Area between x=g(y) and y Axis

Q.

What is the null space of a matrix?

Q.

What will be the cost of fencing a rectangular compound if the wire cost $\mathrm{Rs}.20$ per meter? Also, the area is $40{\mathrm{m}}^2$ and $\mathrm{length}=2\times \mathrm{breadth}$?

Q. Area bounded between the curves $y=\sqrt{4-x^2}$ and $y^2=3|x|$ is/are

1. $\frac{\pi -1}{\sqrt{3}}$
2. $\frac{2\pi -1}{3\sqrt{3}}$
   
3. $\frac{2\pi -\sqrt{3}}{3\sqrt{3}}$
4. $\frac{2\pi -\sqrt{3}}{3}$
   

Q.

Find the area bounded by the curve $x^2=4y$ and the line x = 4y - 2.

Q.

The complex numbers $z_1,z_2\mathrm{and}{z}_3$ satisfying $\frac{\left(z_1-z_3\right)}{\left(z_2-z_3\right)}=\frac{1-\sqrt{3}i}{2}$ are the vertices of a triangle which is

1. of area zero

2. right angled isosceles

3. equilateral

4. obtuse-angled isosceles

Q.

The area enclosed by the curves $y=\sin x+\cos x$ and $y=\left|\cos x-\sin x\right|$ over the interval$\left[0,\frac{\mathrm{\pi }}{2}\right]$ is

1. $4\left(\sqrt{2}-1\right)$

2. $2\sqrt{2}\left(\sqrt{2}-1\right)$

3. $2\left(\sqrt{2}+1\right)$

4. $2\sqrt{2}\left(\sqrt{2}+1\right)$

Q.

If ${\sum }_{i-l}^{2n}co{s}^{-1}{x}_i=0$, then ${\sum }_{i-l}^{2n}co{s}^{-1}{x}_i$ is

1. 2n

2. n(n+1)/2

3. 3n

4. n

Q.

The differential equation of the family of curves represented by the equation $x^{2}y=a$, is

1. 
   

2. 
   

3. 
   

4. 
   

Q.

The feasible region for the following constraints $L_1\le 0,L_2\ge 0,L_3=0,x\ge 0,y\ge 0$ in the diagram shown is

1. area $DHF$

2. area $AHC$

3. line segment $EG$

4. line segment $GI$

5. line segment $IC$

Q.

Let $f\left(x\right)=max(x+\left|x\right|,x-\left[x\right])$ where [x] = the greatest integer in $x\le x$. Then ${\int }_{-2}^{2}f\left(x\right)dx$ is equal to

1. 3

2. 2

3. 1

4. None of these

Q.

Smaller area enclosed by the circle x² + y² = 4 and the line x + y = 2 is

A. 2 (π – 2)

B. π – 2

C. 2π – 1

D. 2 (π + 2)

Q.

Area of the region bounded by the curve y² = 2y - x and y-axis is:

1. 4 sq. units

2. 

3. 

4. 3 sq. units

Q.

What is the area bounded by $y=\log x,x-axis$ and ordinates $x=1,x=2$?

1. $\frac{1}{2}{\left(\log x\right)}^2$

2. $\log \left(\frac{2}{e}\right)$

3. $\log \left(\frac{4}{e}\right)$

4. $\log 4$

Q.

^{_{​​​​​​A rod AB of length 4 units moves horizontally with its left end A always on the circle} ​​​}x _{​​​​​​}²+y²-4x-18y-29=0 then the locus of the circle is

Q. Let $S$ be the region bounded by the curves $y=x^3$ and $y^2=x$. The curve $y=2|x|$ divides $S$ into two regions of areas $R_1$ and $R_2$. If $max\{R_1,R_2\}=R_2$, then $\frac{R_2}{R_1}$ is equal to

Q.

If the line x-3y+k =0 touches the parabola $3y^2=4x$ then the value of k is

1. 5

2. 7

3. 6

4. 3

Q. The area of the region between the curve y=3x square and the x axis in the interval x=0 to x = b is (b is +ve)

Q. Find the area of the minor segment of the circle $x^2+y^2=a^2$ cut off by the line $x=\frac{a}{2}$.

Q. Let $OABC$ $(O$ is the origin$)$ be a tetrahedron with edges length $BC=\sqrt{2}$, $CA=\sqrt{3}$, $AB=\sqrt{4}$, $OA=\sqrt{5}$, $OB=\sqrt{6}$ and $OC=\sqrt{7}$. Then which of the following is (are) CORRECT?

1. Volume of the tetrahedron $OABC$ is $\frac{\sqrt{11}}{4}$
2. Volume of the tetrahedron $OABC$ is $\sqrt{\frac{11}{4}}$
3. Perpendicular distance between the point $O$ and the plane $ABC$ is $3\sqrt{\frac{11}{23}}$
4. Perpendicular distance between the point $O$ and the plane $ABC$ is $\sqrt{\frac{11}{92}}$

Q. Find the area of shaded region of the figure given below.

Q.

A circle of maximum area is inscribed inside an ellipse. If p is the probability that a point within the ellipse chosen at random lies outside the circle, then the eccentricity of the ellipse is

A.√(1-p) B. √{1-(1-p)²} C. √(1-p²) D.√{(1+p)²-1}

Q.

The value of ${\int }_0^{\mathrm{\pi }}\left({\sin }^{50}\left(x\right)·{\cos }^{49}\left(x\right)\right)dx$ is

1. $0$

2. $\frac{\mathrm{\pi }}{4}$

3. $\frac{\mathrm{\pi }}{2}$

4. $1$

Q.

Find the area of the region bounded by the curves y = x² + 2, y = x, x = 0 and x = 3

Q.

The value of $k$ which makes $\text{f(x)=}\left\{\sin \left(\frac{1}{\text{x}}\right)\text{, x≠0}\right\}\text{(k, x=0)}$ continuous at $\text{x=0}$ is

1. $8$

2. $1$

3. $-1$

4. none of these

Q.

The number of values of 'a' for which the equation $(x-1{)}^2=|x-a|$ has exactly three solutions is

1. 1

2. 2

3. 3

4. 4

Q.

The differential equation of the family of curves represented by the equation $x^2+y^2=a^2$ is

1. None of these

2. 
   

3. 
   

4. 
   

Q.

Determine the area under the curve$y=\sqrt{a^2-x^2}$ included between the lines x = 0 and x = a.

Q.

You have $64$ feet of fencing to enclose a rectangular plot that borders on a river. If you do not fence the side along the river find the length and width of the plot will maximize the area.

1. length: $33$ feet, width: $32$ feet

2. length: $16$ feet, width: $16$ feet

3. length: $48$ feet, width: $16$ feet

4. length: $32$ feet, width: $16$ feet

Q. In an acute angled triangle $ABC,\cos A+\cos B+\cos C\le \lambda ,$ then $\lambda$ is equal to

1. $\frac{5}{2}$
2. $\frac{3}{2}$
3. $3$
4. $2$

Q.

If the circumference of a circle and the perimeter of a square are equal, then

1. Area of the circle $=$Area of the square

2. Area of the circle $>$ Area of the square

3. Area of the circle $<$ Area of the square

4. Nothing definite can be said about the relation between the areas of the circle & square.