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1. If \( \frac{5}{\sqrt{2}}-\frac{\sqrt{8}}{8}=m \sqrt{2} \), find the value of \( m \). (A) \( \frac{12}{5} \) (B) \( \frac{9}{4} \) (C) \( \frac{7}{3} \) (D) \( \frac{5}{2} \) 2. Given that \( f: x \rightarrow \sqrt{x} \) and \( g: x \rightarrow 25-x^{2} \), find the value of \( \log (3) \). (A) 4 (B) 3 3. If \( \sqrt{x}-\frac{6}{\sqrt{x}}=1 \), find the value of \( x \). (A) 9 (B) 16 (C) 25 (D) 36 4. If \( 5 x+7=P(x+3)+Q(x-1) \), find the value of \( P \). (A) 3 (B) 2 (C) 1 (D) \( 0 \cdot\left(4 A^{\circ}\right)= \) 5. If \( y=x \sin x \), find \( \frac{d y}{d x} \). (A) \( \sin x-x \cos x \) (B) \( \sin x-\cos x \) (C) \( \sin x+x \cos x \) (D) \( \sin x+\cos x \) 6. A binary operation \( * \) is defined on the set of real numbers, \( R \) by \( * y=\frac{y^{2}-x^{2}}{2 x y}, x, y \neq 0 \), where \( x \) ar (A) \( \frac{13}{12} \) (B) \( \frac{5}{12} \) (C) \( -\frac{5}{12} \) (D) \( =\frac{13}{12} \) 7. Calculate the value of \( \lambda \) for which vectors \( (5 \lambda i+2 j) \) and \( (4 i-3 j) \) are perpendicular. (A) \( \frac{1}{2} \) (B) (C) \( \frac{10}{3} \) (D) \( \frac{3}{10} \) 8. If \( h(x)=x^{2}+p x+2 \) is divided by \( (x+3) \), the remainder is 5 , find \( p \). (A) 1 (B) 2 (C) 3 (D) 4 9. If the nth term of a linear sequence (A.P.) is \( (5 n-2) \), find the sum of the first 12 terms of \( t \) l sequence. (A) 120 (B) 183 (C) 366 (D) 732 10. Find the stationary point of the curve \( =3 x^{2}-2 x^{3} \). (A) \( (1,0) \) (B) \( (-1,0) \) (C) \( (1,1) \) (D) \( (-1,-1) \) 11. Solve: \( 2^{2 x}-5\left(2^{x}\right)+4=0 \) (A) \( x=0 \) and 1 (B) \( x=1 \) and 2 (C) \( x=0 \) and 2 (D) \( x=2 \) and 12. Express \( 75^{\circ} \) in radians leaving your answer in terms of \( \pi \). (A) \( \frac{3}{4} \pi \) (B) \( \frac{5}{6} \pi \) (C) \( \frac{5}{12} \pi \) (D) \( \frac{7}{6} \pi \) 13. A body of mass 42 kg increases its speed from \( 15 \mathrm{~m} / \mathrm{s} \) to \( 43 \mathrm{~m} / \mathrm{s} \) in 12 seconds. Find the force acting c the body. (A) 52 N (B) 98 N (C) 150 N (D) 203 N
Calculus Jan 22, 2025
EXERCISE 5.1 1. Find the volume of the parallelopiped with adjacent sides. \[ \overline{O A}=3 \hat{i}-\hat{j}, \quad \overline{O B}=\hat{j}+2 \hat{k} \text {, and } \overline{O C}=\hat{i}+5 \hat{j}+4 \hat{k} \] extending from the origin of co-ordinates \( O \)
Geometry Jan 22, 2025
EXERCISE 5.1 1. Find the volume of the parallelopiped with adjacent sides. \[ \overline{O A}=3 \hat{i}-\hat{j}, \quad \overline{O B}=\hat{j}+2 \hat{k} \text {, and } \overline{O C}=\hat{i}+5 \hat{j}+4 \hat{k} \] extending from the origin of co-ordinates \( O \)
Geometry Jan 22, 2025
EXERCISE 5.1 1. Find the volume of the parallelopiped with adjacent sides. \[ \overline{O A}=3 \hat{i}-\hat{j}, \quad \overline{O B}=\hat{j}+2 \hat{k} \text {, and } \overline{O C}=\hat{i}+5 \hat{j}+4 \hat{k} \] extending from the origin of co-ordinates \( O \)
Geometry Jan 22, 2025
2. Find the volume of the tetrahedron whose vertices are the points \( A(2,-1,-3), B(4,1,3) \) \( C(3,2,-1) \) and \( D(1,4,2) \). Ans. \( 7 \frac{1}{3} \)
Geometry Jan 22, 2025
The equation of a line is \( y=5 x+2 \). Find the oquation of a line perpendiculat to it and passing through \( \left(4,-\frac{3)}{3}\right. \)
Geometry Jan 21, 2025
4 A line passos through \( (1,1) \) and \( (3,5) \). ind wein Ard the equation of a line perpendicular to this ine passing through \( (2,-1) \)
Geometry Jan 21, 2025
Aline passos through \( (1,1) \) and \( (3,5) \). Ard the the equation of 9 line perpendicular to this ine passing through \( (z,-1) \)
Geometry Jan 21, 2025
2 Find the equation of a line paralle) to \( y=1 / 3 x-4 \) and passiog through \( (5,0) \)
Algebra Jan 21, 2025
Assignment Aline passes through \( (0,-2) \) and \( (4,6) \) Find the equation of a line parallel to this Nine passing through \( (-3,-1) \)
Algebra Jan 21, 2025
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