Math Master - Impetus Gurukul

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Description Math Master Impetus Gurukul is an established name in the field on Online Education for competitive exams like IIT-JEE, AIMCA, NIMCET, NDA, CAT, UPSC, etc. Our approach is to first build a strong foundation and then gradually scale up to an advanced level program. Hence, we lay lot of emphasis on conceptual clarity. The teaching approach is such that complex problems are explained in a simplified manner. The teachers at Impetus are highly experienced and have in-depth understanding of the subject. Teachers are also available for the doubt clearing sessions.

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If two circles x^2+y^2-4x-2y-4=0 & (x+1)^2+(y+4)^2=r^2 intersect at two distinct points and range

If two circles x^2+y^2-4x-2y-4=0 & (x+1)^2+(y+4)^2=r^2 intersect at two distinct points and range Math Master - Impetus Gurukul

22 views - 17 hours ago

The coefficient of x^48 in 1(1+x)+2(1+x)^2+3(1+x)^3+⋯+100(1+x)^100 is

The coefficient of x^48 in 1(1+x)+2(1+x)^2+3(1+x)^3+⋯+100(1+x)^100 is Math Master - Impetus Gurukul

60 views - 1 day ago

$If domain of f(x)=sin^(-1)⁡〖((5-x)/(2x+3))+1/log_e⁡〖(10-x)〗〗 is (-∞,α]∪(β,γ)-}{δ} then value of$ 5:01

If domain of f(x)=sin^(-1)⁡〖((5-x)/(2x+3))+1/log_e⁡〖(10-x)〗〗 is (-∞,α]∪(β,γ)-}{δ} then value of Math Master - Impetus Gurukul

33 views - 1 day ago

If probability distribution is given by X 0 1 2 3 4 5 6 7, P(x) 0 k 2k 2k 3k k^2 2k^2 7k^2+k Then

If probability distribution is given by X 0 1 2 3 4 5 6 7, P(x) 0 k 2k 2k 3k k^2 2k^2 7k^2+k Then Math Master - Impetus Gurukul

29 views - 1 day ago

If ∫▒(sin⁡x )^(-11/2) (cos⁡x )^(-5/2) dx=-p_1/q_1 (cot⁡x )^(9/2)-p_2/q_2 (cot⁡x )^(5/2)-p_3/q_3

If ∫▒(sin⁡x )^(-11/2) (cos⁡x )^(-5/2) dx=-p_1/q_1 (cot⁡x )^(9/2)-p_2/q_2 (cot⁡x )^(5/2)-p_3/q_3 Math Master - Impetus Gurukul

62 views - 4 days ago

The no. of solution in x∈(-1/(2√6),1/(2√6)) of equation tan^(-1)⁡〖4x+tan^(-1)⁡6x 〗=π/6 is

The no. of solution in x∈(-1/(2√6),1/(2√6)) of equation tan^(-1)⁡〖4x+tan^(-1)⁡6x 〗=π/6 is Math Master - Impetus Gurukul

80 views - 4 days ago

The number of real solution of equation x|x+4|+3|x+2|+10=0 is/are

The number of real solution of equation x|x+4|+3|x+2|+10=0 is/are Math Master - Impetus Gurukul

94 views - 4 days ago

If the sum of first 4 terms of an AP is 6 and sum of first 6 terms is 4, then sum of first 12

If the sum of first 4 terms of an AP is 6 and sum of first 6 terms is 4, then sum of first 12 Math Master - Impetus Gurukul

129 views - 5 days ago

If S={1,2…50}, two numbers α and β are selected at random find the probability that product is

If S={1,2…50}, two numbers α and β are selected at random find the probability that product is Math Master - Impetus Gurukul

51 views - 5 days ago

If the value of cos^2⁡〖48°-sin^2⁡〖12°〗〗/sin^2⁡〖24°-sin^2⁡〖6°〗〗 is (α+β√5)/γ then value of (α+β+γ)

If the value of cos^2⁡〖48°-sin^2⁡〖12°〗〗/sin^2⁡〖24°-sin^2⁡〖6°〗〗 is (α+β√5)/γ then value of (α+β+γ) Math Master - Impetus Gurukul

89 views - 5 days ago

If A=[■(2&3@3&5)] then value of det⁡(A^2025-3A^2024+A^2023 ) | JEE Main 2026 January 22 Shift 1

If A=[■(2&3@3&5)] then value of det⁡(A^2025-3A^2024+A^2023 ) | JEE Main 2026 January 22 Shift 1 Math Master - Impetus Gurukul

62 views - 1 week ago

If a line αx+y=1 does not intersect the hyperbola x^2-9y^2=9 then a possible value of α is

If a line αx+y=1 does not intersect the hyperbola x^2-9y^2=9 then a possible value of α is Math Master - Impetus Gurukul

117 views - 1 week ago

If (9+7α-7β)^20+(9α+7β-7)^20+(9β+7-7α)^20+(14+7α+7β)^20 is m^10 then the value of m ism^10 then

If (9+7α-7β)^20+(9α+7β-7)^20+(9β+7-7α)^20+(14+7α+7β)^20 is m^10 then the value of m ism^10 then Math Master - Impetus Gurukul

132 views - 1 week ago

If 6∫_1^x▒〖f(x)〗 dx=3xf(x)+x^3-4,x≥1 then value of (f(2)-f(3)) | JEE Main 2026 January 22 Shift 1

If 6∫_1^x▒〖f(x)〗 dx=3xf(x)+x^3-4,x≥1 then value of (f(2)-f(3)) | JEE Main 2026 January 22 Shift 1 Math Master - Impetus Gurukul

141 views - 1 week ago

If xdy-ydx=(√(x^2+y^2 ))dx. If y=y(x) & y(1)=0 then y(3) is | JEE Main 2026 January 22 Shift 1 Maths

If xdy-ydx=(√(x^2+y^2 ))dx. If y=y(x) & y(1)=0 then y(3) is | JEE Main 2026 January 22 Shift 1 Maths Math Master - Impetus Gurukul

175 views - 1 week ago

If the end points of chord of parabola y^2=12x are (x_1,y_1 ) and (x_2,y_2 ) and it subtend 90°

If the end points of chord of parabola y^2=12x are (x_1,y_1 ) and (x_2,y_2 ) and it subtend 90° Math Master - Impetus Gurukul

208 views - 1 week ago

Let the line L pass through the point (–3, 5, 2) and make equal angle with the positive coordinate

Let the line L pass through the point (–3, 5, 2) and make equal angle with the positive coordinate Math Master - Impetus Gurukul

176 views - 1 week ago

Let y^2=16x, from point (16, 16) a focal chord is passing. Point (α,β) divides the focal chord inter

Let y^2=16x, from point (16, 16) a focal chord is passing. Point (α,β) divides the focal chord inter Math Master - Impetus Gurukul

118 views - 1 week ago

Line L_1 & L_2 are (x-1)/2=y/1=(z+1)/2 & x/2=y/(-1)=(z+1)/1 respectively, if a line L with direction

Line L_1 & L_2 are (x-1)/2=y/1=(z+1)/2 & x/2=y/(-1)=(z+1)/1 respectively, if a line L with direction Math Master - Impetus Gurukul

109 views - 1 week ago

Let α and β be the roots of an equation x^2+2ax+(3a+10)=0 such that α LT 1 LH β Then the set of all

Let α and β be the roots of an equation x^2+2ax+(3a+10)=0 such that α LT 1 LH β Then the set of all Math Master - Impetus Gurukul

290 views - 1 week ago

Given A=[■(3&-4@1&-1)] & B=[■(-29&49@-13&18)] suchthat (A^15+B)[█(x@y)]=[█(0@0)] then value of (x,y)

Given A=[■(3&-4@1&-1)] & B=[■(-29&49@-13&18)] suchthat (A^15+B)[█(x@y)]=[█(0@0)] then value of (x,y) Math Master - Impetus Gurukul

134 views - 1 week ago

Let O be the vertex of the parabola y^2=16x. The locus of centroid of ∆OPA. When P lies on parabola

Let O be the vertex of the parabola y^2=16x. The locus of centroid of ∆OPA. When P lies on parabola Math Master - Impetus Gurukul

117 views - 2 weeks ago

If the line αx+4y-√7=0,α∈R touches the ellipse 3x^2+4y^2=1 at the point P in the first quadrant

If the line αx+4y-√7=0,α∈R touches the ellipse 3x^2+4y^2=1 at the point P in the first quadrant Math Master - Impetus Gurukul

248 views - 2 weeks ago

If angle between p ⃗ and q ⃗ is θ and cos⁡〖θ=1/√3〗 |p ⃗ |=2√3,|q ⃗ |=2 then find |p ⃗×(q ⃗-3r ⃗ )|^2

If angle between p ⃗ and q ⃗ is θ and cos⁡〖θ=1/√3〗 |p ⃗ |=2√3,|q ⃗ |=2 then find |p ⃗×(q ⃗-3r ⃗ )|^2 Math Master - Impetus Gurukul

73 views - 2 weeks ago

If x∈[(-√3)/2,1/√2] then max value of the expression (sin^(-1)⁡x )^2+(cos^(-1)⁡x )^2 is (nπ^2)/(n+7)

If x∈[(-√3)/2,1/√2] then max value of the expression (sin^(-1)⁡x )^2+(cos^(-1)⁡x )^2 is (nπ^2)/(n+7) Math Master - Impetus Gurukul

112 views - 2 weeks ago

a_1,a_2/2,a_3/2^2 …,a_10/2^9 are in G.P. with common ratio 1/√2 and a_1+a_2+⋯+a_10=62, then a_1=

a_1,a_2/2,a_3/2^2 …,a_10/2^9 are in G.P. with common ratio 1/√2 and a_1+a_2+⋯+a_10=62, then a_1= Math Master - Impetus Gurukul

249 views - 2 weeks ago

If area bounded by curve 1-2x≤y≤4-x^2 & x,y≥0 is equal to α/β where G.C.D (α,β)=1. Find α+β

If area bounded by curve 1-2x≤y≤4-x^2 & x,y≥0 is equal to α/β where G.C.D (α,β)=1. Find α+β Math Master - Impetus Gurukul

168 views - 2 weeks ago

The largest n∈N for which 7^n divides 101! is | JEE Main 2026 January 21 Shift 2

The largest n∈N for which 7^n divides 101! is | JEE Main 2026 January 21 Shift 2 Math Master - Impetus Gurukul

205 views - 2 weeks ago

Let f(x)=x^3+x^2 f^' (1)+2xf^'' (2)+f'''(3), then the value of f^' (5)= | JEE Main 2026 Jan 21 Sh 2

Let f(x)=x^3+x^2 f^' (1)+2xf^'' (2)+f'''(3), then the value of f^' (5)= | JEE Main 2026 Jan 21 Sh 2 Math Master - Impetus Gurukul

155 views - 2 weeks ago

The number of solutions of equation tan⁡〖3x=cot⁡x 〗in x∈(0,2π) is | JEE Main 2026 January 21 Shift 2

The number of solutions of equation tan⁡〖3x=cot⁡x 〗in x∈(0,2π) is | JEE Main 2026 January 21 Shift 2 Math Master - Impetus Gurukul

117 views - 2 weeks ago

$Consider set S={1,2,3,…,50} where m,n,∈S If P is the no. of ways such that 6^m+9^n is divisible by 5$ 3:34

Consider set S={1,2,3,…,50} where m,n,∈S If P is the no. of ways such that 6^m+9^n is divisible by 5 Math Master - Impetus Gurukul

210 views - 2 weeks ago

The value of integral I=∫_(-π/6)^(π/6)▒(2π+4x^11)/(1-sin⁡(|x|+π/6) ) dx is | JEE Main 26 Jan 21 S 1

The value of integral I=∫_(-π/6)^(π/6)▒(2π+4x^11)/(1-sin⁡(|x|+π/6) ) dx is | JEE Main 26 Jan 21 S 1 Math Master - Impetus Gurukul

176 views - 2 weeks ago

Area bounded inside ellipse x^2+4y^2=4 and outside area bounded by curve y=|x|-1 and y=1-|x|

Area bounded inside ellipse x^2+4y^2=4 and outside area bounded by curve y=|x|-1 and y=1-|x| Math Master - Impetus Gurukul

142 views - 2 weeks ago

The value of 6∫_0^π▒|sin⁡x+sin⁡3x+sin⁡2x | dx is | JEE Main 2026 January 21 Shift 1 Question Paper

The value of 6∫_0^π▒|sin⁡x+sin⁡3x+sin⁡2x | dx is | JEE Main 2026 January 21 Shift 1 Question Paper Math Master - Impetus Gurukul

250 views - 2 weeks ago

If a_1,a_2,a_3… are increasing geometric progression such that a_1+a_3+a_5=21 and a_1 a_3 a_5=64

If a_1,a_2,a_3… are increasing geometric progression such that a_1+a_3+a_5=21 and a_1 a_3 a_5=64 Math Master - Impetus Gurukul

127 views - 2 weeks ago

If y=y(x) and (1+x^2 )dy+(1-tan^(-1)⁡x)dx=0 and y(0)=1 then y(1) | JEE Main 2026 January 21 Shift 1

If y=y(x) and (1+x^2 )dy+(1-tan^(-1)⁡x)dx=0 and y(0)=1 then y(1) | JEE Main 2026 January 21 Shift 1 Math Master - Impetus Gurukul

123 views - 3 weeks ago

Let H be a Hyperbola confocal with ellipse x^2/36+y^2/16=1 having eccentricity ‘5’, then length

Let H be a Hyperbola confocal with ellipse x^2/36+y^2/16=1 having eccentricity ‘5’, then length Math Master - Impetus Gurukul

133 views - 3 weeks ago

Let f:R→R be twice differentiable function such that f(x)m^2-2" " m⋅f^' (x)+f^' (x)=0 for all m∈R

Let f:R→R be twice differentiable function such that f(x)m^2-2" " m⋅f^' (x)+f^' (x)=0 for all m∈R Math Master - Impetus Gurukul

219 views - 3 weeks ago

Given two set A={1,2,3,…,6} and B={1,2,3,…,9}, the find the number of increasing funcitons f:A→B

Given two set A={1,2,3,…,6} and B={1,2,3,…,9}, the find the number of increasing funcitons f:A→B Math Master - Impetus Gurukul

225 views - 3 weeks ago

If A=[■(α&2@1&2)] and B=A=[■(1&1@1&β)] and A^2-4" " A+2I=O and B^2=3" " B+I=O then the value

If A=[■(α&2@1&2)] and B=A=[■(1&1@1&β)] and A^2-4" " A+2I=O and B^2=3" " B+I=O then the value Math Master - Impetus Gurukul

129 views - 3 weeks ago

The value of cosec 10°-√3 sec⁡〖10°〗 is | JEE Main 2026 January 21 Shift 1 Question Paper

The value of cosec 10°-√3 sec⁡〖10°〗 is | JEE Main 2026 January 21 Shift 1 Question Paper Math Master - Impetus Gurukul

187 views - 3 weeks ago

Tangent are drawn from P to the circle x^2+y^2-4x-6y+12=0 touching at A & B such that ∠AOB=60°

Tangent are drawn from P to the circle x^2+y^2-4x-6y+12=0 touching at A & B such that ∠AOB=60° Math Master - Impetus Gurukul

181 views - 3 weeks ago

L_1 & L_2 are two parallel lines and ABC is an equilateral triangle, such that A & B lie on L_1 & L_

L_1 & L_2 are two parallel lines and ABC is an equilateral triangle, such that A & B lie on L_1 & L_ Math Master - Impetus Gurukul

191 views - 3 weeks ago

If Domain of f(x)=cos^(-1)⁡((2x-5)/(11-3x))+sin^(-1)⁡〖⁡(2x^2-3x+1)〗 is [a,b], find value of (a+2b)

If Domain of f(x)=cos^(-1)⁡((2x-5)/(11-3x))+sin^(-1)⁡〖⁡(2x^2-3x+1)〗 is [a,b], find value of (a+2b) Math Master - Impetus Gurukul

305 views - 3 weeks ago

Let a twice differentiable function f(x) on R such that f(3)=18,f^' (3)=0 and f^'' (3)=4

Let a twice differentiable function f(x) on R such that f(3)=18,f^' (3)=0 and f^'' (3)=4 Math Master - Impetus Gurukul

196 views - 3 weeks ago

Let the parabola x^2=4y and consider its vertex O and a variable point P on the parabola an consider

Let the parabola x^2=4y and consider its vertex O and a variable point P on the parabola an consider Math Master - Impetus Gurukul

176 views - 3 weeks ago

If α & β are roots of the quadratic equation x^2+x+1=0, then the value of (α+β)^4+(α^2+┤ ├ β^2 )^4

If α & β are roots of the quadratic equation x^2+x+1=0, then the value of (α+β)^4+(α^2+┤ ├ β^2 )^4 Math Master - Impetus Gurukul

180 views - 3 weeks ago

Last Minute tips for IIT-JEE Aspirants | Impetus Gurukul | Sharad Sir

Last Minute tips for IIT-JEE Aspirants | Impetus Gurukul | Sharad Sir Math Master - Impetus Gurukul

189 views - 4 weeks ago

If a ∆ABC has vertices A(-1,7),B(-7,1) and C(5,-5), then its orthocentre has coordinates

If a ∆ABC has vertices A(-1,7),B(-7,1) and C(5,-5), then its orthocentre has coordinates Math Master - Impetus Gurukul

127 views - 1 month ago

A factory is operating in two shifts, day and night, with 70 and 30 workers respectively. If per day

A factory is operating in two shifts, day and night, with 70 and 30 workers respectively. If per day Math Master - Impetus Gurukul

108 views - 1 month ago

Let a die be rolled n times. Let the probability of getting odd numbers seven times be equal to the

Let a die be rolled n times. Let the probability of getting odd numbers seven times be equal to the Math Master - Impetus Gurukul

139 views - 1 month ago

A bag contains 8 balls, whose colours are either white or black. 4 balls are drawn at random without

A bag contains 8 balls, whose colours are either white or black. 4 balls are drawn at random without Math Master - Impetus Gurukul

141 views - 1 month ago

If three letter s can be posted to any one of the 5 different addresses, then the probability that

If three letter s can be posted to any one of the 5 different addresses, then the probability that Math Master - Impetus Gurukul

169 views - 1 month ago

Let A=[■(2&1&0@1&2&-1@0&-1&2)]. If |adj(adj(adj 2A))| =(16)^n, then n is equal to

Let A=[■(2&1&0@1&2&-1@0&-1&2)]. If |adj(adj(adj 2A))| =(16)^n, then n is equal to Math Master - Impetus Gurukul

168 views - 1 month ago

Let A=[■(1&0&0@0&α&β@0&β&α)] and |2A|^3=2^21, where a,β∈Z. Then a value of α is

Let A=[■(1&0&0@0&α&β@0&β&α)] and |2A|^3=2^21, where a,β∈Z. Then a value of α is Math Master - Impetus Gurukul

117 views - 1 month ago

Let A=[a_ij ]_(2×2), where a_ij=0 for all i,j and A^2=I. Let a be the sum of all diagonal elements

Let A=[a_ij ]_(2×2), where a_ij=0 for all i,j and A^2=I. Let a be the sum of all diagonal elements Math Master - Impetus Gurukul

139 views - 1 month ago

If 1/(√1+√2)+1/(√2+√3)+⋯+1/(√99+√100)=m and 1/(1⋅2)+1/(2⋅3)+⋯+1/99.100=n, then the point (m,n) lies

If 1/(√1+√2)+1/(√2+√3)+⋯+1/(√99+√100)=m and 1/(1⋅2)+1/(2⋅3)+⋯+1/99.100=n, then the point (m,n) lies Math Master - Impetus Gurukul

171 views - 1 month ago

Let 3,a,b,c be in A.P. and 3,a-1,b+1,c+9 be in G.P. Then, the arithmetic mean of a,b and c is

Let 3,a,b,c be in A.P. and 3,a-1,b+1,c+9 be in G.P. Then, the arithmetic mean of a,b and c is Math Master - Impetus Gurukul

109 views - 1 month ago

In an arithmetic progression, if S_40=1030 and S_12=57, then S_30-S_10 is equal to

In an arithmetic progression, if S_40=1030 and S_12=57, then S_30-S_10 is equal to Math Master - Impetus Gurukul

127 views - 1 month ago

The number of triangles whose vertices are at the vertices of a regular octagon but none of whose

The number of triangles whose vertices are at the vertices of a regular octagon but none of whose Math Master - Impetus Gurukul

289 views - 1 month ago