43030 + Interview Questions in Mathematics Page 73 InterviewSolution

3601.	Find the value of the trigonometric function sin(−11π3).
Answer» Find the value of the trigonometric function $sin (- \frac{11 π}{3})$ .

Discussion

3602.	44. f(x) = (2008^x + 2008^(-x))/2. Find its range.
Answer» 44. f(x) = (2008^x + 2008^(-x))/2. Find its range.

Discussion

3603.	if A is an invoutory matrix and I is a unit matrix of the same order then (I-A)(I+A) is
Answer» if A is an invoutory matrix and I is a unit matrix of the same order then (I-A)(I+A) is

Discussion

3604.	Find:∫sin2x−cos2xsinx cosxdx.
Answer» Find: $\int \frac{s i n^{2} x - c o s^{2} x}{s i n x c o s x} d x .$

Discussion

3605.	Findthe modulus and the argument of the complex number
Answer» Find the modulus and the argument of the complex number

Discussion

3606.	∫π−π2x(1+sinx)1+cos2xdx is
Answer» $\int_{- π}^{π} \frac{2 x (1 + s i n x)}{1 + c o s^{2} x} d x i s$

Discussion

3607.	The value of limn→∞(15)log√5(14+18+116+⋯to n terms) is
Answer» The value of $lim n \to \infty {(\frac{1}{5})}^{{log}_{\sqrt{5}} (\frac{1}{4} + \frac{1}{8} + \frac{1}{16} + \dots to n terms)}$ is

Discussion

3608.	If A=⎡⎢⎣12101−13−11⎤⎥⎦, then
Answer» If $A = ⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 1 0 & 1 & - 1 3 & - 1 & 1 \end{matrix} ⎤ ⎥ ⎦$ , then

Discussion

3609.	Suppose a girl throws a die. If she gets 1 or 2, she tosses a coin three times and notes the number of tails. If she gets 3, 4, 5 or 6, she tosses a coin once and notes whether a 'head' or 'tail' is obtained. If she obtained exactly one 'tail', then what is the probability that she threw 3, 4, 5 or 6 with the die? [CBSE 2015]
Answer» Suppose a girl throws a die. If she gets 1 or 2, she tosses a coin three times and notes the number of tails. If she gets 3, 4, 5 or 6, she tosses a coin once and notes whether a 'head' or 'tail' is obtained. If she obtained exactly one 'tail', then what is the probability that she threw 3, 4, 5 or 6 with the die? [CBSE 2015]

Discussion

3610.	The value of f(0) so that the function f(x)=1−cos(1−cos x)x4 is continuous everywhere is
Answer» The value of f(0) so that the function $f (x) = \frac{1 - c o s (1 - c o s x)}{x^{4}}$ is continuous everywhere is

Discussion

3611.	The value of ∣∣∣∣x+42x2x2xx+42x2x2xx+4∣∣∣∣,x∈R−{−45,4} is
Answer» The value of $∣ ∣∣ ∣ \begin{matrix} x + 4 & 2 x & 2 x 2 x & x + 4 & 2 x 2 x & 2 x & x + 4 \end{matrix} ∣ ∣∣ ∣, x \in R - {\frac{- 4}{5}, 4}$ is

Discussion

3612.	How come K2+4(k+1) is (k+2)2 ?
Answer» How come $K^{2} + 4 (k + 1)$ is $(k + 2)^{2}$ ?

Discussion

3613.	The value of 2∫0xex+e2−xdx is
Answer» The value of $2 \int 0 \frac{x}{e^{x} + e^{2 - x}} d x$ is

Discussion

3614.	If both the roots of x2+2(k+2)x+9k−1=0 are negative, then k lies in
Answer» If both the roots of $x^{2} + 2 (k + 2) x + 9 k - 1 = 0$ are negative, then $k$ lies in

Discussion

3615.	Find the equation of the normal tocurve y2 = 4x at the point (1, 2).
Answer» Find the equation of the normal to curve y² = 4x at the point (1, 2).

Discussion

3616.	If the coefficients of 2nd, 3rd and the 4th terms in the expansion of (1 + x)n are in A.P., then the value of n is(a) 2(b) 7(c) 11(d) 14
Answer» If the coefficients of 2^nd, 3^rd and the 4^th terms in the expansion of (1 + x)ⁿ are in A.P., then the value of n is (a) 2 (b) 7 (c) 11 (d) 14

Discussion

3617.	The general solution of the differential equation xy(y+1)dy=(1+x2)dx is(where c is constant of integration)
Answer» The general solution of the differential equation $x y (y + 1) d y = (1 + x^{2}) d x$ is (where $c$ is constant of integration)

Discussion

3618.	How a-b=root(a+b)^2-4ab
Answer» How a-b=root(a+b)^2-4ab

Discussion

3619.	The remainder when the determinant ∣∣∣∣∣201420142015201520162016201720172018201820192019202020202021202120222022∣∣∣∣∣ is divided by 5 is.
Answer» The remainder when the determinant $∣ ∣∣∣ ∣ \begin{matrix} 2014^{2014} & 2015^{2015} & 2016^{2016} 2017^{2017} & 2018^{2018} & 2019^{2019} 2020^{2020} & 2021^{2021} & 2022^{2022} \end{matrix} ∣ ∣∣∣ ∣$ is divided by 5 is.

3619.

The remainder when the determinant ∣∣∣∣∣201420142015201520162016201720172018201820192019202020202021202120222022∣∣∣∣∣ is divided by 5 is.

Answer»

The remainder when the determinant

$∣ ∣∣∣ ∣ \begin{matrix} 2014^{2014} & 2015^{2015} & 2016^{2016} 2017^{2017} & 2018^{2018} & 2019^{2019} 2020^{2020} & 2021^{2021} & 2022^{2022} \end{matrix} ∣ ∣∣∣ ∣$

is divided by 5 is.

Discussion

3620.	In triangle ABC, BC is produced to D, AL is bisector of angle A. Prove thatangle ABC+ angle ACD=twice of angle ALD
Answer» In triangle ABC, BC is produced to D, AL is bisector of angle A. Prove thatangle ABC+ angle ACD=twice of angle ALD

Discussion

3621.	Find the distance of the point (2, 5) from the line 3 x + y + 4 = 0 measured parallel to a line having slope 3/4.
Answer» Find the distance of the point (2, 5) from the line 3 x + y + 4 = 0 measured parallel to a line having slope $3 / 4.$

Discussion

3622.	In a box containing 100 eggs, 10 eggs are rotten. The probability that out of a sample of 5 eggs none is rotten if the sampling is with replacement is[MP PET 1991;MNR 1986; RPET 1995; UPSEAT 2000]
Answer» In a box containing 100 eggs, 10 eggs are rotten. The probability that out of a sample of 5 eggs none is rotten if the sampling is with replacement is [MP PET 1991; MNR 1986; RPET 1995; UPSEAT 2000]

3622.

In a box containing 100 eggs, 10 eggs are rotten. The probability that out of a sample of 5 eggs none is rotten if the sampling is with replacement is[MP PET 1991;MNR 1986; RPET 1995; UPSEAT 2000]

Answer»

In a box containing 100 eggs, 10 eggs are rotten. The probability that out of a sample of 5 eggs none is rotten if the sampling is with replacement is

[MP PET 1991;

MNR 1986; RPET 1995; UPSEAT 2000]

Discussion

3623.	Which of the following should be the SECOND sentence after rearrangement?
Answer» Which of the following should be the SECOND sentence after rearrangement?

Discussion

3624.	If is a differentiable function and if does not vanish anywhere, then prove that .
Answer» If is a differentiable function and if does not vanish anywhere, then prove that .

Discussion

3625.	Round up 2808 upto three significant figures.
Answer» Round up 2808 upto three significant figures.

Discussion

3626.	For small angles sin(theta)=theta.Why?
Answer» For small angles sin(theta)=theta.Why?

Discussion

3627.	The number of words that can be formed using all the letters of the word "KANPUR" when the vowels are in even places is
Answer» The number of words that can be formed using all the letters of the word "KANPUR" when the vowels are in even places is

Discussion

3628.	Find a vector of magnitude 5 units, and parallel to the resultant of the vectors .
Answer» Find a vector of magnitude 5 units, and parallel to the resultant of the vectors .

Discussion

3629.	105.The number of real solutions of 1-cos2x=2 sin^° (sinx)-≤x≤÷ 2
Answer» 105.The number of real solutions of 1-cos2x=2 sin^° (sinx)-≤x≤÷ 2

Discussion

3630.	Let f(x)=[cos x+sin x], 0<x<2π, where [x] denotes the greatest integer less than of equal to x. The number of points of discontinuity of f(x) is
Answer» Let $f (x) = [c o s x + s i n x], 0 < x < 2 π,$ where [x] denotes the greatest integer less than of equal to x. The number of points of discontinuity of f(x) is

Discussion

3631.	Find the smallest value of (−8p7) for which \|x2−5x+7−p\|=6+\|x2−5x+1−p\| for all xϵ[−1,3]. ___
Answer» Find the smallest value of $(\frac{- 8 p}{7})$ for which $\| x^{2} - 5 x + 7 - p \| = 6 + \| x^{2} - 5 x + 1 - p \|$ for all $x ϵ [- 1, 3]$ . ___

Discussion

3632.	The value of 4∫0(\|x−1\|+\|x−3\|)dx is
Answer» The value of $4 \int 0 (\| x - 1 \| + \| x - 3 \|) d x$ is

Discussion

3633.	Tangents are drawn from the point (4,2) to the curve x2+9y2=9, then the tangent of acute angle between the tangents is
Answer» Tangents are drawn from the point $(4, 2)$ to the curve $x^{2} + 9 y^{2} = 9,$ then the tangent of acute angle between the tangents is

Discussion

3634.	In a regular hexagon ABCDEF,−−→AE=
Answer» In a regular hexagon $A B C D E F, - - \to A E =$

Discussion

3635.	Statements: R c U, U ? Q, W $ R Conclusions: I. W c U II. WU
Answer» Statements: R c U, U ? Q, W $ R Conclusions: I. W c U II. WU

3635.

Statements: R c U, U ? Q, W $ R Conclusions: I. W c U II. WU

Answer»

Statements: R c U, U ? Q, W $ R

Conclusions:

I. W c U

II. WU

Discussion

3636.	Find thevalues of θandp, if the equation isthe normal form of the line.
Answer» Find the values of θand p, if the equation is the normal form of the line.

Discussion

3637.	Find the area of a triangle whose sides are represented by the graphs of the equations x=0 , y=0 and 4x+5y=20
Answer» Find the area of a triangle whose sides are represented by the graphs of the equations x=0 , y=0 and 4x+5y=20

Discussion

3638.	The value of b−cb+ccotA2+b+cb−ctanA2 is equal to:
Answer» The value of $\frac{b - c}{b + c} cot \frac{A}{2} + \frac{b + c}{b - c} tan \frac{A}{2}$ is equal to:

Discussion

3639.	Area of the rectangle formed by the ends of latusrecta of the Ellipse 4x2+9y2 = 144 is
Answer» Area of the rectangle formed by the ends of latusrecta of the Ellipse $4 x^{2} + 9 y^{2}$ = 144 is

Discussion

3640.	A dice is rolled three times, then the probability of getting a larger number than the previous number each time is:
Answer» A dice is rolled three times, then the probability of getting a larger number than the previous number each time is:

Discussion

3641.	What's the equation of tangent to the parabola y2=4ax having a slope 'm'.
Answer» What's the equation of tangent to the parabola $y^{2} = 4 a x$ having a slope 'm'.

Discussion

3642.	Find the intervals in which f(x) is increasing or decreasing:(i) f(x) = x\|x\|, x ∈R(ii) f(x) = sinx + \|sinx\|, 0 < x ≤2π(iii) f(x) = sinx(1 + cosx), 0 < x < π2 [CBSE 2014]
Answer» Find the intervals in which f(x) is increasing or decreasing: (i) f(x) = x\|x\|, x $\in$ R (ii) f(x) = sinx + \|sinx\|, 0 < x $\leq 2 π$ (iii) f(x) = sinx(1 + cosx), 0 < x < $\frac{π}{2}$ [CBSE 2014]

Discussion

3643.	The ratio of area of a regular polygon of n sides inscribed in a circle to that of the polygon of same number of sides circumscribing the same circle is 3:4. Then the value of n is
Answer» The ratio of area of a regular polygon of $n$ sides inscribed in a circle to that of the polygon of same number of sides circumscribing the same circle is $3 : 4$ . Then the value of $n$ is

Discussion

3644.	The least positive integer n such that (2i1+i)n is a positive integer, is
Answer» The least positive integer n such that ${(\frac{2 i}{1 + i})}^{n}$ is a positive integer, is

Discussion

3645.	Convert the given complex number in polar form: -3
Answer» Convert the given complex number in polar form: -3

Discussion

3646.	15.-49-4x2
Answer» 15.-49-4x2

Discussion

3647.	A car is driven east for a distance of 50 km, then north for 30km, and then in a direction 30° east of north for 25 km. Sketch thevector diagram and determine (a) the magnitude and (b) the angleof the car’s total displacement from its starting point.
Answer» A car is driven east for a distance of 50 km, then north for 30 km, and then in a direction 30° east of north for 25 km. Sketch the vector diagram and determine (a) the magnitude and (b) the angle of the car’s total displacement from its starting point.

Discussion

3648.	Evaluate the given limit :limx→0sinaxsinbx,a,b≠0
Answer» Evaluate the given limit : $lim x \to 0 \frac{sin a x}{sin b x}, a, b \neq 0$

Discussion

3649.	The value of sec60∘[sin(40∘+θ)cos(10∘+θ)−cos(40∘+θ)sin(10∘+θ)] is
Answer» The value of $sec 60^{\circ} [sin (40^{\circ} + θ) cos (10^{\circ} + θ) - cos (40^{\circ} + θ) sin (10^{\circ} + θ)]$ is

Discussion

3650.	The length of latusrectum of (x−1)225−y29=1 is
Answer» The length of latusrectum of $\frac{(x - 1)^{2}}{25} - \frac{y^{2}}{9} = 1$ is

Discussion

Explore topic-wise InterviewSolutions in .

Find the value of the trigonometric function sin(−11π3).

44. f(x) = (2008^x + 2008^(-x))/2. Find its range.

if A is an invoutory matrix and I is a unit matrix of the same order then (I-A)(I+A) is

Find:∫sin2x−cos2xsinx cosxdx.

Findthe modulus and the argument of the complex number

∫π−π2x(1+sinx)1+cos2xdx is

The value of limn→∞(15)log√5(14+18+116+⋯to n terms) is​​​​​​​

If A=⎡⎢⎣12101−13−11⎤⎥⎦, then

The value of f(0) so that the function f(x)=1−cos(1−cos x)x4 is continuous everywhere is

The value of ∣∣∣∣x+42x2x2xx+42x2x2xx+4∣∣∣∣,x∈R−{−45,4} is

How come K2+4(k+1) is (k+2)2 ?

The value of 2∫0xex+e2−xdx is

If both the roots of x2+2(k+2)x+9k−1=0 are negative, then k lies in

Find the equation of the normal tocurve y2 = 4x at the point (1, 2).

If the coefficients of 2nd, 3rd and the 4th terms in the expansion of (1 + x)n are in A.P., then the value of n is(a) 2(b) 7(c) 11(d) 14

The general solution of the differential equation xy(y+1)dy=(1+x2)dx is(where c is constant of integration)

How a-b=root(a+b)^2-4ab

The remainder when the determinant ∣∣∣∣∣201420142015201520162016201720172018201820192019202020202021202120222022∣∣∣∣∣ is divided by 5 is.

In triangle ABC, BC is produced to D, AL is bisector of angle A. Prove thatangle ABC+ angle ACD=twice of angle ALD

Find the distance of the point (2, 5) from the line 3 x + y + 4 = 0 measured parallel to a line having slope 3/4.

In a box containing 100 eggs, 10 eggs are rotten. The probability that out of a sample of 5 eggs none is rotten if the sampling is with replacement is[MP PET 1991;MNR 1986; RPET 1995; UPSEAT 2000]

Which of the following should be the SECOND sentence after rearrangement?

If is a differentiable function and if does not vanish anywhere, then prove that .

Round up 2808 upto three significant figures.

For small angles sin(theta)=theta.Why?

The number of words that can be formed using all the letters of the word "KANPUR" when the vowels are in even places is

Find a vector of magnitude 5 units, and parallel to the resultant of the vectors .

105.The number of real solutions of 1-cos2x=2 sin^° (sinx)-≤x≤÷ 2

Let f(x)=[cos x+sin x], 0&lt;x&lt;2π, where [x] denotes the greatest integer less than of equal to x. The number of points of discontinuity of f(x) is

Find the smallest value of (−8p7) for which |x2−5x+7−p|=6+|x2−5x+1−p| for all xϵ[−1,3]. ___

The value of 4∫0(|x−1|+|x−3|)dx is

Tangents are drawn from the point (4,2) to the curve x2+9y2=9, then the tangent of acute angle between the tangents is

In a regular hexagon ABCDEF,−−→AE=

Statements: R c U, U ? Q, W $ R Conclusions: I. W c U II. WU

Find thevalues of θandp, if the equation isthe normal form of the line.

Find the area of a triangle whose sides are represented by the graphs of the equations x=0 , y=0 and 4x+5y=20

The value of b−cb+ccotA2+b+cb−ctanA2 is equal to:

Area of the rectangle formed by the ends of latusrecta of the Ellipse 4x2+9y2 = 144 is

A dice is rolled three times, then the probability of getting a larger number than the previous number each time is:

What's the equation of tangent to the parabola y2=4ax having a slope 'm'.

Find the intervals in which f(x) is increasing or decreasing:(i) f(x) = x|x|, x ∈R(ii) f(x) = sinx + |sinx|, 0 < x ≤2π(iii) f(x) = sinx(1 + cosx), 0 < x < π2 [CBSE 2014]

The ratio of area of a regular polygon of n sides inscribed in a circle to that of the polygon of same number of sides circumscribing the same circle is 3:4. Then the value of n is

The least positive integer n such that (2i1+i)n is a positive integer, is

Convert the given complex number in polar form: -3

15.-49-4x2

A car is driven east for a distance of 50 km, then north for 30km, and then in a direction 30° east of north for 25 km. Sketch thevector diagram and determine (a) the magnitude and (b) the angleof the car’s total displacement from its starting point.

Evaluate the given limit :limx→0sinaxsinbx,a,b≠0

The value of sec60∘[sin(40∘+θ)cos(10∘+θ)−cos(40∘+θ)sin(10∘+θ)] is

The length of latusrectum of (x−1)225−y29=1 is

The value of limn→∞(15)log√5(14+18+116+⋯to n terms) is

Let f(x)=[cos x+sin x], 0<x<2π, where [x] denotes the greatest integer less than of equal to x. The number of points of discontinuity of f(x) is