Explore topic-wise InterviewSolutions in .

Let $P=\left[a_{ij}\right]$ be a $3\times 3$ matrix and let $Q=\left[b_{ij}\right]$, where $b_{ij}=2^{i+j}\cdot a_{ij}$ for $1\le i,j\le 3$. If the determinant of $P$ is $2,$ then the determinant of the matrix $Q$ is

50 men took a dip in a water tank 40 m long and 20 m broad on a religious day. If the average displacement of water by a man is 4 m${}^3$, then the rise in the water level in the tank will be:

Choose the correct choice in the following and justify

I. 30^th term of the A.P: 10, 7, 4, …, is

A. 97 B. 77 C. − 77 D. − 87

II 11^th term of the A.P. is

A. 28 B. 22 C. − 38 D.

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}-->

The equation $x^2+bx+c=0$ would have real roots if ____.

In the given figure, P is a point on AB such that AP : PB = 4 : 3. PQ is parallel to AC.
(i) Calculate the ratio PQ : AC, giving reason for your answer. (ii) In triangle ARC, $\angle$ ARC = ${90}^{\circ }$ and in triangle PQS, $\angle$ PSQ = ${90}^{\circ }$. Given QS = 6 cm, calculate the length of AR.

Describe the locus for questions 1 to 13 given below:

The locus of a runner running around a circular track and always keeping a distance of 1.5 m from the inner edge.

The roots of $2x^2–6x+8=0$ are :

Match the following based on the construction of similar triangles, if scale factor $\left(\frac{m}{n}\right)$ is
$\begin{array}{cc}I.>1& a)Thesimilartriangleissmallerthantheoriginaltriangle.\\ II.<1& b)Thetwotrianglesarecongruenttriangles.\\ III.=1& c)Thesimilartriangleislargerthantheoriginaltriangle.\end{array}$

If the Equation $\frac{x(x-1)-(M+1)}{(x-1)(M-1)}=\frac{x}{M}$ has Equal roots, then

Which of the following is the standard form of a quadratic equation?

Question 3

Does a quadratic equation with integral coefficient has integral roots. Justify your answer.

The sum up to n terms of an AP with first term $a$, last term $l$ and common difference $d$ is

Prove the following identities:

$(secA-cosecA)(1+tanA+cotA)=tanAsecA-cotAcosecA$

9 sec70° sin20° + cosec70° cos20° = ___.

Choose a figure which would most closely resemble the unfolded form of Figure (Z).

An ice cream vendor puts a hemispherical scoop of ice cream on a cone which has radius 7 cm and height 15 cm. Find the volume of ice cream put on the cone.

If $132300=2^2\times 3^3\times 5^2\times a^b,$ then which of the following is true ?

In the given figure, $△FEC\cong △GBD$ and $\angle 1=\angle 2$. Prove that $△ADE\sim △ABC$.

Solution for ax + by = a - b and bx - ay = a + b is

Which of the following is an example of an arithmetic progression?

$△$ABC and $△$PQR are two similar triangles as shown in the figure such that $\frac{AreaofABC}{AreaofPQR}$ = $\frac{9}{25}$. AM and PN are the medians on $△$ABC and $△$PQR respectively. If AM = PO = 5 cm, find the value of 3ON.

__

If the mean of the following frequency distribution is $7.5,$ find the missing frequency $f.$

$\begin{array}{ccccccccc}Variable& 5& 6& 7& 8& 9& 10& 11& 12\\ Frequency& 20& 17& f& 10& 8& 6& 7& 6\end{array}$

A rectangular paper of length l and breadth h is wrapped around a cylindrical can of radius r and height h.

S1 : The length of rectangular sheet required equals circumference of circle

S2 : The area of rectangular sheet required = 2πrh

Given a triangle with side AB = 8 cm. To get a line segment AB' = ³/₄ of AB, it is required to divide the line segment AB in the ratio:

if alpha and beta are zeroes of F(x)=X^2-P(x+1)-c show that (alpha+1)into (beta +1)=1-c

Find the sum of the first $24$ terms of an AP whose $n^{\text{th}}$ term is given by $t_n=3+2n.$

A right triangle is formed by connecting the 3 coordinates A, B and C. Find the area of the $\Delta ABC$, if AB and BC are parallel to the coordinate axes as shown in the figure.