2 & 7 3 & 4 4 & 2 5 & 0 6 & 1 7 & 8 8 & 13 9 & 7 10 & 2 \end{matrix}$

Discussion

12721.	If α, β are the zeros of the polynomial f(x) = x2 + x + 1, then 1α+1β=(a) 1(b) −1(c) 0(d) None of these
Answer» If α, β are the zeros of the polynomial f(x) = x² + x + 1, then $\frac{1}{α} + \frac{1}{β} =$ (a) 1 (b) −1 (c) 0 (d) None of these

Discussion

12722.	On selling apples at Rs 40 per kg, a vendor incurs 10% loss. If he incurs a total loss of Rs 120, calculate the quantity (in kg) of apples he sold.
Answer» On selling apples at Rs 40 per kg, a vendor incurs 10% loss. If he incurs a total loss of Rs 120, calculate the quantity (in kg) of apples he sold.

Discussion

12723.	Construct ∆ XYZ, such that YZ = 7.4 cm, ∠XYZ = 45° and XY - XZ = 2.7 cm.
Answer» Construct $∆$ XYZ, such that YZ = 7.4 cm, $∠$ XYZ = $45^{°}$ and XY $-$ XZ = 2.7 cm.

Discussion

12724.	29. If A+B+C=pi , then prove that cos2A+cos2B+cos2C =-1-4 cosA cosB cosC .
Answer» 29. If A+B+C=pi , then prove that cos2A+cos2B+cos2C =-1-4 cosA cosB cosC .

Discussion

12725.	In a ∆ABC, point D is on side AB and point E is on side AC, such that BCED is a trapezium. If DE : BC = 3 : 5, then Area (∆ ADE) : Area (◻BCED) =(a) 3 : 4(b) 9 : 16(c) 3 : 5(d) 9 : 25
Answer» In a ∆ABC, point D is on side AB and point E is on side AC, such that BCED is a trapezium. If DE : BC = 3 : 5, then Area (∆ ADE) : Area (◻BCED) = (a) 3 : 4 (b) 9 : 16 (c) 3 : 5 (d) 9 : 25

Discussion

12726.	A two digit number is formed with digits 2, 3, 5, 7, 9 without repetition. What is the probability that the number formed is(1) an odd number ?(2) a multiple of 5 ?
Answer» A two digit number is formed with digits 2, 3, 5, 7, 9 without repetition. What is the probability that the number formed is (1) an odd number ? (2) a multiple of 5 ?

Discussion

12727.	Show that the semi-vertical angle ofthe cone of the maximum volume and of given slant height is.
Answer» Show that the semi-vertical angle of the cone of the maximum volume and of given slant height is.

Discussion

12728.	Tan(55-A)-cot(35+A)
Answer» Tan(55-A)-cot(35+A)

Discussion

12729.	Find the value(s) of k so that PQ will be parallel to RS. Given :(i) P (2, 4), Q (3, 6), R (8, 1) and S (10, k)(ii) P (5, -1), Q (6, 11), R (6, -4k) and S (7, k2)
Answer» Find the value(s) of k so that PQ will be parallel to RS. Given : (i) P (2, 4), Q (3, 6), R (8, 1) and S (10, k) (ii) P (5, -1), Q (6, 11), R (6, -4k) and S (7, $k^{2}$ )

12729.

Find the value(s) of k so that PQ will be parallel to RS. Given :(i) P (2, 4), Q (3, 6), R (8, 1) and S (10, k)(ii) P (5, -1), Q (6, 11), R (6, -4k) and S (7, k2)

Answer»

Find the value(s) of k so that PQ will be parallel to RS. Given :

(i) P (2, 4), Q (3, 6), R (8, 1) and S (10, k)

(ii) P (5, -1), Q (6, 11), R (6, -4k) and S (7, $k^{2}$ )

Discussion

12730.	Question 14 (iv)One card is drawn from a well–shuffled deck of 52 cards. Find the probability of getting the jack of heart.
Answer» Question 14 (iv) One card is drawn from a well–shuffled deck of 52 cards. Find the probability of getting the jack of heart.

Discussion

12731.	If Δ=∣∣∣∣∣(1+ax)2(1+bx)2(1+cx)2(1+ay)2(1+by)2(1+cy)2(1+az)2(1+bz)2(1+cz)2∣∣∣∣∣ and Δ=λ∣∣∣∣∣1xx21yy21zz2∣∣∣∣∣×∣∣∣∣∣1aa21bb21cc2∣∣∣∣∣,then the value of λ is
Answer» If $Δ = ∣ ∣∣∣ ∣ \begin{matrix} (1 + a x)^{2} & (1 + b x)^{2} & (1 + c x)^{2} (1 + a y)^{2} & (1 + b y)^{2} & (1 + c y)^{2} (1 + a z)^{2} & (1 + b z)^{2} & (1 + c z)^{2} \end{matrix} ∣ ∣∣∣ ∣$ and $Δ = λ ∣ ∣∣∣ ∣ \begin{matrix} 1 & x & x^{2} 1 & y & y^{2} 1 & z & z^{2} \end{matrix} ∣ ∣∣∣ ∣ \times ∣ ∣∣∣ ∣ \begin{matrix} 1 & a & a^{2} 1 & b & b^{2} 1 & c & c^{2} \end{matrix} ∣ ∣∣∣ ∣,$ then the value of $λ$ is

Discussion

12732.	If Pa2, 4 is the midpoint of the line segment joining the points A(−6, 5) and B(−2, 3) then the value of a is [CBSE 2011](a) −8 (b) 3 (c) −4 (d) 4
Answer» If $P (\frac{a}{2}, 4)$ is the midpoint of the line segment joining the points A(−6, 5) and B(−2, 3) then the value of a is [CBSE 2011] (a) −8 (b) 3 (c) −4 (d) 4

Discussion

12733.	If a pair of linear equations is consistent with a unique solution, then the lines representing them are _______.
Answer» If a pair of linear equations is consistent with a unique solution, then the lines representing them are _______.

Discussion

12734.	A trapezium ABCD is inscribed into a semi-circle of radius l so that the base AD of the trapezium is diameter and the vertices B and C lie on the circumference. Then the value of base angle θ (in degree) of the trapezium ABCD which has the greatest perimeter, is
Answer» A trapezium $A B C D$ is inscribed into a semi-circle of radius $l$ so that the base $A D$ of the trapezium is diameter and the vertices $B$ and $C$ lie on the circumference. Then the value of base angle $θ$ (in degree) of the trapezium $A B C D$ which has the greatest perimeter, is

Discussion

12735.	Refer to the following figure. Three squares are constructed on each side of the triangle as shown, with the length of each square equal to the side on which it is constructed. If the largest side is 13, sum of the areas of the three squares is __. The angle opposite to the blue colour square is the right angle.
Answer» Refer to the following figure. Three squares are constructed on each side of the triangle as shown, with the length of each square equal to the side on which it is constructed. If the largest side is 13, sum of the areas of the three squares is __. The angle opposite to the blue colour square is the right angle.

12735.

Refer to the following figure. Three squares are constructed on each side of the triangle as shown, with the length of each square equal to the side on which it is constructed. If the largest side is 13, sum of the areas of the three squares is __. The angle opposite to the blue colour square is the right angle.

Answer»

Refer to the following figure. Three squares are constructed on each side of the triangle as shown, with the length of each square equal to the side on which it is constructed. If the largest side is 13, sum of the areas of the three squares is __. The angle opposite to the blue colour square is the right angle.

Discussion

12736.	Find the number of terms in each of the following APs:(i) 7,13,19....,205 (ii) 18,312,13,...−47
Answer» Find the number of terms in each of the following APs: (i) $7, 13, 19...., 205$ (ii) $18, \frac{31}{2}, 13, . . . - 47$

Discussion

12737.	Find the point on the X–axis which is equidistant from A(–3, 4) and B(1, –4).
Answer» Find the point on the X–axis which is equidistant from A(–3, 4) and B(1, –4).

Discussion

12738.	(i) Is circle a polygon ?(ii) Is the chord of a circle also a radius of the circle ?
Answer» (i) Is circle a polygon ? (ii) Is the chord of a circle also a radius of the circle ?

Discussion

12739.	Ali was asked to construct a square for which only the length of the diagonal alone is given. He was given a compass and a straight edge (a ruler with NO markings). The square is ACBD with AB as one of its diagonal. P is said to be the point of intersection of the diagonals of the square. Which of the following is constructed as a first step in this construction?
Answer» Ali was asked to construct a square for which only the length of the diagonal alone is given. He was given a compass and a straight edge (a ruler with NO markings). The square is ACBD with AB as one of its diagonal. P is said to be the point of intersection of the diagonals of the square. Which of the following is constructed as a first step in this construction?

Discussion

12740.	In Fig. 3, APB and AQO are semicircles, and AO=OB. If the perimeter of the figure is 40 cm, find the area of the shaded region. Use π=227
Answer» In Fig. 3, APB and AQO are semicircles, and AO=OB. If the perimeter of the figure is 40 cm, find the area of the shaded region. Use $π = \frac{22}{7}$

Discussion

12741.	Construct ∆ PQR, such that QR = 7.4 cm, ∠PQR= 60° and PQ - PR = 2.5 cm.
Answer» Construct $∆$ PQR, such that QR = 7.4 cm, $∠$ PQR= $60^{°}$ and PQ $-$ PR = 2.5 cm.

Discussion

12742.	What is the remainder when x3+2x2–3 is divided by x – 2?
Answer» What is the remainder when $x^{3} + 2 x^{2} - 3$ is divided by x – 2?

Discussion

12743.	In the given figure, PA and PB are two tangents to the circle with center O. If ∠APB=40∘, find ∠AQB and ∠AMB. [4 MARKS]
Answer» In the given figure, PA and PB are two tangents to the circle with center O. If $∠ A P B = 40^{\circ}$ , find $∠ A Q B$ and $∠ A M B$ . [4 MARKS]

12743.

In the given figure, PA and PB are two tangents to the circle with center O. If ∠APB=40∘, find ∠AQB and ∠AMB. [4 MARKS]

Answer»

In the given figure, PA and PB are two tangents to the circle with center O. If $∠ A P B = 40^{\circ}$ , find $∠ A Q B$ and $∠ A M B$ . [4 MARKS]

Discussion

12744.	Zero polynomial is a special case of a constant polynomial.
Answer» Zero polynomial is a special case of a constant polynomial.

Discussion

12745.	Using an appropriate method, find the mean of the following frequency distribution: Classinterval84−9090−9696−102102−108108−114114−120Frequency81016231211 Which method did you use and why?
Answer» Using an appropriate method, find the mean of the following frequency distribution: $\begin{matrix} Class interval & 84 - 90 & 90 - 96 & 96 - 102 & 102 - 108 & 108 - 114 & 114 - 120 Frequency & 8 & 10 & 16 & 23 & 12 & 11 \end{matrix}$ Which method did you use and why?

Discussion

12746.	The rain water from a 22 m × 20 m roof drains into a cylindrical vessel of diameter 2 m and height 3.5 m. If the rain water collected from the roof fills 45th of the cylindrical vessel, then find the rainfall in centimetre. [CBSE 2015]
Answer» The rain water from a 22 m $\times$ 20 m roof drains into a cylindrical vessel of diameter 2 m and height 3.5 m. If the rain water collected from the roof fills $\frac{4}{5}$ th of the cylindrical vessel, then find the rainfall in centimetre. [CBSE 2015]

Discussion

12747.	A circular ground of radius 50 m has to be covered with a waterproof sheet. The same amount of waterproof sheet is also used for making a conical tent. If the base area of the tent is 625π m2, then the height of the tent is____m.
Answer» A circular ground of radius 50 $m$ has to be covered with a waterproof sheet. The same amount of waterproof sheet is also used for making a conical tent. If the base area of the tent is $625 π m^{2}$ , then the height of the tent is____ $m$ .

Discussion

12748.	If sinθ=cc2+d2, where d > 0 then find the values of cos θ and tan θ.
Answer» If $sinθ = \frac{c}{\sqrt{c^{2} + d^{2}}}$ , where d > 0 then find the values of cos θ and tan θ.

Discussion

12749.	Find the product of x-intercept and y-intercept of the line 2x+4y=10.12.5
Answer» Find the product of x-intercept and y-intercept of the line $2 x + 4 y = 10$ . 12.5

Discussion

12750.

In the given figure, a circle touches the side BC of △ABC at P and AB and AC produced at Q and R respectively. If AQ=15 cm, then the perimeter of △ABC is ___ cm

Answer»

In the given figure, a circle touches the side BC of $△$ ABC at P and AB and AC produced at Q and R respectively. If $A Q = 15 c m,$ then the perimeter of $△$ ABC is ___ $c m$

Discussion

Explore topic-wise InterviewSolutions in .

When constructing a histogram with non-uniform (unequal) class widths, we must ensure that the areas of the rectangles are proportional to the ___________.

If the sum of the roots of the equation x2 − x = λ(2x − 1) is zero, then λ =(a) −2(b) 2(c) -12(d) 12

Which of the following debts is an example of a ‘Treasury bill’?

Suppose P,Q are two points on the same side of the line AB, R is a point on the segment PQ such that PR = (lambda) * PQ. Prove that Area of ABR = Area of ABP * (1-lambda) + (lambda) * Area of ABQ.

Michael's meeting with Sebastian Shultz had been a chance meeting. Where had it taken place and how?

Question 5If we subtract −3x2y2 from x2y2, then we geta) −4x2y2b) −2x2y2c) 2x2y2d) 4x2y2

In the figure AB &amp; CD are 2 || chords &amp; O is the centre. If the radius of the circle is 15 cm, find the distance MN between the two chords of length 24cm &amp; 18cm respectively.

16. In the given figure triangle PQRis revolved about PR and a solid in the shape of a cone is formed . The volume of cone is?(see the figure in the picture)

In the given figure, AB and CD are two diameters of a circle (with centre O) perpendicular to each other and OD is the diameter of the smaller circle. If OA = 7 cm, find the area of the shaded region.

In ∆ABC, a line XY parallel to BC cuts AB at X and AC at Y. If BY bisects ∠XYC, then(a) BC = CY(b) BC = BY(c) BC ≠ CY(d) BC ≠ BY

A chord AB of a circle is equal to the radius of the circle. Find the angles subtended by the chord at points on the major arc and the minor arc.

Question 30Find the sum of last ten terms of the AP 8, 10, 12,…., 126.

If A and B are square matrices of order n such that |A|=1 and |B|=2, then the value of ||3A|B| is

Whether following sequences are APs or not?(i) 2, 4, 8, 16…….. (ii) 2, 3, 5, 7, 11…….. (iii) -1, -1.25, -1.5, -1.75……. (iv) 1, -1, -3, -5, -7…………

The time complexity of an efficient algorithm to merge two binary heaps each of size n into a single heap is

What are angles in alternate segments?

A card is chosen from a well-shuffled deck of 52 cards. Calculate the probability that a card randomly picked will not be an ace.0.923

The following table records the number of books read by fifteen year old kids. Find the median of the data.No. of booksFrequency021427344250617881397102

If α, β are the zeros of the polynomial f(x) = x2 + x + 1, then 1α+1β=(a) 1(b) −1(c) 0(d) None of these

On selling apples at Rs 40 per kg, a vendor incurs 10% loss. If he incurs a total loss of Rs 120, calculate the quantity (in kg) of apples he sold.

Construct ∆ XYZ, such that YZ = 7.4 cm, ∠XYZ = 45° and XY - XZ = 2.7 cm.

29. If A+B+C=pi , then prove that cos2A+cos2B+cos2C =-1-4 cosA cosB cosC .

In a ∆ABC, point D is on side AB and point E is on side AC, such that BCED is a trapezium. If DE : BC = 3 : 5, then Area (∆ ADE) : Area (◻BCED) =(a) 3 : 4(b) 9 : 16(c) 3 : 5(d) 9 : 25

A two digit number is formed with digits 2, 3, 5, 7, 9 without repetition. What is the probability that the number formed is(1) an odd number ?(2) a multiple of 5 ?

Show that the semi-vertical angle ofthe cone of the maximum volume and of given slant height is.

Tan(55-A)-cot(35+A)

Find the value(s) of k so that PQ will be parallel to RS. Given :(i) P (2, 4), Q (3, 6), R (8, 1) and S (10, k)(ii) P (5, -1), Q (6, 11), R (6, -4k) and S (7, k2)

Question 14 (iv)One card is drawn from a well–shuffled deck of 52 cards. Find the probability of getting the jack of heart.

If Δ=∣∣∣∣∣(1+ax)2(1+bx)2(1+cx)2(1+ay)2(1+by)2(1+cy)2(1+az)2(1+bz)2(1+cz)2∣∣∣∣∣ and Δ=λ∣∣∣∣∣1xx21yy21zz2∣∣∣∣∣×∣∣∣∣∣1aa21bb21cc2∣∣∣∣∣,then the value of λ is

If Pa2, 4 is the midpoint of the line segment joining the points A(−6, 5) and B(−2, 3) then the value of a is [CBSE 2011](a) −8 (b) 3 (c) −4 (d) 4

If a pair of linear equations is consistent with a unique solution, then the lines representing them are _______.

A trapezium ABCD is inscribed into a semi-circle of radius l so that the base AD of the trapezium is diameter and the vertices B and C lie on the circumference. Then the value of base angle θ (in degree) of the trapezium ABCD which has the greatest perimeter, is

Find the number of terms in each of the following APs:(i) 7,13,19....,205 (ii) 18,312,13,...−47

Find the point on the X–axis which is equidistant from A(–3, 4) and B(1, –4).

(i) Is circle a polygon ?(ii) Is the chord of a circle also a radius of the circle ?

In Fig. 3, APB and AQO are semicircles, and AO=OB. If the perimeter of the figure is 40 cm, find the area of the shaded region. Use π=227

Construct ∆ PQR, such that QR = 7.4 cm, ∠PQR= 60° and PQ - PR = 2.5 cm.

What is the remainder when x3+2x2–3 is divided by x – 2?

In the given figure, PA and PB are two tangents to the circle with center O. If ∠APB=40∘, find ∠AQB and ∠AMB. [4 MARKS]

Zero polynomial is a special case of a constant polynomial.

Using an appropriate method, find the mean of the following frequency distribution: Classinterval84−9090−9696−102102−108108−114114−120Frequency81016231211 Which method did you use and why?

The rain water from a 22 m × 20 m roof drains into a cylindrical vessel of diameter 2 m and height 3.5 m. If the rain water collected from the roof fills 45th of the cylindrical vessel, then find the rainfall in centimetre. [CBSE 2015]

A circular ground of radius 50 m has to be covered with a waterproof sheet. The same amount of waterproof sheet is also used for making a conical tent. If the base area of the tent is 625π m2, then the height of the tent is____m.

If sinθ=cc2+d2, where d > 0 then find the values of cos θ and tan θ.

Find the product of x-intercept and y-intercept of the line 2x+4y=10.12.5

In the given figure, a circle touches the side BC of △ABC at P and AB and AC produced at Q and R respectively. If AQ=15 cm, then the perimeter of △ABC is ___ cm

In the figure AB & CD are 2 || chords & O is the centre. If the radius of the circle is 15 cm, find the distance MN between the two chords of length 24cm & 18cm respectively.