Quantitative Ability

Q. What is the area of the quadrilateral AMND in the given figure (in $c{m}^2$)?

1. $42\sqrt{3}$
2. $48\sqrt{3}$
3. $36\sqrt{3}$
4. $24\sqrt{3}$

Q. ABCD is a parallelogram. W, X, Y and Z are points on sides AB, BC, CD, and DA respectively, such that $AW=DY$. If ar$\left(ABCD\right)=400c{m}^2$, what is the area of quadrilateral WXYZ?

1. $250c{m}^2$
2. $200c{m}^2$
3. $50c{m}^2$
4. $100c{m}^2$

Q. The ratio of the diameter of the vessels A and B is 9:4. The vessel A is filled with water till the brim. If half of the water from vessel A would leave quarter of the vessel B empty, what is the ratio of the heights of the vessels?

1. 6:25
2. 8:27
3. 4:29
4. 2:13

Q. What is the probability of getting a sum of 15, if 3 dice are thrown simultaneously?

1. $\frac{3}{108}$
2. $\frac{15}{216}$
3. $\frac{5}{216}$
4. $\frac{5}{108}$

Q.

The length of longer diagonal of the parallelogram constructed on $5\overrightarrow{a}+2\overrightarrow{b}$and $\overrightarrow{a}-3\overrightarrow{b}$, if it is given that $\left|\overrightarrow{a}\right|=2\sqrt{2}$, $\left|\overrightarrow{b}\right|=3$ and the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$ is $\frac{\pi }{4}$ is?

1. $15$

2. $\sqrt{113}$

3. $\sqrt{593}$

4. $\sqrt{369}$

Q. What is the area of the quadrilateral AMND in the given figure (in \(cm^2\))?

Q.

The product of two consecutive positive integers is divisible by $2.$Is this statement true or false? Give reasons.

1. True
2. False

Q. Three numbers p, q, and, r are pairwise coprime. If the product of p and q is 629 and the product of q and r is 391 then find the sum of p, q, r.

1. 147
2. 77
3. 67
4. 123

Q. Water level in a cylinder raises by 16 cm when three spheres are dropped in it. If the ratio of the radii of the spheres is 1:2:3 and the radius of the cylinder is 6 cm, what is the volume (in cm${}^3$) of the smallest sphere?

1. $16\pi$
2. $24\pi$
3. $12\pi$
4. $8\pi$

Q. What is the area (in $c{m}^2$) of the quadrilateral formed by joining the mid-points of the sides of a square of area 144 cm${}^2$ ?

1. 72
2. 36
3. 108
4. 144

Q. If P(4, -3) is a point that lies on the circumference of a circle on a cartesian plane with origin ‘O’ as its centre, which of the following points would lie on the circumference?

1. (5, 4)
2. (-3, 3)
3. (0, 4)
4. (0, -5)

Q. What is the probability of getting a sum of 15, if 3 dice are thrown simultaneously?

Q. For a quiz competition, a group of 3 students is selected randomly from a class consisting of 5 boys and 5 girls. What is the probability that one boy and two girls are selected?

1. $\frac{2}{5}$
2. $\frac{7}{13}$
3. $\frac{2}{3}$
4. $\frac{5}{12}$

Q. The ratio of the diameter of the vessels A and B is 9:4. The vessel A is filled with water till the brim. If half of the water from vessel A would leave quarter of the vessel B empty, what is the ratio of the heights of the vessels?

1. 8:27
2. 4:29
3. 2:13
4. 6:25

Q. If P(4, -3) is a point that lies on the circumference of a circle on a cartesian plane with origin ‘O’ as its centre, which of the following points would lie on the circumference?

1. (0, -5)
2. (0, 4)
3. (-3, 3)
4. (5, 4)

Q. A square is inscribed in a circle of diameter ‘D’. If one side of the blue square is the diagonal of the red square, what is the ratio of the area of the smaller square and the circle?

1. $2:\pi$
2. $1:\pi$
3. $D:\pi$
4. $D:2\pi$

Q. ABCD is a parallelogram. W, X, Y and Z are points on sides AB, BC, CD, and DA respectively, such that $AW=DY$. If ar$\left(ABCD\right)=400c{m}^2$, what is the area of quadrilateral WXYZ?

1. $50c{m}^2$
2. $250c{m}^2$
3. $200c{m}^2$
4. $100c{m}^2$

Q. What is the probability of getting a sum of 15, if 3 dice are thrown simultaneously?

1. $\frac{5}{108}$
2. $\frac{5}{216}$
3. $\frac{3}{108}$
4. $\frac{15}{216}$