Tamilnadu Board Maths Question papers for 12th Standard (English Medium) Question paper & Study Materials

12th Standard Maths - Applications of Vector Algebra Model Question Paper - by Meera - Namakkal View & Read

  • 1)

    If \(\vec{a}\) and \(\vec{b}\) are parallel vectors, then \([\vec { a } ,\vec { c } ,\vec { b } ]\) is equal to

  • 2)

    \(\vec { a } .\vec { b } =\vec { b } .\vec { c } =\vec { c } .\vec { a } =0\) , then the value of \([\vec { a } ,\vec { b } ,\vec { c } ]\) is

  • 3)

    If \(\vec { a } =\hat { i } +\hat { j } +\hat { k } \)\(\vec { b } =\hat { i } +\hat { j } \)\(\vec { c } =\hat { i } \) and \((\vec { a } \times \vec { b } )\times\vec { c } \) = \(\lambda \vec { a } +\mu \vec { b } \) then the value of \(\lambda +\mu \) is

  • 4)

    Consider the vectors \(\vec { a } ,\vec { b } ,\vec { c } ,\vec { c } \) such that \((\vec { a } \times \vec { b } )\times (\vec { c } \times \vec { d } )\) = \(\vec { 0 } \) Let \({ P }_{ 1 }\) and \({ P }_{ 2 }\) be the planes determined by the pairs of vectors \(\vec { a } ,\vec { b } \) and \(\vec { c } ,\vec { d } \) respectively. Then the angle between \({ P }_{ 1 }\) and \({ P }_{ 2 }\) is

  • 5)

    If \(\vec { a } =2\hat { i } +3\hat { j } -\hat { k } ,\vec { b } =\hat { i } +2\hat { j } +5\hat { k } ,\vec { c } =3\hat { i } +5\hat { j } -\hat { k } \) then a vector perpendicular to \(\vec { a } \) and lies in the plane containing \(\vec { b } \) and \(\vec { c } \) is

12th Standard Maths - Two Dimensional Analytical Geometry-II Model Question Paper - by Meera - Namakkal View & Read

  • 1)

    The equation of the circle passing through(1,5) and (4,1) and touching y -axis is x2+y2−5x−6y+9+(4x+3y−19)=0 whereλ is equal to

  • 2)

    The radius of the circle3x2+by2+4bx−6by+b2 =0 is

  • 3)

    The equation of the normal to the circle x2+y2−2x−2y+1=0 which is parallel to the line
    2x+4y=3 is

  • 4)

    The radius of the circle passing through the point(6,2) two of whose diameter arex+y=6
    and x+2y=4 is

  • 5)

    If x+y=k is a normal to the parabola y2 =12x, then the value of k is

12th Standard Maths - Inverse Trigonometric Functions Model Question Paper - by Meera - Namakkal View & Read

  • 1)

    The value of sin-1 (cos x),0\(\le x\le\pi\) is

  • 2)

    sin−1(cos x)\(=\frac{\pi}{2}-x \) is valid for

  • 3)

    The domain of the function defined by f(x)=sin−1\(\sqrt{x-1} \) is

  • 4)

    \({ sin }^{ -1 }\left( tan\frac { \pi }{ 4 } \right) -{ sin }^{ -1 }\left( \sqrt { \frac { 3 }{ x } } \right) =\frac { \pi }{ 6 } \).Then x is a root of the equation

  • 5)

    sin(tan-1x), |x|<1 ia equal to

12th Standard Maths - Theory of Equations Model Question Paper - by Meera - Namakkal View & Read

  • 1)

    A zero of x3 + 64 is

  • 2)

    The number of real numbers in [0,2π] satisfying sin4x-2sin2x+1 is

  • 3)

    The number of positive zeros of the polynomial \(\overset { n }{ \underset { j=0 }{ \Sigma } } { n }_{ C_{ r } }\)(-1)rxr is

  • 4)

    For real x, the equation \(\left| \frac { x }{ x-1 } \right| +|x|=\frac { { x }^{ 2 } }{ |x-1| } \) has

  • 5)

    If x2 - hx - 21 = 0 and x2 - 3hx + 35 = 0 (h > 0) have a common root, then h = ___________

12th Maths - Applications of Vector Algebra Three Marks Questions - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    Dot product of a vector with vector \(\overset { \wedge }{ 3i } -5\overset { \wedge }{ k } \)\(2\overset { \wedge }{ i } +7\overset { \wedge }{ j } \) and \(\overset { \wedge }{ i } +\overset { \wedge }{ j } +\overset { \wedge }{ k } \) are respectively -1, 6 and 5. Find the vector.

  • 2)

    Find the Cartesian form of the equation of the plane \(\overset { \rightarrow }{ r } =\left( s-2t \right) \overset { \wedge }{ i } +\left( 3-t \right) \overset { \wedge }{ j } +\left( 2s+t \right) \overset { \wedge }{ k } \)

  • 3)

    Find the equation of the plane through the intersection of the planes lx-3y+ z-4 -0 and x - y + Z + 1 - 0 and perpendicular to the plane x + 2y - 3z + 6 = 0

  • 4)

    Find the angle between the line \(\frac { x-2 }{ 3 } =\frac { y-1 }{ -1 } =\frac { z-3 }{ 2 } \) and the plane 3x + 4y + z + 5 = 0

  • 5)

    If \(\overset { \rightarrow }{ a } =\overset { \wedge }{ i } -\overset { \wedge }{ j } ,\overset { \rightarrow }{ b } =\overset { \wedge }{ j } -\overset { \wedge }{ k } ,\overset { \rightarrow }{ c } =\overset { \wedge }{ k } -\overset { \wedge }{ i } \) then find \(\left[ \overset { \rightarrow }{ a } -\overset { \rightarrow }{ b } ,\overset { \rightarrow }{ b } -\overset { \rightarrow }{ c } ,\overset { \rightarrow }{ c } -\overset { \rightarrow }{ a } \right] \)

12th Maths - Two Dimensional Analytical Geometry-II Three Marks Questions - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    Find the circumference and area of the circle x2 +y2 - 2x + 5y + 7 = 0

  • 2)

    Find the value of p so that 3x + 4y - p = 0 is a tangent to the circle x2 +y2 - 64 = 0.

  • 3)

    Find the condition for the line lx + my + n = 0 is Rtangent to the circle x2 + y2 = a2

  • 4)

    Find the area of th triangle found by the Unel Joining the vertex of the parabola x2 = -36y to the ends of the latus rectum.

  • 5)

    Find the equatlon of the ellipse whose e = \(\frac34\), foci ony-axl ,centre at origin and passing through (6,4).

12th Maths - Inverse Trigonometric Functions Three Marks Questions - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    Prove that \({ cos }^{ -1 }\left( \cfrac { 4 }{ 5 } \right) +{ tan }^{ -1 }\left( \cfrac { 3 }{ 5 } \right) ={ tan }^{ -1 }\left( \cfrac { 27 }{ 11 } \right) \)

  • 2)

    Evaluate \(cos\left[ { sin }^{ -1 }\cfrac { 3 }{ 5 } +{ sin }^{ -1 }\cfrac { 5 }{ 13 } \right] \)

  • 3)

    Prove that \({ tan }^{ -1 }\left( \cfrac { m }{ n } \right) -{ tan }^{ -1 }\left( \cfrac { m-n }{ m+n } \right) =\cfrac { \pi }{ 4 } \)
     

  • 4)

    Solve: \({ tan }^{ -1 }\left( \cfrac { x-1 }{ x-2 } \right) +{ tan }^{ -1 }\left( \cfrac { x+1 }{ x+2 } \right) =\cfrac { \pi }{ 4 } \)

  • 5)

    Solve \({ tan }^{ -1 }\left( \cfrac { 2x }{ 1-{ x }^{ 2 } } \right) +{ cot }^{ -1 }\left( \cfrac { 1-{ x }^{ 2 } }{ 2x } \right) =\cfrac { \pi }{ 3 } ,x>0\)

12th Maths - Theory of Equations Three Marks Questions - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    If α, β, and γ are the roots of the polynomial equation ax3+bx2+cx+d=0 , find the value of \(\Sigma \frac { \alpha }{ \beta \gamma } \) in terms of the coefficients.

  • 2)

    If p and q are the roots of the equation lx2+nx+n = 0, show that \(\sqrt { \frac { p }{ q } } +\sqrt { \frac { q }{ p } } +\sqrt { \frac { n }{ l } } \)=0.

  • 3)

    If the equations x2+px+q= 0 and x2+p'x+q'= 0 have a common root, show that it must  be equal to \(\frac { pq'-p'q }{ q-q' } \) or \(\frac { q-q' }{ p'-p } \).

  • 4)

    Solve the equation 9x-36x2+44x-16=0 if the roots form an arithmetic progression.

  • 5)

    Solve the equation 3x3-26x2+52x-24=0 if its roots form a geometric progression.

12th Maths - Complex Numbers Three Marks Questions - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    Explain the falacy:

  • 2)

    Find the circle roots of -27.

  • 3)

    Find the principal value of -2i.

  • 4)

    Show that \(\left| \frac { z-3 }{ z+3 } \right| \) = 2 represent a circle.

  • 5)

    Show that the complex numbers 3 + 2i, 5i, -3 + 2i and -i form a square.

12th Maths - Application of Matrices and Determinants Three Marks Questions - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    If A = \(\frac { 1 }{ 9 } \left[ \begin{matrix} -8 & 1 & 4 \\ 4 & 4 & 7 \\ 1 & -8 & 4 \end{matrix} \right] \), prove that A−1 = AT.

  • 2)

    If A = \(\left[ \begin{matrix} 8 & -4 \\ -5 & 3 \end{matrix} \right] \), verify that A(adj A) = |A|I2.

  • 3)

    If A = \(\left[ \begin{matrix} 3 & 2 \\ 7 & 5 \end{matrix} \right] \) and B = \(\left[ \begin{matrix} -1 & -3 \\ 5 & 2 \end{matrix} \right] \), verify that (AB)-1 = B-1A-1

  • 4)

    Decrypt the received encoded message \(\left[ \begin{matrix} 2 & -3 \end{matrix} \right] \left[ \begin{matrix} 20 & 4 \end{matrix} \right] \) with the encryption matrix \(\left[ \begin{matrix} -1 & -1 \\ 2 & 1 \end{matrix} \right] \)
    and the decryption matrix as its inverse, where the system of codes are described by the numbers 1 - 26 to the letters A - Z respectively, and the number 0 to a blank space.

  • 5)

    Find the rank of the following matrices by row reduction method:
    \(\left[ \begin{matrix} 1 \\ \begin{matrix} 3 \\ \begin{matrix} 1 \\ 1 \end{matrix} \end{matrix} \end{matrix}\begin{matrix} 2 \\ \begin{matrix} -1 \\ \begin{matrix} -2 \\ -1 \end{matrix} \end{matrix} \end{matrix}\begin{matrix} -1 \\ \begin{matrix} 2 \\ \begin{matrix} 3 \\ 1 \end{matrix} \end{matrix} \end{matrix} \right] \)

12th Standard Maths - Complex Numbers Model Question Paper - by Meera - Namakkal View & Read

  • 1)

    If z is a non zero complex number, such that 2iz2=\(\bar { z } \) then |z| is

  • 2)

    The solution of the equation |z|-z=1+2i is

  • 3)

    If \(\cfrac { z-1 }{ z+1 } \) is purely imaginary, then |z| is

  • 4)

    If (1+i)(1+2i)(1+3i)...(1+ni)=x+iy, then \(2\cdot 5\cdot 10...\left( 1+{ n }^{ 2 } \right) \) is

  • 5)

    If \(\omega =cis\cfrac { 2\pi }{ 3 } \), then the number of distinct roots of \(\left| \begin{matrix} z+1 & \omega & { \omega }^{ 2 } \\ \omega & z+{ \omega }^{ 2 } & 1 \\ { \omega }^{ 2 } & 1 & z+\omega \end{matrix} \right| \)

12th Maths- Application of Matrices and Determinants Model Question Paper - by Meera - Namakkal View & Read

  • 1)

    If |adj(adj A)| = |A|9, then the order of the square matrix A is

  • 2)

    If A = \(\left[ \begin{matrix} 2 & 0 \\ 1 & 5 \end{matrix} \right] \) and B = \(\left[ \begin{matrix} 1 & 4 \\ 2 & 0 \end{matrix} \right] \) then |adj (AB)| = 

  • 3)

    If A = \(\left[ \begin{matrix} \frac { 3 }{ 5 } & \frac { 4 }{ 5 } \\ x & \frac { 3 }{ 5 } \end{matrix} \right] \) and AT = A−1 , then the value of x is

  • 4)

    If ρ(A) = ρ([A | B]), then the system AX = B of linear equations is

  • 5)

    If A = \(\left[ \begin{matrix} 3 & -3 & 4 \\ 2 & -3 & 4 \\ 0 & -1 & 1 \end{matrix} \right] \), then adj(adj A) is

12th Maths Quarterly Exam Question Paper 2019 - by Satyadevi - Tiruchirappalli View & Read

12th Maths - Term 1 Model Question Paper - by Meera - Namakkal View & Read

  • 1)

    If |adj(adj A)| = |A|9, then the order of the square matrix A is

  • 2)

    The number of solutions of the system of equations 2x+y = 4, x - 2y = 2, 3x + 5y = 6 is

  • 3)

    The value of \(\sum _{ i=1 }^{ 13 }{ \left( { i }^{ n }+i^{ n-1 } \right) } \) is

  • 4)

    According to the rational root theorem, which number is not possible rational root of 4x7+2x4-10x3-5?

  • 5)

    If sin-1 x+sin-1 y+sin-1 z=\(\frac{3\pi}{2}\), the value of x2017+y2018+z2019\(-\frac { 9 }{ { x }^{ 101 }+{ y }^{ 101 }+{ z }^{ 101 } } \)is

12th Maths - Term 1 Five Mark Model Question Paper - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    If A = \(\left[ \begin{matrix} 5 & 3 \\ -1 & -2 \end{matrix} \right] \), show that A2 - 3A - 7I2 = O2. Hence find A−1.

  • 2)

    If ax2 + bx + c is divided by x + 3, x − 5, and x − 1, the remainders are 21,61 and 9 respectively. Find a,b and c. (Use Gaussian elimination method.)

  • 3)

    Solve the system: x + y − 2z = 0, 2x − 3y + z = 0, 3x − 7y + 10z = 0, 6x − 9y + 10z = 0.

  • 4)

    Solve the following systems of linear equations by Cramer’s rule:
     3x + 3y − z = 11, 2x − y + 2z = 9, 4x + 3y + 2z = 25.

  • 5)

    Solve the equation z3+27=0 .

12th Maths - Applications of Vector Algebra Two Marks Questions - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    Find the parametric form of vector equation and Cartesian equations of the straight line passing through the point (−2,3, 4) and parallel to the straight line \(\frac { x-1 }{ -4 } =\frac { y-3 }{ 5 } =\frac { z-8 }{ 6 } \)

  • 2)

    Find the vector and Cartesian equations of the plane passing through the point with position vector \(4\hat { i } +2\hat { j } -3\hat { k } \) and normal to vector \(2\hat { i } -\hat { j } +\hat { k } \)

  • 3)

    A variable plane moves in such a way that the sum of the reciprocals of its intercepts on the coordinate axes is a constant. Show that the plane passes through a fixed point

  • 4)

    Find the vector and Cartesian equations of the plane passing through the point with position vector \(2\hat { i } +6\hat { j } +3\hat { k } \) and normal to the vector \(\hat { i } +3\hat { j } +5\hat { k } \)

  • 5)

    A plane passes through the point (−1,1, 2) and the normal to the plane of magnitude \(3\sqrt { 3 } \) makes equal acute angles with the coordinate axes. Find the equation of the plane.

12th Maths - Two Dimensional Analytical Geometry II Two Marks Questions - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    Find the general equation of a circle with centre(-3,-4) and radius 3 units.

  • 2)

    Find the general equation of the circle whose diameter is the line segment joining the points (−4,−2)and (1,1).

  • 3)

    Examine the position of the point (2,3) with respect to the circle x2+y2−6x−8y+12=0.

  • 4)

    Find the equation of the circle with centre (2,-1) and passing through the point (3,6) in standard form.

  • 5)

    Obtain the equation of the circle for which (3,4) and (2,-7) are the ends of a diameter.

12th Maths - Inverse Trigonometric Functions Two Marks Questions - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    State the reason for cos-1\([cos(-\frac{\pi}{6})]\neq \frac{\pi}{6}.\)

  • 2)

    Is cos-1(-x)=\(\pi\)-cos−1(x) true? Justify your answer.

  • 3)

    Find the principal value of cos-1\((\frac{1}{2})\).

  • 4)

    Find the value of sec−1\(\left( -\frac { 2\sqrt { 3 } }{ 3 } \right) \)

  • 5)

    If cot-1\(\frac{1}{7}=\theta\), find the value of cos\(\theta\).
     

12th Maths - Theory of Equations Two Marks Questions - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    A 12 metre tall tree was broken into two parts. It was found that the height of the part which was left standing was the cube root of the length of the part that was cut away. Formulate this into a mathematical problem to find the height of the part which was cut away.

  • 2)

    Find the monic polynomial equation of minimum degree with real coefficients having 2-\(\sqrt{3}\)i as a root.

  • 3)

    Find a polynomial equation of minimum degree with rational coefficients, having 2+\(\sqrt{3}\)i as a root.

  • 4)

    Find a polynomial equation of minimum degree with rational coefficients, having 2i+3 as a root.

  • 5)

    Show that the polynomial 9x9+2x5-x4-7x2+2 has at least six imaginary roots.

12th Maths - Complex Numbers Two Marks Questions - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    If z=x+iy, find the following in rectangular form.
    \(Re\left( \cfrac { 1 }{ z } \right) \)

  • 2)

    Represent the complex number −1−i

  • 3)

    Write the following in the rectangular form:
    \(\cfrac { 10-5i }{ 6+2i } \)

  • 4)

    Find the square roots of −6+8i

  • 5)

    Obtain the Cartesian form of the locus of z=x+iy in
    \(\overline { z } =2^{ -1 }\)

12th Maths Unit 1 Application of Matrices and Determinants Two Marks Questions - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    If A = \(\left[ \begin{matrix} a & b \\ c & d \end{matrix} \right] \) is non-singular, find A−1.

  • 2)

    If adj A = \(\left[ \begin{matrix} -1 & 2 & 2 \\ 1 & 1 & 2 \\ 2 & 2 & 1 \end{matrix} \right] \), find A−1.

  • 3)

    Find the rank of the following matrices which are in row-echelon form :
    \(\left[ \begin{matrix} 2 & 0 & -7 \\ 0 & 3 & 1 \\ 0 & 0 & 1 \end{matrix} \right] \)

  • 4)

    Find the rank of the following matrices by minor method:
    \(\left[ \begin{matrix} 0 \\ \begin{matrix} 0 \\ 8 \end{matrix} \end{matrix}\begin{matrix} 1 \\ \begin{matrix} 2 \\ 1 \end{matrix} \end{matrix}\begin{matrix} 2 \\ \begin{matrix} 4 \\ 0 \end{matrix} \end{matrix}\begin{matrix} 1 \\ \begin{matrix} 3 \\ 2 \end{matrix} \end{matrix} \right] \)

  • 5)

    Find the rank of the following matrices which are in row-echelon form :
    \(\left[ \begin{matrix} 6 \\ \begin{matrix} 0 \\ \begin{matrix} 0 \\ 0 \end{matrix} \end{matrix} \end{matrix}\begin{matrix} 0 \\ \begin{matrix} 2 \\ \begin{matrix} 0 \\ 0 \end{matrix} \end{matrix} \end{matrix}\begin{matrix} -9 \\ \begin{matrix} 0 \\ \begin{matrix} 0 \\ 0 \end{matrix} \end{matrix} \end{matrix} \right] \)

12th Maths Quarterly Model Question Paper - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    If |adj(adj A)| = |A|9, then the order of the square matrix A is

  • 2)

    If A = \(\left[ \begin{matrix} 1 & \tan { \frac { \theta }{ 2 } } \\ -\tan { \frac { \theta }{ 2 } } & 1 \end{matrix} \right] \) and AB = I , then B = 

  • 3)

    If xayb = em, xcyd = en, Δ1 = \(\left| \begin{matrix} m & b \\ n & d \end{matrix} \right| \), Δ2 = \(\left| \begin{matrix} a & m \\ c & n \end{matrix} \right| \), Δ3 = \(\left| \begin{matrix} a & b \\ c & d \end{matrix} \right| \), then the values of x and y are respectively,

  • 4)

    If AT is the transpose of a square matrix A, then

  • 5)

    If \(\rho\)(A) = \(\rho\)([A/B]) = number of unknowns, then the system is

TN 12th Standard Maths Official Model Question Paper 2019 - 2020 - by Satyadevi - Tiruchirappalli View & Read

unit test - by Maths TAMILMedium - New syllabus 2019 View & Read

  • 1)

    If |adj(adj A)| = |A|9, then the order of the square matrix A is

  • 2)

    If A is a 3 × 3 non-singular matrix such that AAT = ATA and B = A-1AT, then BBT = 

  • 3)

    If A = \(\left[ \begin{matrix} 3 & 5 \\ 1 & 2 \end{matrix} \right] \), B = adj A and C = 3A, then \(\frac { \left| adjB \right| }{ \left| C \right| } \)

  • 4)

    If A = \(\left[ \begin{matrix} 2 & 0 \\ 1 & 5 \end{matrix} \right] \) and B = \(\left[ \begin{matrix} 1 & 4 \\ 2 & 0 \end{matrix} \right] \) then |adj (AB)| = 

  • 5)

    If P = \(\left[ \begin{matrix} 1 & x & 0 \\ 1 & 3 & 0 \\ 2 & 4 & -2 \end{matrix} \right] \) is the adjoint of 3 × 3 matrix A and |A| = 4, then x is

12th Standard Maths Unit 6 Applications of Vector Algebra Book Back Questions - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    If \(\vec{a}\) and \(\vec{b}\) are parallel vectors, then \([\vec { a } ,\vec { c } ,\vec { b } ]\) is equal to

  • 2)

    If \(\vec { a } \) and \(\vec { b } \) are unit vectors such that \([\vec { a } ,\vec { b },\vec { a } \times \vec { b } ]=\frac { \pi }{ 4 } \), then the angle between \(\vec { a } \) and \(\vec { b } \) is

  • 3)

    If \(\vec { a } ,\vec { b } ,\vec { c } \) are three non-coplanar vectors such that \(\vec { a } \times (\vec { b } \times \vec { c } )=\frac { \vec { b } +\vec { c } }{ \sqrt { 2 } } \), then the angle between

  • 4)

    If \(\vec { a } \times (\vec { b } \times \vec { c } )=(\vec { a } \times \vec { b } )\times \vec { c } \) where \(\vec { a } ,\vec { b } ,\vec { c } \) are any three vectors such that \(\vec { a } ,\vec { b } \) \(\neq \) 0 and  \(\vec { a } .\vec { b } \) \(\neq \) 0 then \(\vec { a } \) and \(\vec { c } \) are

  • 5)

    The angle between the line \(\vec { r } =(\hat { i } +2\hat { j } -3\hat { k } )+t(2\hat { i } +\hat { j } -2\hat { k } )\) and the plane \(\vec { r } .(\hat { i } +\hat { j } )+4=0\) is

12th Maths - Two Dimensional Analytical Geometry-II Book Back Questions - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    The equation of the circle passing through(1,5) and (4,1) and touching y -axis is x2+y2−5x−6y+9+(4x+3y−19)=0 whereλ is equal to

  • 2)

    The radius of the circle3x2+by2+4bx−6by+b2 =0 is

  • 3)

    If P(x, y) be any point on 16x2+25y2=400 with foci F1 (3,0) and F2 (-3,0) then PF1 PF2 +
    is

  • 4)

    The ellipse E1\(\frac { { x }^{ 2 } }{ 9 } +\frac { { y }^{ 2 } }{ 4 } =1\) is inscribed in a rectangle R whose sides are parallel to the coordinate axes. Another ellipse E2 passing through the point(0,4) circumscribes the rectangle R . The eccentricity of the ellipse is

  • 5)

    Tangents are drawn to the hyperbola  \(\frac { { x }^{ 2 } }{ 9 } +\frac { { y }^{ 2 } }{ 4 } =1\) 1parallel to the straight line2x−y=1. One of the points of contact of tangents on the hyperbola is

12th Standard Maths - Theory of Equations Book Back Questions - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    If α,β and γ are the roots of x3+px2+qx+r, then \(\Sigma \frac { 1 }{ \alpha } \) is

  • 2)

    According to the rational root theorem, which number is not possible rational root of 4x7+2x4-10x3-5?

  • 3)

    The number of real numbers in [0,2π] satisfying sin4x-2sin2x+1 is

  • 4)

    The polynomial x3+2x+3 has

  • 5)

    The number of positive zeros of the polynomial \(\overset { n }{ \underset { j=0 }{ \Sigma } } { n }_{ C_{ r } }\)(-1)rxr is

12th Standard Maths - Inverse Trigonometric Functions Book Back Questions - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    The value of sin-1 (cos x),0\(\le x\le\pi\) is

  • 2)

    If cot−1x=\(\frac{2\pi}{5}\) for some x\(\in\)R, the value of tan-1 x is

  • 3)

    The domain of the function defined by f(x)=sin−1\(\sqrt{x-1} \) is

  • 4)

    \({ tan }^{ -1 }\left( \frac { 1 }{ 4 } \right) +{ tan }^{ -1 }\left( \frac { 2 }{ 3 } \right) \)is equal to

  • 5)

    If the function f(x)sin-1(x2-3), then x belongs to

12th Standard Maths Unit 2 Complex Numbers Book Back Questions - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    If \(z=\cfrac { \left( \sqrt { 3 } +i \right) ^{ 3 }\left( 3i+4 \right) ^{ 2 } }{ \left( 8+6i \right) ^{ 2 } } \) , then |z| is equal to 
     

  • 2)

    If |z-2+i|≤2, then the greatest value of |z| is

  • 3)

    If |z|=1, then the value of \(\cfrac { 1+z }{ 1+\overline { z } }\) is

  • 4)

    If |z1|=1,|z2|=2|z3|=3 and |9z1z2+4z1z3+z2z3|=12, then the value of |z1+z2+z3| is 

  • 5)

    The principal argument of \(\cfrac { 3 }{ -1+i } \)

12th Standard Maths Unit 1 Application of Matrices and Determinants Book Back Questions - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    If |adj(adj A)| = |A|9, then the order of the square matrix A is

  • 2)

    If A is a 3 × 3 non-singular matrix such that AAT = ATA and B = A-1AT, then BBT = 

  • 3)

    If A = \(\left[ \begin{matrix} 3 & 5 \\ 1 & 2 \end{matrix} \right] \), B = adj A and C = 3A, then \(\frac { \left| adjB \right| }{ \left| C \right| } \)

  • 4)

    If A = \(\left[ \begin{matrix} 7 & 3 \\ 4 & 2 \end{matrix} \right] \), then 9I - A = 

  • 5)

    If A = \(\left[ \begin{matrix} 2 & 0 \\ 1 & 5 \end{matrix} \right] \) and B = \(\left[ \begin{matrix} 1 & 4 \\ 2 & 0 \end{matrix} \right] \) then |adj (AB)| = 

12th Standard Maths Unit 3 Theory of Equations One Mark Question and Answer - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    A zero of x3 + 64 is

  • 2)

    If f and g are polynomials of degrees m and n respectively, and if h(x) =(f 0 g)(x), then the degree of h is

  • 3)

    A polynomial equation in x of degree n always has

  • 4)

    If a, b, c ∈ Q and p +√q (p,q ∈ Q) is an irrational root of ax2+bx+c=0 then the other root is

  • 5)

    The quadratic equation whose roots are ∝ and β is

12th Standard Maths Unit 2 Complex Numbers One Mark Question and Answer - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    in+in+1+in+2+in+3 is

  • 2)

    The value of \(\sum _{ i=1 }^{ 13 }{ \left( { i }^{ n }+i^{ n-1 } \right) } \) is

  • 3)

    The area of the triangle formed by the complex numbers z,iz, and z+iz in the Argand’s diagram is

  • 4)

    The principal value of the amplitude of (1+i) is

  • 5)

    The least positive integer n such that \(\left( \frac { 2i }{ 1+i } \right) ^{ n }\)  is a positive integer is

12th Standard Maths - Application of Matrices and Determinants One Mark Question and Answer - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    If A is a 3 × 3 non-singular matrix such that AAT = ATA and B = A-1AT, then BBT = 

  • 2)

    If A = \(\left[ \begin{matrix} 7 & 3 \\ 4 & 2 \end{matrix} \right] \), then 9I - A = 

  • 3)

    If A = \(\left[ \begin{matrix} 3 & 1 & -1 \\ 2 & -2 & 0 \\ 1 & 2 & -1 \end{matrix} \right] \) and A-1 = \(\left[ \begin{matrix} { a }_{ 11 } & { a }_{ 12 } & { a }_{ 13 } \\ { a }_{ 21 } & { a }_{ 22 } & { a }_{ 23 } \\ { a }_{ 31 } & { a }_{ 32 } & { a }_{ 33 } \end{matrix} \right] \) then the value of a23 is

  • 4)

    Let A be a 3 x 3 matrix and B its adjoint matrix If |B|=64, then |A|=

  • 5)

    If AT is the transpose of a square matrix A, then

12th Standard Physics Unit 6 Applications of Vector Algebra One Mark Question and Answer - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    If \(\vec{a}\) and \(\vec{b}\) are parallel vectors, then \([\vec { a } ,\vec { c } ,\vec { b } ]\) is equal to

  • 2)

    If \(\vec { a } \) and \(\vec { b } \) are unit vectors such that \([\vec { a } ,\vec { b },\vec { a } \times \vec { b } ]=\frac { \pi }{ 4 } \), then the angle between \(\vec { a } \) and \(\vec { b } \) is

  • 3)

    If \(\vec { a } =\hat { i } +\hat { j } +\hat { k } \)\(\vec { b } =\hat { i } +\hat { j } \)\(\vec { c } =\hat { i } \) and \((\vec { a } \times \vec { b } )\times\vec { c } \) = \(\lambda \vec { a } +\mu \vec { b } \) then the value of \(\lambda +\mu \) is

  • 4)

    If \(\vec { a } ,\vec { b } ,\vec { c } \) are non-coplanar, non-zero vectors such that \([\vec { a } ,\vec { b } ,\vec { c } ]\) = 3, then \({ \{ [\vec { a } \times \vec { b } ,\vec { b } \times \vec { c } ,\vec { c } \times \vec { a } }]\} ^{ 2 }\) is equal to

  • 5)

    The number of vectors of unit length perpendicular to the vectors \(\left( \overset { \wedge }{ i } +\overset { \wedge }{ j } \right) \) and \(\left( \overset { \wedge }{ j } +\overset { \wedge }{ k } \right) \)is

12th Physics Chapter 5 Two Dimensional Analytical Geometry-II One Mark Question and Answer - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    The equation of the circle passing through(1,5) and (4,1) and touching y -axis is x2+y2−5x−6y+9+(4x+3y−19)=0 whereλ is equal to

  • 2)

    The radius of the circle3x2+by2+4bx−6by+b2 =0 is

  • 3)

    The centre of the circle inscribed in a square formed by the lines x2−8x−12=0 and y2−14y+45 = 0 is

  • 4)

    Equation of tangent at (-4, -4) on x2 = -4y is

  • 5)

    y2 - 2x - 2y + 5 = 0 is a

12th Standard Physics Chapter 4 Inverse Trigonometric Functions One Mark Question and Answer - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    The value of sin-1 (cos x),0\(\le x\le\pi\) is

  • 2)

    \({ sin }^{ -1 }\frac { 3 }{ 5 } -{ cos }^{ -1 }\frac { 12 }{ 13 } +{ sec }^{ -1 }\frac { 5 }{ 3 } { -cosec }^{ 1- }\frac { 13 }{ 2 } \)is equal to

  • 3)

    If sin-1 x+sin-1 y+sin-1 z=\(\frac{3\pi}{2}\), the value of x2017+y2018+z2019\(-\frac { 9 }{ { x }^{ 101 }+{ y }^{ 101 }+{ z }^{ 101 } } \)is

  • 4)

    If \({ sin }^{ -1 }x-cos^{ -1 }x=\cfrac { \pi }{ 6 } \) then

  • 5)

    The number of solutions of the equation \({ tan }^{ -1 }2x+{ tan }^{ -1 }3x=\cfrac { \pi }{ 4 } \) 

12th Physics Unit 2 Theory of Equations One Mark Question with Answer Key - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    If α,β and γ are the roots of x3+px2+qx+r, then \(\Sigma \frac { 1 }{ \alpha } \) is

  • 2)

    The polynomial x3-kx2+9x has three real zeros if and only if, k satisfies

  • 3)

    If x3+12x2+10ax+1999 definitely has a positive zero, if and only if

  • 4)

    The number of positive zeros of the polynomial \(\overset { n }{ \underset { j=0 }{ \Sigma } } { n }_{ C_{ r } }\)(-1)rxr is

  • 5)

    If a, b, c ∈ Q and p +√q (p,q ∈ Q) is an irrational root of ax2+bx+c=0 then the other root is

12th Maths Chapter 2 Complex Numbers One Mark Question Paper - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    The value of \(\sum _{ i=1 }^{ 13 }{ \left( { i }^{ n }+i^{ n-1 } \right) } \) is

  • 2)

    If z is a non zero complex number, such that 2iz2=\(\bar { z } \) then |z| is

  • 3)

    If |z-2+i|≤2, then the greatest value of |z| is

  • 4)

    If |z|=1, then the value of \(\cfrac { 1+z }{ 1+\overline { z } }\) is

  • 5)

    The solution of the equation |z|-z=1+2i is

Unit test 12th Standard Maths New syllabus - by Maths TAMILMedium - New syllabus 2019 View & Read

  • 1)

    If A = \(\left[ \begin{matrix} 7 & 3 \\ 4 & 2 \end{matrix} \right] \), then 9I - A = 

  • 2)

    If P = \(\left[ \begin{matrix} 1 & x & 0 \\ 1 & 3 & 0 \\ 2 & 4 & -2 \end{matrix} \right] \) is the adjoint of 3 × 3 matrix A and |A| = 4, then x is

  • 3)

    If A, B and C are invertible matrices of some order, then which one of the following is not true?

  • 4)

    If (AB)-1 = \(\left[ \begin{matrix} 12 & -17 \\ -19 & 27 \end{matrix} \right] \) and A-1 = \(\left[ \begin{matrix} 1 & -1 \\ -2 & 3 \end{matrix} \right] \), then B-1 = 

  • 5)

    If ATA−1 is symmetric, then A2 =

12th Maths Chapter 1 Application of Matrices and Determinants One Mark Questions - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    If |adj(adj A)| = |A|9, then the order of the square matrix A is

  • 2)

    If A is a 3 × 3 non-singular matrix such that AAT = ATA and B = A-1AT, then BBT = 

  • 3)

    If A = \(\left[ \begin{matrix} 2 & 0 \\ 1 & 5 \end{matrix} \right] \) and B = \(\left[ \begin{matrix} 1 & 4 \\ 2 & 0 \end{matrix} \right] \) then |adj (AB)| = 

  • 4)

    If P = \(\left[ \begin{matrix} 1 & x & 0 \\ 1 & 3 & 0 \\ 2 & 4 & -2 \end{matrix} \right] \) is the adjoint of 3 × 3 matrix A and |A| = 4, then x is

  • 5)

    If A, B and C are invertible matrices of some order, then which one of the following is not true?

12th Maths Quarterly Exam Model Two Marks Question Paper - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    If A = \(\left[ \begin{matrix} a & b \\ c & d \end{matrix} \right] \) is non-singular, find A−1.

  • 2)

    Reduce the matrix \(\left[ \begin{matrix} 3 & -1 & 2 \\ -6 & 2 & 4 \\ -3 & 1 & 2 \end{matrix} \right] \) to a row-echelon form.

  • 3)

    Find the rank of the following matrices by minor method:
    \(\left[ \begin{matrix} 1 & -2 & 3 \\ 2 & 4 & -6 \\ 5 & 1 & -1 \end{matrix} \right] \)

  • 4)

    Simplify \(\left( \cfrac { 1+i }{ 1-i } \right) ^{ 3 }-\left( \cfrac { 1-i }{ 1+i } \right) ^{ 3 }\)

  • 5)

    Represent the complex number −1−i

12th Maths Unit 6 Applications of Vector Algebra Model Question Paper - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    If a vector \(\vec { \alpha } \) lies in the plane of \(\vec { \beta } \) and \(\vec { \gamma } \) , then

  • 2)

    If \(\vec { a } \) and \(\vec { b } \) are unit vectors such that \([\vec { a } ,\vec { b },\vec { a } \times \vec { b } ]=\frac { \pi }{ 4 } \), then the angle between \(\vec { a } \) and \(\vec { b } \) is

  • 3)

    If \(\vec { a } ,\vec { b } ,\vec { c } \) are three non-coplanar vectors such that \(\vec { a } \times (\vec { b } \times \vec { c } )=\frac { \vec { b } +\vec { c } }{ \sqrt { 2 } } \), then the angle between

  • 4)

    The angle between the lines \(\frac { x-2 }{ 3 } =\frac { y+1 }{ -2 } \), z=2 and \(\frac { x-1 }{ 1 } =\frac { 2y+3 }{ 3 } =\frac { z+5 }{ 2 } \)

  • 5)

    Distance from the origin to the plane 3x - 6y + 2z 7 = 0 is

12th Standard Maths Quarterly Exam Model One Mark Question Paper - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    If |adj(adj A)| = |A|9, then the order of the square matrix A is

  • 2)

    If A = \(\left[ \begin{matrix} 3 & 5 \\ 1 & 2 \end{matrix} \right] \), B = adj A and C = 3A, then \(\frac { \left| adjB \right| }{ \left| C \right| } \)

  • 3)

    If A\(\left[ \begin{matrix} 1 & -2 \\ 1 & 4 \end{matrix} \right] =\left[ \begin{matrix} 6 & 0 \\ 0 & 6 \end{matrix} \right] \), then A = 

  • 4)

    If A = \(\left[ \begin{matrix} 7 & 3 \\ 4 & 2 \end{matrix} \right] \), then 9I - A = 

  • 5)

    If A = \(\left[ \begin{matrix} \frac { 3 }{ 5 } & \frac { 4 }{ 5 } \\ x & \frac { 3 }{ 5 } \end{matrix} \right] \) and AT = A−1 , then the value of x is

Plus 2 Maths Chapter 5 Two Dimensional Analytical Geometry - II Model Questions - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    The equation of the circle passing through(1,5) and (4,1) and touching y -axis is x2+y2−5x−6y+9+(4x+3y−19)=0 whereλ is equal to

  • 2)

    The centre of the circle inscribed in a square formed by the lines x2−8x−12=0 and y2−14y+45 = 0 is

  • 3)

    If x+y=k is a normal to the parabola y2 =12x, then the value of k is

  • 4)

    Equation of tangent at (-4, -4) on x2 = -4y is

  • 5)

    y2 - 2x - 2y + 5 = 0 is a

12th Standard Maths First Mid Term Model Question Paper - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    If A\(\left[ \begin{matrix} 1 & -2 \\ 1 & 4 \end{matrix} \right] =\left[ \begin{matrix} 6 & 0 \\ 0 & 6 \end{matrix} \right] \), then A = 

  • 2)

    If A, B and C are invertible matrices of some order, then which one of the following is not true?

  • 3)

    The system of linear equations x + y + z  = 6, x + 2y + 3z =14 and 2x + 5y + λz =μ (λ, μ \(\in \) R) is consistent with unique solution if

  • 4)

    The value of (1+i)4 + (1-i)4 is

  • 5)

    The value of \(\frac { (cos{ 45 }^{ 0 }+isin{ 45 }^{ 0 })^{ 2 }(cos{ 30 }^{ 0 }-isin{ 30 }^{ 0 }) }{ cos{ 30 }^{ 0 }+isin{ 30 }^{ 0 } } \) is

11th Standard Mathematics Chapter 4 Inverse Trigonometric Functions Important Question Paper - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    The value of sin-1 (cos x),0\(\le x\le\pi\) is

  • 2)

    If sin-1 x+sin-1 y=\(\frac{2\pi}{3};\)then cos-1x+cos-1 y is equal to

  • 3)

    \({ sin }^{ -1 }\frac { 3 }{ 5 } -{ cos }^{ -1 }\frac { 12 }{ 13 } +{ sec }^{ -1 }\frac { 5 }{ 3 } { -cosec }^{ 1- }\frac { 13 }{ 2 } \)is equal to

  • 4)

    If \(\alpha ={ tan }^{ -1 }\left( tan\cfrac { 5\pi }{ 4 } \right) \) and \(\beta ={ tan }^{ -1 }\left( -tan\cfrac { 2\pi }{ 3 } \right) \) then

  • 5)

    The number of real solutions of the equation \(\sqrt { 1+cos2x } ={ 2sin }^{ -1 }\left( sinx \right) ,-\pi <x<\pi \) is

12th Standard Maths Chapter 3 Theory of Equations Important Question Paper - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    A zero of x3 + 64 is

  • 2)

    The number of real numbers in [0,2π] satisfying sin4x-2sin2x+1 is

  • 3)

    If x3+12x2+10ax+1999 definitely has a positive zero, if and only if

  • 4)

    The polynomial x3+2x+3 has

  • 5)

    Ifj(x) = 0 has n roots, thenf'(x) = 0 has __________ roots

Model MID-TERM - by MUTHU M View & Read

Model MID-TERM - by MUTHU M View & Read

12th Maths Unit 2 Important Question Paper - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    The value of \(\sum _{ i=1 }^{ 13 }{ \left( { i }^{ n }+i^{ n-1 } \right) } \) is

  • 2)

    If z is a non zero complex number, such that 2iz2=\(\bar { z } \) then |z| is

  • 3)

    z1, z2 and z3 are complex number such that z1+z2+z3=0 and |z1|=|z2|=|z3|=1 then z12+z22+z33 is

  • 4)

    If z1, z2, z3 are the vertices of a parallelogram, then the fourth vertex z4 opposite to z2 is _____

  • 5)

    If xr=\(cos\left( \frac { \pi }{ 2^{ r } } \right) +isin\left( \frac { \pi }{ 2^{ r } } \right) \) then x1, x2 ... x is

Slip Test Unit 3 (A2) - by MUTHU M View & Read

  • 1)

    Find the sum of squares of roots of the equation 2x4-8x+6x2-3=0.

  • 2)

    If α, β, γ  and \(\delta\) are the roots of the polynomial equation 2x4+5x3−7x2+8=0 , find a quadratic equation with integer coefficients whose roots are α + β + γ + \(\delta\) and αβ૪\(\delta\).

  • 3)

    Find a polynomial equation of minimum degree with rational coefficients, having \(\sqrt{5}\)\(\sqrt{3}\) as a root.

  • 4)

    Solve: (2x-1)(x+3)(x-2)(2x+3)+20=0

  • 5)

    Solve the equation 3x3-26x2+52x-24=0 if its roots form a geometric progression.

slip test - by MUTHU M View & Read

  • 1)

    Find the sum of squares of roots of the equation 2x4-8x+6x2-3=0.

  • 2)

    If the equations x2+px+q= 0 and x2+p'x+q'= 0 have a common root, show that it must  be equal to \(\frac { pq'-p'q }{ q-q' } \) or \(\frac { q-q' }{ p'-p } \).

  • 3)

    A 12 metre tall tree was broken into two parts. It was found that the height of the part which was left standing was the cube root of the length of the part that was cut away. Formulate this into a mathematical problem to find the height of the part which was cut away.

  • 4)

    If α and β are the roots of the quadratic equation 17x2+43x−73 = 0 , construct a quadratic equation whose roots are α + 2 and β + 2.

  • 5)

    If α and β are the roots of the quadratic equation 2x2−7x+13 = 0 , construct a quadratic equation whose roots are α2 and β2.

Weekly test-1:JUNE2019 - by MUTHU M View & Read

  • 1)

    If A\(\left[ \begin{matrix} 1 & -2 \\ 1 & 4 \end{matrix} \right] =\left[ \begin{matrix} 6 & 0 \\ 0 & 6 \end{matrix} \right] \), then A = 

  • 2)

    If A is a non-singular matrix such that A-1 = \(\left[ \begin{matrix} 5 & 3 \\ -2 & -1 \end{matrix} \right] \), then (AT)−1 =

  • 3)

    If A = \(\left[ \begin{matrix} 1 & \tan { \frac { \theta }{ 2 } } \\ -\tan { \frac { \theta }{ 2 } } & 1 \end{matrix} \right] \) and AB = I , then B = 

  • 4)

    If A =\(\left( \begin{matrix} cosx & sinx \\ -sinx & cosx \end{matrix} \right) \) and A(adj A) =\(\lambda \) \(\left( \begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix} \right) \) then \(\lambda \) is

  • 5)

    In a square matrix the minor Mij and the' co-factor Aij of and element aij are related by _____

12th Maths - Unit 1 Full Important Question Paper - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    If |adj(adj A)| = |A|9, then the order of the square matrix A is

  • 2)

    If A is a 3 × 3 non-singular matrix such that AAT = ATA and B = A-1AT, then BBT = 

  • 3)

    If A = \(\left[ \begin{matrix} 3 & 5 \\ 1 & 2 \end{matrix} \right] \), B = adj A and C = 3A, then \(\frac { \left| adjB \right| }{ \left| C \right| } \)

  • 4)

    If A\(\left[ \begin{matrix} 1 & -2 \\ 1 & 4 \end{matrix} \right] =\left[ \begin{matrix} 6 & 0 \\ 0 & 6 \end{matrix} \right] \), then A = 

  • 5)

    If A = \(\left[ \begin{matrix} 7 & 3 \\ 4 & 2 \end{matrix} \right] \), then 9I - A = 

frequently asked two marks in twelfth standard maths english medium - by Mythily View & Read

  • 1)

    For any 2 x 2 matrix, if A (adj A) =\(\left[ \begin{matrix} 10 & 0 \\ 0 & 10 \end{matrix} \right] \) then find |A|.

  • 2)

    For the matrix A, if A3 = I, then find A-1.

  • 3)

    If A is a square matrix such that A3 = I, then prove that A is non-singular.

  • 4)

    Show that the system of equations is inconsistent. 2x + 5y= 7, 6x + 15y = 13.

  • 5)

    Flod the rank of the matrix \(\left[ \begin{matrix} 3 & -1 & 1 \\ -15 & 6 & -5 \\ 5 & -2 & 2 \end{matrix} \right] \).

+2 english medium creative multiple choice questions in maths chapter one - by Mythily View & Read

  • 1)

    The system of linear equations x + y + z  = 6, x + 2y + 3z =14 and 2x + 5y + λz =μ (λ, μ \(\in \) R) is consistent with unique solution if

  • 2)

    If the system of equations x = cy + bz, y = az + cx and z = bx + ay has a non - trivial solution then

  • 3)

    Let A be a 3 x 3 matrix and B its adjoint matrix If |B|=64, then |A|=

  • 4)

    If AT is the transpose of a square matrix A, then

  • 5)

    The number of solutions of the system of equations 2x+y = 4, x - 2y = 2, 3x + 5y = 6 is

Important one mark questions 12th maths english medium chapter one - by Mythily View & Read

  • 1)

    If |adj(adj A)| = |A|9, then the order of the square matrix A is

  • 2)

    If A is a 3 × 3 non-singular matrix such that AAT = ATA and B = A-1AT, then BBT = 

  • 3)

    If A = \(\left[ \begin{matrix} 3 & 5 \\ 1 & 2 \end{matrix} \right] \), B = adj A and C = 3A, then \(\frac { \left| adjB \right| }{ \left| C \right| } \)

  • 4)

    If A\(\left[ \begin{matrix} 1 & -2 \\ 1 & 4 \end{matrix} \right] =\left[ \begin{matrix} 6 & 0 \\ 0 & 6 \end{matrix} \right] \), then A = 

  • 5)

    If A = \(\left[ \begin{matrix} 7 & 3 \\ 4 & 2 \end{matrix} \right] \), then 9I - A = 

UNIT TEST - 1 - by Palanivel View & Read

  • 1)

    If F(\(\alpha\)) = \(\left[ \begin{matrix} \cos { \alpha } & 0 & \sin { \alpha } \\ 0 & 1 & 0 \\ -\sin { \alpha } & 0 & \cos { \alpha } \end{matrix} \right] \), show that [F(\(\alpha\))]-1 = F(-\(\alpha\)).

  • 2)

    If A = \(\left[ \begin{matrix} 5 & 3 \\ -1 & -2 \end{matrix} \right] \), show that A2 - 3A - 7I2 = O2. Hence find A−1.

  • 3)

    If A = \(\frac { 1 }{ 9 } \left[ \begin{matrix} -8 & 1 & 4 \\ 4 & 4 & 7 \\ 1 & -8 & 4 \end{matrix} \right] \), prove that A−1 = AT.

  • 4)

    If A = \(\left[ \begin{matrix} 3 & 2 \\ 7 & 5 \end{matrix} \right] \) and B = \(\left[ \begin{matrix} -1 & -3 \\ 5 & 2 \end{matrix} \right] \), verify that (AB)-1 = B-1A-1

  • 5)

    If adj(A) = \(\left[ \begin{matrix} 2 & -4 & 2 \\ -3 & 12 & -7 \\ -2 & 0 & 2 \end{matrix} \right] \), find A.