1. A=[1−236],B=[3721],C=[0128] \mathrm{A}=\left[\begin{array}{cc}1 & -2 \\ 3 & 6\end{array}\right], \mathrm{B}=\left[\begin{array}{ll}3 & 7 \\ 2 & 1\end{array}\right], \mathrm{C}=\left[\begin{array}{ll}0 & 1 \\ 2 & 8\end{array}\right] A=[13−26],B=[3271],C=[0218]
M=[x+2y+3z2x+y+4z3x+2y+z] and N=[−123] M=\left[\begin{array}{ll} x+2 y+3 z & 2 x+y+4 z \quad 3 x+2 y+z \end{array}\right] \text { and } N=\left[\begin{array}{lll} -1 & 2 & 3 \end{array}\right] M=[x+2y+3z2x+y+4z3x+2y+z] and N=[−123]
What are the conditions of two matrices to be equal?
Find: AB+Bt−2C A B+B^{t}-2 C AB+Bt−2C.
If M=N M=N M=N, then solve with the help of Cramer's rule
2.
Prove that : sin78∘19′cos18∘19′−sin11∘41′sin18∘19′=3/2 \sin 78^{\circ} 19^{\prime} \cos 18^{\circ} 19^{\prime}-\sin 11^{\circ} 41^{\prime} \sin 18^{\circ} 19^{\prime}=\sqrt{3}/2 sin78∘19′cos18∘19′−sin11∘41′sin18∘19′=3/2.
If a=b2+bc+c2 a=\sqrt{b^{2}+b c+c^{2}} a=b2+bc+c2, then find the sum of the two acute angles of the triangle.
Prove that, a−bccosecA−B2=secC2 \frac{a-b}{c} \operatorname{cosec} \frac{A-B}{2}=\sec \frac{C}{2} ca−bcosec2A−B=sec2C for the triangle.
3.
If the two vectors 4i^+2j^−3k^ 4 \hat{i}+2 \hat{j}-3 \hat{k} 4i^+2j^−3k^ and 3i^−4j^+ak^ 3 \hat{i}-4 \hat{j}+a \hat{k} 3i^−4j^+ak^ are perpendicular, then what is the value of a a a ?
Find the equations of the tangent and the normal at the point P P P of the circle whose centre is 0 .
Find the co-ordinates of the points A \mathrm{A} A and B \mathrm{B} B.
4. The date of birth of 'MUAZUL' is 24.06.1987.24.06.1987.24.06.1987.
If nC2=3P1 { }^{n} C_{2}={ }^{3} P_{1} nC2=3P1 then find the value of n n n.
How many numbers of 8 significant digits can be formed with the digits that are used date of birth using each digit only once in a number?
Find the number of combination of the letters of the word that are used in stem taken 4 letters at a time. 4
5. f(x)=x... ... ...(i)f\left(x\right)=x...\ ...\ ...\left(i\right)f(x)=x... ... ...(i)
g(x)=cos−1x2………(ii)y2=7x…… (iii) \begin{array}{l} g(x)=\cos ^{-1} x^{2} \ldots \ldots \ldots(ii) \\ y^{2}=7 x \ldots \ldots \text { (iii) } \end{array} g(x)=cos−1x2………(ii)y2=7x…… (iii)
Find: ∫(cot27x+sec29x)dx \int\left(\cot ^{2} 7 x+\sec ^{2} 9 x\right) d x ∫(cot27x+sec29x)dx.
Integrate: ∫f(x)g(x)dx \int f(x) g(x) d x ∫f(x)g(x)dx.
Find the area bounded by the straight line (i) and the curve (iii).
