43030 + Interview Questions in Mathematics Page 153 InterviewSolution

7601.	cos 4 x = cos 2x·
Answer» cos 4 x = cos 2x·

Discussion

7602.	Find theequation of a curve passing through the point (0, 0) and whosedifferential equation is.
Answer» Find the equation of a curve passing through the point (0, 0) and whose differential equation is.

Discussion

7603.	6. A bag contains 36 tickets, numbered from 0 to 35. Three of the tickets are drawn at random. Find the probability of the sum of the numbers in the three tickets drawn to be 36
Answer» 6. A bag contains 36 tickets, numbered from 0 to 35. Three of the tickets are drawn at random. Find the probability of the sum of the numbers in the three tickets drawn to be 36

Discussion

7604.	If a,b,c are in H.P. and ab+bc+ca=15, then ca=
Answer» If $a, b, c$ are in H.P. and $a b + b c + c a = 15,$ then $c a =$

Discussion

7605.	Prove that Sin3x+sin2x-sinx=4sinx * cos(x/2)cos(3x/2)
Answer» Prove that Sin3x+sin2x-sinx=4sinx * cos(x/2)cos(3x/2)

Discussion

7606.	The range of the function, f(x)=cot−1x+sec−1x+cosec−1x is
Answer» The range of the function, $f (x) = {cot}^{- 1} x + {sec}^{- 1} x + {cosec}^{- 1} x$ is

Discussion

7607.	If t - 1 and -t -1, t ∈ R, are the roots of (a + 2) x2 + 2ax - 1 = 0 then complete set of values of 'a' is :
Answer» If t - 1 and -t -1, t ∈ R, are the roots of (a + 2) $x^{2}$ + 2ax - 1 = 0 then complete set of values of 'a' is :

Discussion

7608.	29.Sin2 (51-x) +sin (39 + x) =
Answer» 29.Sin2 (51-x) +sin (39 + x) =

Discussion

7609.	Solve the following system of linear equations, using matrix method x−y+z=4,2x+y−2z=0,x+y+z=2
Answer» Solve the following system of linear equations, using matrix method $x - y + z = 4, 2 x + y - 2 z = 0, x + y + z = 2$

7609.

Solve the following system of linear equations, using matrix method x−y+z=4,2x+y−2z=0,x+y+z=2

Answer»

Solve the following system of linear equations, using matrix method

$x - y + z = 4, 2 x + y - 2 z = 0, x + y + z = 2$

Discussion

7610.	find period of f(x) if f(x+3/2)+f(x-3/2)=f(x),x∈
Answer» find period of f(x) if f(x+3/2)+f(x-3/2)=f(x),x∈

Discussion

7611.	sinA+sin2A+sin4A+sin5AcosA+cos2A+cos4A+cos5A=
Answer» $\frac{sin A + sin 2 A + sin 4 A + sin 5 A}{cos A + cos 2 A + cos 4 A + cos 5 A} =$

Discussion

7612.	Let A={x:x is a root of the equation x3+2x2−x−2=0} and B={x:x is a prime divisor of 720 }, then n(A×B) is
Answer» Let $A = {x : x is a root of the equation x^{3} + 2 x^{2} - x - 2 = 0}$ and $B = {x : x is a prime divisor of 720},$ then $n (A \times B)$ is

Discussion

7613.	Solve the following inequations and graph the solution on the number line 2 < 2 – 3 < 5, ε R.
Answer» Solve the following inequations and graph the solution on the number line 2 < 2 – 3 < 5, ε R.

Discussion

7614.	Let P1:x+y+z=0 P2:x+2y+3z=0 P3:x+3y+5z=0 be three planes L1 is the line of intersection of P1 & P2. Let P(2,1,−1) be point on P3. If (α,β,γ) is image of point P in the line L1 then the value of \|α+β+γ\| is
Answer» Let $P_{1} : x + y + z = 0$ $P_{2} : x + 2 y + 3 z = 0$ $P_{3} : x + 3 y + 5 z = 0$ be three planes $L_{1}$ is the line of intersection of $P_{1}$ & $P_{2} . Let P (2, 1, - 1)$ be point on $P_{3}$ . If $(α, β, γ)$ is image of point $P$ in the line $L_{1}$ then the value of $\| α + β + γ \|$ is

Discussion

7615.	How many words can be formed with the letters of the word MATHEMATICS by rearranging them
Answer» How many words can be formed with the letters of the word MATHEMATICS by rearranging them

Discussion

7616.	The sum of n terms of the seriescosec−1√10+cosec−1√50+cosec−1√170+⋯+cosec−1√(n2+1)(n2+2n+2) is
Answer» The sum of $n$ terms of the series ${cosec}^{- 1} \sqrt{10} + {cosec}^{- 1} \sqrt{50} + {cosec}^{- 1} \sqrt{170} + \dots + {cosec}^{- 1} \sqrt{(n^{2} + 1) (n^{2} + 2 n + 2)}$ is

Discussion

7617.	If a , b , c , d are in G.P, prove that are in G.P.
Answer» If a , b , c , d are in G.P, prove that are in G.P.

Discussion

7618.	If r>1 and x=a+ar+ar2 y=b+br+br2 z=c+cr+cr2, then the value of xyz2 is ___.
Answer» If $r > 1$ and $x = a + \frac{a}{r} + \frac{a}{r^{2}}$ $y = b + \frac{b}{r} + \frac{b}{r^{2}}$ $z = c + \frac{c}{r} + \frac{c}{r^{2}},$ then the value of $\frac{x y}{z^{2}}$ is ___.

7618.

If r>1 and x=a+ar+ar2 y=b+br+br2 z=c+cr+cr2, then the value of xyz2 is ___.

Answer»

If $r > 1$ and
$x = a + \frac{a}{r} + \frac{a}{r^{2}}$
$y = b + \frac{b}{r} + \frac{b}{r^{2}}$
$z = c + \frac{c}{r} + \frac{c}{r^{2}},$

then the value of $\frac{x y}{z^{2}}$ is ___.

Discussion

7619.	∫cosθsinθf(x tanθ) dx is (where θ≠nπ2,n∈I)
Answer» $\int_{sin θ}^{cos θ} f (x tan θ) d x$ is $(w h e r e θ \neq \frac{n π}{2}, n \in I)$

Discussion

7620.	∫π2π3 √1+cos x(1−cos x)52dx= [AI CBSE 1980]
Answer» $\int_{\frac{π}{3}}^{\frac{π}{2}} \frac{\sqrt{1 + c o s x}}{(1 - c o s x)^{\frac{5}{2}}} d x =$ [AI CBSE 1980]

Discussion

7621.	1∫0tan−1xxdx is equal to
Answer» $1 \int 0 \frac{{tan}^{- 1} x}{x} d x$ is equal to

Discussion

7622.	Find , if and .
Answer» Find , if and .

Discussion

7623.	A room has 8 doors. In how many ways, a man can enter in the room through one door and exit through a different door?
Answer» A room has 8 doors. In how many ways, a man can enter in the room through one door and exit through a different door?

Discussion

7624.	The total number of terms in the expansion of (1 + x)2n – (1 – x)2n ___________.
Answer» The total number of terms in the expansion of (1 + x)²ⁿ – (1 – x)²ⁿ ___________.

Discussion

7625.	In a Young’s double slit experiment, I0 is the intensity at the central maximum and β is the fringe width. The intensity at a point P distant x from the centre will be
Answer» In a Young’s double slit experiment, $I_{0}$ is the intensity at the central maximum and $β$ is the fringe width. The intensity at a point P distant x from the centre will be

Discussion

7626.	The vector equation of the line though the points (3, 4, –7) and (1, –1, 6) is ___________.
Answer» The vector equation of the line though the points (3, 4, –7) and (1, –1, 6) is ___________.

Discussion

7627.	If (x+iy)13=a+ib, then xa+yb =
Answer» If $(x + i y)^{\frac{1}{3}}$ =a+ib, then $\frac{x}{a} + \frac{y}{b}$ =

Discussion

7628.	Find thegeneral solution of the equation
Answer» Find the general solution of the equation

Discussion

7629.	Slope of tangent to the curve y3=3ax2+6x+b at (1,1) is 2, then the absolute value of a+b is
Answer» Slope of tangent to the curve $y^{3} = 3 a x^{2} + 6 x + b$ at $(1, 1)$ is $2,$ then the absolute value of $a + b$ is

Discussion

7630.	If α,β are the complex roots of x2+2x+2=0, then find the value of \|(α−β)\|
Answer» If $α, β$ are the complex roots of $x^{2} + 2 x + 2 = 0$ , then find the value of $\| (α - β) \|$

Discussion

7631.	A natural number x is chosen at random from the first one hundred natural numbers. The probability that (x−20)(x−40)x−30<0 is
Answer» A natural number x is chosen at random from the first one hundred natural numbers. The probability that $\frac{(x - 20) (x - 40)}{x - 30} < 0$ is

Discussion

7632.	If ∫1(sec x+cosec x+tan x+cot x)2dx=xα+cos(x+π4)β+cos 2xγ+c,then \|α+√2β+γ\| is , (where c is an arbitrary constant)
Answer» $If \int \frac{1}{(sec x + cosec x + tan x + cot x)^{2}} d x = \frac{x}{α} + \frac{cos (x + \frac{π}{4})}{β} + \frac{cos 2 x}{γ} + c, then \| α + \sqrt{2} β + γ \| is$ , (where $c$ is an arbitrary constant)

Discussion

7633.	If alpha and beta are zeroes of polynomial x-ax+b then value of alpha ( alpha/beta -beta) + beta (beta/alpha-alpha) is?
Answer» If alpha and beta are zeroes of polynomial x-ax+b then value of alpha ( alpha/beta -beta) + beta (beta/alpha-alpha) is?

Discussion

7634.	In a hospital five children are born on a particular day. What is the probability of three male children?
Answer» In a hospital five children are born on a particular day. What is the probability of three male children?

Discussion

7635.	If,prove that
Answer» If, prove that

Discussion

7636.	If t1 and t2 are roots of the equation t2−2√3t+2=0, then the distance between the points (at21,2at1) and (at22,2at2), where a>0 is
Answer» If $t_{1}$ and $t_{2}$ are roots of the equation $t^{2} - 2 \sqrt{3} t + 2 = 0$ , then the distance between the points $(a t_{1}^{2}, 2 a t_{1})$ and $(a t_{2}^{2}, 2 a t_{2})$ , where $a > 0$ is

Discussion

7637.	In an entrance test there are multiple choice questions. There are four possible answers to each questions, of which one is correct. The probability that a student knows the answer to a question is 9/10. If he gets the correct answer to a question, then the probability that he was guessing is
Answer» In an entrance test there are multiple choice questions. There are four possible answers to each questions, of which one is correct. The probability that a student knows the answer to a question is 9/10. If he gets the correct answer to a question, then the probability that he was guessing is

Discussion

7638.	The value of 0.23¯ + 0.22¯ is(a) 0.45¯(b) 0.43¯(c) 0.45¯(d) 0.45
Answer» The value of $0 . \bar{23}$ + $0 . \bar{22}$ is (a) $0 . \bar{45}$ (b) $0 . \bar{43}$ (c) $0 . \bar{45}$ (d) $0.45$

Discussion

7639.	Consider the functions f(x)={x+1, x≤12x+1, 1<x≤2g(x)={x2, −1≤x<2x+2, 2≤x≤3The number of roots of the equation f(g(x))=2 is
Answer» Consider the functions $f (x) = {\begin{matrix} x + 1, x \leq 1 2 x + 1, 1 < x \leq 2 \end{matrix}$ $g (x) = {\begin{matrix} x^{2}, - 1 \leq x < 2 x + 2, 2 \leq x \leq 3 \end{matrix}$ The number of roots of the equation $f (g (x)) = 2$ is

Discussion

7640.	∫02πcos-1cosxdx
Answer» $\int_{0}^{2 π} \cos^{- 1} (\cos x) d x$

Discussion

7641.	8. n (n+1) (n+4).
Answer» 8. n (n+1) (n+4).

Discussion

7642.	The set of all real value(s) of a for which function f(x)={2x,−1≤x≤0−3x+a,0<x≤2 has a local maxima at x=0, is
Answer» The set of all real value(s) of $a$ for which function $f (x) = {\begin{matrix} 2 x, & - 1 \leq x \leq 0 - 3 x + a, & 0 < x \leq 2 \end{matrix}$ has a local maxima at $x = 0,$ is

Discussion

7643.	16. integration of e raise to power tanx (xsec square x+sin2x)
Answer» 16. integration of e raise to power tanx (xsec square x+sin2x)

Discussion

7644.	If cos2 π8 is a root of equation x2 + ax + b = 0 where a, b ϵ Q then a + b = ___
Answer» If $c o s^{2} \frac{π}{8}$ is a root of equation $x^{2}$ + ax + b = 0 where a, b $ϵ$ Q then a + b = ___

7644.

If cos2 π8 is a root of equation x2 + ax + b = 0 where a, b ϵ Q then a + b = ___

Answer»

If $c o s^{2} \frac{π}{8}$ is a root of equation $x^{2}$ + ax + b = 0 where a, b $ϵ$ Q then a + b = ___

Discussion

7645.	If pbcaqcabr=0, find the value of pp-a+qq-b+rr-c, p≠a, q≠b, r≠c.
Answer» $If \|\begin{matrix} p & b & c \\ a & q & c \\ a & b & r \end{matrix}\| = 0, find the value of \frac{p}{p - a} + \frac{q}{q - b} + \frac{r}{r - c}, p \neq a, q \neq b, r \neq c .$

Discussion

7646.	The number of diagonals in an octagon will be
Answer» The number of diagonals in an octagon will be

Discussion

7647.	If tan−1x−1x−2+tan−1x+1x+2=π4, then find the value of x.
Answer» If $t a n^{- 1} \frac{x - 1}{x - 2} + t a n^{- 1} \frac{x + 1}{x + 2} = \frac{π}{4}$ , then find the value of x.

Discussion

7648.	AOB is the positive quadrant of the ellipse x2a2+y2b2=1 where OA=a, OB=b, Then the area between the arc AB and the chord AB of the ellipse is
Answer» AOB is the positive quadrant of the ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ where $O A = a, O B = b,$ Then the area between the arc AB and the chord AB of the ellipse is

Discussion

7649.	The area bounded by y=\|\|x−1\|−6\| and y=0 is sq. units
Answer» The area bounded by $y = \| \| x - 1 \| - 6 \|$ and $y = 0$ is sq. units

Discussion

7650.	Solve for x : √3 x2 -2√2 x -2√3=0
Answer» Solve for x : √3 x² -2√2 x -2√3=0

7650.

Solve for x : √3 x2 -2√2 x -2√3=0

Answer»

Solve for x :

√3 x² -2√2 x -2√3=0

Discussion

Explore topic-wise InterviewSolutions in .

cos 4 x = cos 2x·

Find theequation of a curve passing through the point (0, 0) and whosedifferential equation is.

6. A bag contains 36 tickets, numbered from 0 to 35. Three of the tickets are drawn at random. Find the probability of the sum of the numbers in the three tickets drawn to be 36

If a,b,c are in H.P. and ab+bc+ca=15, then ca=

Prove that Sin3x+sin2x-sinx=4sinx * cos(x/2)*cos(3*x/2)

The range of the function, f(x)=cot−1x+sec−1x+cosec−1x is

If t - 1 and -t -1, t ∈ R, are the roots of (a + 2) x2 + 2ax - 1 = 0 then complete set of values of 'a' is :

29.Sin2 (51-x) +sin (39 + x) =

Solve the following system of linear equations, using matrix method x−y+z=4,2x+y−2z=0,x+y+z=2

find period of f(x) if f(x+3/2)+f(x-3/2)=f(x),x∈

sinA+sin2A+sin4A+sin5AcosA+cos2A+cos4A+cos5A=

Let A={x:x is a root of the equation x3+2x2−x−2=0} and B={x:x is a prime divisor of 720 }, then n(A×B) is

Solve the following inequations and graph the solution on the number line 2 &lt; 2 – 3 &lt; 5, ε R.

Let P1:x+y+z=0 P2:x+2y+3z=0 P3:x+3y+5z=0 be three planes L1 is the line of intersection of P1 & P2. Let P(2,1,−1) be point on P3. If (α,β,γ) is image of point P in the line L1 then the value of |α+β+γ| is

How many words can be formed with the letters of the word MATHEMATICS by rearranging them

​​​​​The sum of n terms of the seriescosec−1√10+cosec−1√50+cosec−1√170+⋯+cosec−1√(n2+1)(n2+2n+2) is

If a , b , c , d are in G.P, prove that are in G.P.

If r&gt;1 and x=a+ar+ar2 y=b+br+br2 z=c+cr+cr2, then the value of xyz2 is ___.

∫cosθsinθf(x tanθ) dx is (where θ≠nπ2,n∈I)

∫π2π3 √1+cos x(1−cos x)52dx= [AI CBSE 1980]

1∫0tan−1xxdx is equal to

Find , if and .

A room has 8 doors. In how many ways, a man can enter in the room through one door and exit through a different door?

The total number of terms in the expansion of (1 + x)2n – (1 – x)2n ___________.

In a Young’s double slit experiment, I0 is the intensity at the central maximum and β is the fringe width. The intensity at a point P distant x from the centre will be

The vector equation of the line though the points (3, 4, –7) and (1, –1, 6) is ___________.

If (x+iy)13=a+ib, then xa+yb =

Find thegeneral solution of the equation

Slope of tangent to the curve y3=3ax2+6x+b at (1,1) is 2, then the absolute value of a+b is

If α,β are the complex roots of x2+2x+2=0, then find the value of |(α−β)|

A natural number x is chosen at random from the first one hundred natural numbers. The probability that (x−20)(x−40)x−30&lt;0 is

If ∫1(sec x+cosec x+tan x+cot x)2dx=xα+cos(x+π4)β+cos 2xγ+c,then |α+√2β+γ| is , (where c is an arbitrary constant)

If alpha and beta are zeroes of polynomial x-ax+b then value of alpha ( alpha/beta -beta) + beta (beta/alpha-alpha) is?

In a hospital five children are born on a particular day. What is the probability of three male children?

If,prove that

If t1 and t2 are roots of the equation t2−2√3t+2=0, then the distance between the points (at21,2at1) and (at22,2at2), where a&gt;0 is

In an entrance test there are multiple choice questions. There are four possible answers to each questions, of which one is correct. The probability that a student knows the answer to a question is 9/10. If he gets the correct answer to a question, then the probability that he was guessing is

The value of 0.23¯ + 0.22¯ is(a) 0.45¯(b) 0.43¯(c) 0.45¯(d) 0.45

Consider the functions f(x)={x+1, x≤12x+1, 1&lt;x≤2g(x)={x2, −1≤x&lt;2x+2, 2≤x≤3The number of roots of the equation f(g(x))=2 is

∫02πcos-1cosxdx

8. n (n+1) (n+4).

The set of all real value(s) of a for which function f(x)={2x,−1≤x≤0−3x+a,0&lt;x≤2 has a local maxima at x=0, is

16. integration of e raise to power tanx (xsec square x+sin2x)

If cos2 π8 is a root of equation x2 + ax + b = 0 where a, b ϵ Q then a + b = ___

If pbcaqcabr=0, find the value of pp-a+qq-b+rr-c, p≠a, q≠b, r≠c.

The number of diagonals in an octagon will be

If tan−1x−1x−2+tan−1x+1x+2=π4, then find the value of x.

AOB is the positive quadrant of the ellipse x2a2+y2b2=1 where OA=a, OB=b, Then the area between the arc AB and the chord AB of the ellipse is

The area bounded by y=||x−1|−6| and y=0 is sq. units

Solve for x : √3 x2 -2√2 x -2√3=0

Prove that Sin3x+sin2x-sinx=4sinx * cos(x/2)cos(3x/2)

Solve the following inequations and graph the solution on the number line 2 < 2 – 3 < 5, ε R.

The sum of n terms of the seriescosec−1√10+cosec−1√50+cosec−1√170+⋯+cosec−1√(n2+1)(n2+2n+2) is

If r>1 and x=a+ar+ar2 y=b+br+br2 z=c+cr+cr2, then the value of xyz2 is ___.

A natural number x is chosen at random from the first one hundred natural numbers. The probability that (x−20)(x−40)x−30<0 is

If t1 and t2 are roots of the equation t2−2√3t+2=0, then the distance between the points (at21,2at1) and (at22,2at2), where a>0 is

Consider the functions f(x)={x+1, x≤12x+1, 1<x≤2g(x)={x2, −1≤x<2x+2, 2≤x≤3The number of roots of the equation f(g(x))=2 is

The set of all real value(s) of a for which function f(x)={2x,−1≤x≤0−3x+a,0<x≤2 has a local maxima at x=0, is