32581 + Interview Questions in Mathematics Page 97 InterviewSolution

4801.	Question 26A school has five houses A,B,C,D and E. A class has 23 students, 4 from house A, 8 from house, B, 5 from house C,2 from house D and rest from house E. A single student is selected at random to be the class monitor. The probability that the selected student is not from A, B and C is(a) 423(b) 623(c) 823(d) 1723
Answer» Question 26 A school has five houses A,B,C,D and E. A class has 23 students, 4 from house A, 8 from house, B, 5 from house C,2 from house D and rest from house E. A single student is selected at random to be the class monitor. The probability that the selected student is not from A, B and C is (a) $\frac{4}{23}$ (b) $\frac{6}{23}$ (c) $\frac{8}{23}$ (d) $\frac{17}{23}$

Discussion

4802.	What should be subtracted from 3x3−5x2+4x−3 so that the resulting expression has x + 2 as a factor?
Answer» What should be subtracted from $3 x^{3} - 5 x^{2} + 4 x - 3$ so that the resulting expression has x + 2 as a factor?

Discussion

4803.	If the mode of the data: 16, 15, 17, 16, 15, x, 19, 17, 14 is 15, then x =(a) 15(b) 16(c) 17(d) 19
Answer» If the mode of the data: 16, 15, 17, 16, 15, x, 19, 17, 14 is 15, then x = (a) 15 (b) 16 (c) 17 (d) 19

Discussion

4804.	A number is selected from numbers 1 to 25. The probability that it is prime is(a) 23(b) 16(c) 13(d) 56
Answer» A number is selected from numbers 1 to 25. The probability that it is prime is (a) $\frac{2}{3}$ (b) $\frac{1}{6}$ (c) $\frac{1}{3}$ (d) $\frac{5}{6}$

Discussion

4805.	All edges of a square pyramid are of equal lengths. If the length of the base edge is 20 cm, what is the total surface area?
Answer» All edges of a square pyramid are of equal lengths. If the length of the base edge is $20 c m$ , what is the total surface area?

Discussion

4806.	A card is drawn from a well-shuffled pack of 52 cards. Find the probability that the card drawn is neither a jack nor a queen.
Answer» A card is drawn from a well-shuffled pack of 52 cards. Find the probability that the card drawn is neither a jack nor a queen.

Discussion

4807.	Question 109 (i) Observe the following patterns and fill in the blanks to make the statements true: −5×4=−20 −5×3=−15=−20–(−5) −5×2 =____ = -15 – (-5) −5×1=____=____ −5×0=0=____ −5×(−1)=5=____ −5×(−2)=_____=_____
Answer» Question 109 (i) Observe the following patterns and fill in the blanks to make the statements true: $- 5 \times 4 = - 20$ $- 5 \times 3 = - 15 = - 20 - (- 5)$ $- 5 \times 2$ =____ = -15 – (-5) $- 5 \times 1 =$ ____=____ $- 5 \times 0 = 0 =$ ____ $- 5 \times (- 1) = 5 =$ ____ $- 5 \times (- 2) =$ _____=_____

4807.

Question 109 (i) Observe the following patterns and fill in the blanks to make the statements true: −5×4=−20 −5×3=−15=−20–(−5) −5×2 =__ = -15 – (-5) −5×1== −5×0=0= −5×(−1)=5= −5×(−2)=_=___

Answer»

Question 109 (i)

Observe the following patterns and fill in the blanks to make the statements true:
$- 5 \times 4 = - 20$
$- 5 \times 3 = - 15 = - 20 - (- 5)$
$- 5 \times 2$ =____ = -15 – (-5)
$- 5 \times 1 =$ ____=____
$- 5 \times 0 = 0 =$ ____
$- 5 \times (- 1) = 5 =$ ____
$- 5 \times (- 2) =$ _____=_____

Discussion

4808.	If 2 is added to the numerator of a fraction, it reduces to 1/2 and if 1 is subtracted from the denominator, it reduces to 1/3/. Find the fraction.
Answer» If 2 is added to the numerator of a fraction, it reduces to 1/2 and if 1 is subtracted from the denominator, it reduces to 1/3/. Find the fraction.

Discussion

4809.	A container made of a metal sheet open at the top is of the form of frustum of cone, whose height is 16 cm and the radii of its lower and upper circular edges are 8 cm and 20cm respectively. Find(i) the cost of metal sheet used to make the container if it costs ₹ 10 per 100 cm2 [CBSE 2013](ii) the cost of milk at the rate of ₹ 35 per litre which can fill it completely. [CBSE 2017]
Answer» A container made of a metal sheet open at the top is of the form of frustum of cone, whose height is 16 cm and the radii of its lower and upper circular edges are 8 cm and 20cm respectively. Find (i) the cost of metal sheet used to make the container if it costs ₹ 10 per 100 cm²[CBSE 2013] (ii) the cost of milk at the rate of ₹ 35 per litre which can fill it completely. [CBSE 2017]

Discussion

4810.	Question 2 (i)Find the value of 'k', for which the following points are collinear.(i) (7, -2), (5, 1), (3, k)
Answer» Question 2 (i) Find the value of 'k', for which the following points are collinear. (i) (7, -2), (5, 1), (3, k)

Discussion

4811.	The numerator of a fraction is 3 less than the denominator. If 2 is added to both the numerator and the denominator, then the sum of the new fraction and the original fraction is 2920. Find the original fraction.
Answer» The numerator of a fraction is 3 less than the denominator. If 2 is added to both the numerator and the denominator, then the sum of the new fraction and the original fraction is $\frac{29}{20}$ . Find the original fraction.

Discussion

4812.	The circumference of a circle is 22 cm. Find the area of its quadrant. [CBSE 2012]
Answer» The circumference of a circle is 22 cm. Find the area of its quadrant. [CBSE 2012]

Discussion

4813.	A cubical vessel of height 1 m is full of water the minimum work done in taking out water from The vessel will be
Answer» A cubical vessel of height 1 m is full of water the minimum work done in taking out water from The vessel will be

Discussion

4814.	Given that HCF (306, 657) = 9, find LCM (306, 657)..
Answer» Given that HCF (306, 657) = 9, find LCM (306, 657)..

Discussion

4815.	Let U={1,2,3,4,5,6,7,8,9,10}. If A={1,2,5} and B={6,7}, then A∩B′ is
Answer» Let $U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}$ . If $A = {1, 2, 5}$ and $B = {6, 7},$ then $A \cap B^{'}$ is

Discussion

4816.	The discriminant of the equation 2x2−5x−2=0 is41
Answer» The discriminant of the equation $2 x^{2} - 5 x - 2 = 0$ is 41

Discussion

4817.	Solve \|g(x)+16 –x² \| =\|g(x)\|+\|9-x2 \|+7, given that g(x)≥0
Answer» Solve \|g(x)+16 –x² \| =\|g(x)\|+\|9-x2 \|+7, given that g(x)≥0

Discussion

4818.	Which of the following is not a model for a plane surface?
Answer» Which of the following is not a model for a plane surface?

Discussion

4819.	9 For what values of k ,the following equation has no solution Kx+3y= k-3, 12x+ky= k
Answer» 9 For what values of k ,the following equation has no solution Kx+3y= k-3, 12x+ky= k

Discussion

4820.	The slope of a line parallel to X-axis is ___ .
Answer» The slope of a line parallel to X-axis is ___ .

Discussion

4821.	Question 15The line segment joining the points A(3,2) and B(5,1) is divided at the point P in the ratio 1:2 and it lies on the line 3x-18y+k=0. Find the value of k.
Answer» Question 15 The line segment joining the points A(3,2) and B(5,1) is divided at the point P in the ratio 1:2 and it lies on the line 3x-18y+k=0. Find the value of k.

Discussion

4822.	If a chord of a circle of radius 5 cm subtends 120∘ at the centre of the circle, then the area of the corresponding segment of the circle is
Answer» If a chord of a circle of radius $5 cm$ subtends $120^{\circ}$ at the centre of the circle, then the area of the corresponding segment of the circle is

Discussion

4823.	which of the following polynomials has the factors (x+7) (x-1) ?
Answer» which of the following polynomials has the factors (x+7) (x-1) ?

Discussion

4824.	Question 4If a line intersects two concentric circles (circles with the same centre) with centre O at A, B, C and D, prove that AB = CD.
Answer» Question 4 If a line intersects two concentric circles (circles with the same centre) with centre O at A, B, C and D, prove that AB = CD.

Discussion

4825.	The value of (cos2 23° – sin2 67°) is ____________.
Answer» The value of (cos² 23° – sin² 67°) is ____________.

Discussion

4826.	4+3square root 5/square root 5 = a+b square root 5 . Find the value of b :
Answer» 4+3square root 5/square root 5 = a+b square root 5 . Find the value of b :

Discussion

4827.	tan100°+tan125°+tan100°+tan125° is equal to
Answer» tan100°+tan125°+tan100°+tan125° is equal to

Discussion

4828.	Sum of the areas of two squares is 400cm2. If the difference of their perimeters is 16cm, find the sides of two squares.
Answer» Sum of the areas of two squares is $400 c m^{2} .$ If the difference of their perimeters is 16cm, find the sides of two squares.

Discussion

4829.	if a-B,and a and a+B are the zeroes of the polynomial f(x)=x^3-3px^2+qx-r,then which of the following relation is correct
Answer» if a-B,and a and a+B are the zeroes of the polynomial f(x)=x^3-3px^2+qx-r,then which of the following relation is correct

Discussion

4830.	18 terms are inserted between 3 and 45 such that the resulting sequence is an AP. The sum of the resulting (finite) AP including the terms 3 and 45 is ___.
Answer» 18 terms are inserted between 3 and 45 such that the resulting sequence is an AP. The sum of the resulting (finite) AP including the terms 3 and 45 is ___.

Discussion

4831.	Look at the following figure, the reading on the bottom is the measurement obtained and the reading at the top is the zero error. Find the actual measurement.
Answer» Look at the following figure, the reading on the bottom is the measurement obtained and the reading at the top is the zero error. Find the actual measurement.

4831.

Look at the following figure, the reading on the bottom is the measurement obtained and the reading at the top is the zero error. Find the actual measurement.

Answer»

Look at the following figure, the reading on the bottom is the measurement obtained and the reading at the top is the zero error. Find the actual measurement.

Discussion

4832.	In any triangle, the point of intersection of the medians divides each median in the ratio of _____ .
Answer» In any triangle, the point of intersection of the medians divides each median in the ratio of _____ .

Discussion

4833.	If sinθ=x, then write the value of cotθ.
Answer» $If \sin θ = x, then write the value of \cot θ .$

Discussion

4834.	Question 1 (iii) Fill in the blanks using the correct word in the given bracket. (iii) All____triangles are similar. (isosceles, equilateral)
Answer» Question 1 (iii) Fill in the blanks using the correct word in the given bracket. (iii) All____triangles are similar. (isosceles, equilateral)

Discussion

4835.	How many bricks , each of dimensions 25cm×15cm×8cm will be required to build a wall of dimensions 10m×4m×5m, if 1/10 th of its volume is occupied by mortar?
Answer» How many bricks , each of dimensions 25cm×15cm×8cm will be required to build a wall of dimensions 10m×4m×5m, if 1/10 th of its volume is occupied by mortar?

Discussion

4836.	11. From an external point P tangent PA and PB are drawn to a circle with centre O. If CD is the tangent to the circle at a point E and PA= 14 cm , find the perimeter of Δ PCD.
Answer» 11. From an external point P tangent PA and PB are drawn to a circle with centre O. If CD is the tangent to the circle at a point E and PA= 14 cm , find the perimeter of Δ PCD.

Discussion

4837.	sec theta -tan theta=a/b find tan theta
Answer» sec theta -tan theta=a/b find tan theta

Discussion

4838.	Find the 5th term of an arithmetic sequence whose nth term is 3n - 2.
Answer» Find the 5th term of an arithmetic sequence whose nth term is 3n - 2.

Discussion

4839.	Mark the correct alternative in each of the following:If x-2x-2≥0, then(a) x∈[2, ∞)(b) x∈(2, ∞)(c) x∈(-∞, 2)(d) x∈(-∞, 2]
Answer» Mark the correct alternative in each of the following: If $\frac{\|x - 2\|}{x - 2}$ $\geq$ 0, then (a) x $\in$ [2, $\infty$ ) (b) x $\in$ (2, $\infty$ ) (c) x $\in$ ( $-$ $\infty$ , 2) (d) x $\in$ ( $-$ $\infty$ , 2]

Discussion

4840.	Let a matrix A=⎡⎢⎣−1232−3465−3⎤⎥⎦, then which of the followingstatement(s) is(are) correct?(where Mij is minor of element [aij])
Answer» Let a matrix $A = ⎡ ⎢ ⎣ \begin{matrix} - 1 & 2 & 3 2 & - 3 & 4 6 & 5 & - 3 \end{matrix} ⎤ ⎥ ⎦,$ then which of the following statement(s) is(are) correct? (where $M_{i j}$ is minor of element $[a_{i j}]$ )

Discussion

4841.	The sum of `n' terms of a finite AP is 132 times the sum of its first and last terms. Which term would be the middle term in this AP?
Answer» The sum of `n' terms of a finite AP is $\frac{13}{2}$ times the sum of its first and last terms. Which term would be the middle term in this AP?

Discussion

4842.	Which of the following pair of lines in a circle cannot be parallel? [CBSE 2011](a) two chords(b) a chord and a tangent(c) two tangents(d) two diameters
Answer» Which of the following pair of lines in a circle cannot be parallel? [CBSE 2011] (a) two chords (b) a chord and a tangent (c) two tangents (d) two diameters

Discussion

4843.	What must be added to each of the numbers 1, 10, 46 so that the resulting numbers are in G.P.?2
Answer» What must be added to each of the numbers 1, 10, 46 so that the resulting numbers are in G.P.? 2

Discussion

4844.	In the given figure, O is the centre of the circle and BCD is tangent to it at C. Prove that ∠BAC + ∠ACD = 90°.
Answer» In the given figure, O is the centre of the circle and BCD is tangent to it at C. Prove that ∠BAC + ∠ACD = 90°.

Discussion

4845.	√1+cos A1−cos A = ? (a) cosec A - cot A (b) cosec A + cot A (c) cosec A cot A (d) none of these
Answer» $\sqrt{\frac{1 + c o s A}{1 - c o s A}}$ = ? (a) cosec A - cot A (b) cosec A + cot A (c) cosec A cot A (d) none of these

4845.

√1+cos A1−cos A = ? (a) cosec A - cot A (b) cosec A + cot A (c) cosec A cot A (d) none of these

Answer»

$\sqrt{\frac{1 + c o s A}{1 - c o s A}}$ = ?

(a) cosec A - cot A (b) cosec A + cot A

(c) cosec A cot A (d) none of these

Discussion

4846.	An observe s†an ding 80cm above the surface of pond .A fish is 60cm below the surface of pond .find apparent height of observer seen by fis
Answer» An observe s†an ding 80cm above the surface of pond .A fish is 60cm below the surface of pond .find apparent height of observer seen by fis

Discussion

4847.	If −5 is a root of the quadratic equation 2x2+px−15=0 and the quadratic equation p(x2+x)+k=0 has equal roots, find the value of k.
Answer» If $- 5$ is a root of the quadratic equation $2 x^{2} + p x - 15 = 0$ and the quadratic equation $p (x^{2} + x) + k = 0$ has equal roots, find the value of $k$ .

Discussion

4848.	If A and B are acute angles such that sin A = cos B then (A + B) = ?(a) 45°(b) 60°(c) 90°(d) 180°
Answer» If A and B are acute angles such that sin A = cos B then (A + B) = ? (a) 45° (b) 60° (c) 90° (d) 180°

Discussion

4849.	Draw two congruent circles of radii 3 cm, having their centres 8 cm apart. Draw a transverse common tangent.
Answer» Draw two congruent circles of radii 3 cm, having their centres 8 cm apart. Draw a transverse common tangent.

Discussion

4850.	Show that the altitude of the rightcircular cone of maximum volume that can be inscribed in a sphere ofradius r is.
Answer» Show that the altitude of the right circular cone of maximum volume that can be inscribed in a sphere of radius r is.

Discussion

Explore topic-wise InterviewSolutions in .

What should be subtracted from 3x3−5x2+4x−3 so that the resulting expression has x + 2 as a factor?

If the mode of the data: 16, 15, 17, 16, 15, x, 19, 17, 14 is 15, then x =(a) 15(b) 16(c) 17(d) 19

A number is selected from numbers 1 to 25. The probability that it is prime is(a) 23(b) 16(c) 13(d) 56

All edges of a square pyramid are of equal lengths. If the length of the base edge is 20 cm, what is the total surface area?

A card is drawn from a well-shuffled pack of 52 cards. Find the probability that the card drawn is neither a jack nor a queen.

Question 109 (i) Observe the following patterns and fill in the blanks to make the statements true: −5×4=−20 −5×3=−15=−20–(−5) −5×2 =____ = -15 – (-5) −5×1=____=____ −5×0=0=____ −5×(−1)=5=____ −5×(−2)=_____=_____

If 2 is added to the numerator of a fraction, it reduces to 1/2 and if 1 is subtracted from the denominator, it reduces to 1/3/. Find the fraction.

Question 2 (i)Find the value of 'k', for which the following points are collinear.(i) (7, -2), (5, 1), (3, k)

The numerator of a fraction is 3 less than the denominator. If 2 is added to both the numerator and the denominator, then the sum of the new fraction and the original fraction is 2920. Find the original fraction.

The circumference of a circle is 22 cm. Find the area of its quadrant. [CBSE 2012]

A cubical vessel of height 1 m is full of water the minimum work done in taking out water from The vessel will be

Given that HCF (306, 657) = 9, find LCM (306, 657)..

Let U={1,2,3,4,5,6,7,8,9,10}. If A={1,2,5} and B={6,7}, then A∩B′ is

The discriminant of the equation 2x2−5x−2=0 is41

Solve |g(x)+16 –x² | =|g(x)|+|9-x2 |+7, given that g(x)≥0

Which of the following is not a model for a plane surface?

9 For what values of k ,the following equation has no solution Kx+3y= k-3, 12x+ky= k

The slope of a line parallel to X-axis is ___ .

Question 15The line segment joining the points A(3,2) and B(5,1) is divided at the point P in the ratio 1:2 and it lies on the line 3x-18y+k=0. Find the value of k.

If a chord of a circle of radius 5 cm subtends 120∘ at the centre of the circle, then the area of the corresponding segment of the circle is

which of the following polynomials has the factors (x+7) (x-1) ?

Question 4If a line intersects two concentric circles (circles with the same centre) with centre O at A, B, C and D, prove that AB = CD.

The value of (cos2 23° – sin2 67°) is ____________.

4+3square root 5/square root 5 = a+b square root 5 . Find the value of b :

tan100°+tan125°+tan100°+tan125° is equal to

Sum of the areas of two squares is 400cm2. If the difference of their perimeters is 16cm, find the sides of two squares.

if a-B,and a and a+B are the zeroes of the polynomial f(x)=x^3-3px^2+qx-r,then which of the following relation is correct

18 terms are inserted between 3 and 45 such that the resulting sequence is an AP. The sum of the resulting (finite) AP including the terms 3 and 45 is ___.

Look at the following figure, the reading on the bottom is the measurement obtained and the reading at the top is the zero error. Find the actual measurement.

In any triangle, the point of intersection of the medians divides each median in the ratio of _____ .

If sinθ=x, then write the value of cotθ.

Question 1 (iii) Fill in the blanks using the correct word in the given bracket. (iii) All____triangles are similar. (isosceles, equilateral)

How many bricks , each of dimensions 25cm×15cm×8cm will be required to build a wall of dimensions 10m×4m×5m, if 1/10 th of its volume is occupied by mortar?

11. From an external point P tangent PA and PB are drawn to a circle with centre O. If CD is the tangent to the circle at a point E and PA= 14 cm , find the perimeter of Δ PCD.

sec theta -tan theta=a/b find tan theta

Find the 5th term of an arithmetic sequence whose nth term is 3n - 2.

Mark the correct alternative in each of the following:If x-2x-2≥0, then(a) x∈[2, ∞)(b) x∈(2, ∞)(c) x∈(-∞, 2)(d) x∈(-∞, 2]

Let a matrix A=⎡⎢⎣−1232−3465−3⎤⎥⎦, then which of the followingstatement(s) is(are) correct?(where Mij is minor of element [aij])

The sum of `n' terms of a finite AP is 132 times the sum of its first and last terms. Which term would be the middle term in this AP?

Which of the following pair of lines in a circle cannot be parallel? [CBSE 2011](a) two chords(b) a chord and a tangent(c) two tangents(d) two diameters

What must be added to each of the numbers 1, 10, 46 so that the resulting numbers are in G.P.?2

In the given figure, O is the centre of the circle and BCD is tangent to it at C. Prove that ∠BAC + ∠ACD = 90°.

√1+cos A1−cos A = ? (a) cosec A - cot A (b) cosec A + cot A (c) cosec A cot A (d) none of these

An observe s†an ding 80cm above the surface of pond .A fish is 60cm below the surface of pond .find apparent height of observer seen by fis

If −5 is a root of the quadratic equation 2x2+px−15=0 and the quadratic equation p(x2+x)+k=0 has equal roots, find the value of k.

If A and B are acute angles such that sin A = cos B then (A + B) = ?(a) 45°(b) 60°(c) 90°(d) 180°

Draw two congruent circles of radii 3 cm, having their centres 8 cm apart. Draw a transverse common tangent.

Show that the altitude of the rightcircular cone of maximum volume that can be inscribed in a sphere ofradius r is.

Question 109 (i) Observe the following patterns and fill in the blanks to make the statements true: −5×4=−20 −5×3=−15=−20–(−5) −5×2 =__ = -15 – (-5) −5×1== −5×0=0= −5×(−1)=5= −5×(−2)=_=___