Explore topic-wise InterviewSolutions in Current Affairs.

The product of two consecutive positive odd numbers is 63. Select the correct options.

In three line segments OA, OB, and OC, points L, M, N respectively are so chosen that LM || AB and MN || BC but neither of L, M, N nor of A, B, C are collinera. Show that LN || AC.

cos$1^{\circ }$ $\times$ cos$2^{\circ }$ $\times$ cos$3^{\circ }$ $\times$……..$\times$ cos ${180}^{\circ }$ is equal to ____.

The sum of first 20 terms of the sequence 0.7, 0.77, 0.777, ....., is

Question 24
Factorise
(i) $2x^3–3x^2–17x+30$

(ii) $x^3–6x^2+11x–6$

(iii) $x^3+x^2-4x-4$

(iv) $3x^3–x^2-3x+1$

In the given figure, O is the centre of a circle and PQ is a diameter. If $\angle ROS={40}^{\circ },$ then what is the value of $\angle RTS$?

(a)

A, B, C and D are rectangles.
The length of the diagonal of which rectangles are not irrational and which are irrational?


(b) Solve: $\frac{5}{13}-\frac{-8}{26}$
[4 MARKS]

If $H=\left[\begin{array}{ccc}1& 2& 3\\ 2& 3& 1\\ 3& 1& 2\end{array}\right]G=\left[\begin{array}{ccc}2& 6& -10\\ 0& -4& 8\\ 2& -8& 4\end{array}\right]$

Find $3H-\frac{1}{2}G$

Question 13

In the following question, out of the four options, only one is correct. Write the correct answer:

If y be any non-zero integer, then $y^0$ is equal to:
(a) 1
(b) 0
(c) -1
(d) Not defined

Find the H.C.F of 54 and 82.

If sides of a triangle are proportional then angles are equal??

Prepare Bank Reconciliation Statement on the basis of following information:

$\begin{array}{ccc}& & Rs\\ \left(i\right)& \text{Debit balance as per bank column of the Cash Book}& 3,72,000\\ \left(ii\right)& \text{Cheques issued to creditors, but not yet presented to the bank for payment}& 72,000\\ \left(iii\right)& \text{Dividend received by the Bank, but not entered in the Cash Book}& 5,000\\ \left(iv\right)& \text{Interest allowed by the Bank}& 1,250\\ \left(v\right)& \text{Cheques deposited into Bank for collection, but not collected by Bank}& 15,400\\ \left(vi\right)& \text{Bank charges}& 200\\ \left(vii\right)& \text{A Cheque deposited into Bank was dishonoured but no intimation received}& 320\\ \left(viii\right)& \text{Bank paid House Tax on our behalf, but no information received from Bank}& 350\end{array}$

Find H.C.F of $(x-2{)}^2$, $x^2-4$ and $x^2+x-6$. Put $x=y+2$.

A man has a choice to invest in hundred-rupee shares of two firms at Rs 120 or at Rs 132. The first firm pays a dividend of 5% per annum and the second firm pays a dividend of 6% per annum. Find :

(i) which company is giving a better return.

(ii) if a man invests Rs 26,400 with each firm, how much will be the difference between the annual returns from the two firms ?

AB is a diameter of a circle, where A(-3,-4) and B(3,4). Find its centre and length of diameter.

Find the equation of the line passing through the intersection of $2x+y=8,3x–7=y$ and parallel to $4x+y=11$.

Which of the following should be the LAST sentence after rearrangement?

The numbers $11284$ and $7655$ when divided by a certain number of three digits, leave the same remainder. find that three digit number.

Sam sold his dining table set at a loss of 20%. If he had sold it for ₹800 more, he would have received a profit of 5%. Find the cost price.

The quantities a, 6, 12, and b are in continued proportion. Find the values of a and b.

Mention the proper order of identifying a point D on BC such that $\frac{Ar\left(△ABD\right)}{Ar\left(△ADC\right)}=\frac{2}{3}$?
1) Join $B_{5}C$ and draw a line parallel to $B_{5}C$ from $B_2$.
2) Identify the ratio in which the point D divides BC using the relation given.
3) Mark 5 points B₁, B₂, B₃, B₄ and B₅ on BX such that they are equidistant.
4) Construct a ray BX which makes an acute angle with line segment BC.
5) The point of intersection of the parallel line from B₂ with BC is the point D.

Construct a histogram from the following distribution of total marks obtained by 65 students of X class in the final examination

$\begin{array}{ccccccc}Marks(mid-points):& 150& 160& 170& 180& 190& 200\\ No.ofstudents& 8& 10& 25& 12& 7& 3\end{array}$

When we plot a graph, as x increases, y decreases. The graph thus obtained is a

If 15x > 17x then the set of values of x is

3 women and 6 men can together finish a tailoring job in 5 days, while 4 women and 7 men can finish it in 4 days. Find the time taken by 1 woman alone to finish the work, and also that taken by 1 man alone. The linear equations(in standard form) to solve this problem algebraically are

In the given figure the perpendicular drawn from A to the base BC pass through the center O of the circle. Find the value of $\angle OCB$ if $\angle BAC={60}^{\circ }$.

The graph given below shows graphical representation of the following polynomials.

a) $y=x^3$
b) $y=x^7$
c) $y=x^2$
d) $y=x^6$


Identify the correct relation between the graphs $\left(1\text{to}4\right)$ and the polynomials $\left(a\text{to}d\right)$.

As observed from the top of a 80 m tall light house, the angles of depression of 2 ships on the same side of the light house in horizontal line with its base are 30^o & 60^o respectively. Find the distance between the 2 ships. (give answer to nearest metre)

Two lines intersect perpendicularly at A and a third line meets the two lines at B and C. A line is drawn from A such that the line is equidistant from the two perpendicularly intersecting lines. If ABC is an isosceles triangle, then the line drawn from A will always pass through

For solving each pair of equations, use the method of eliminations by equating coefficients:

$y=2x-6$

$y=0$

If ‘a’ and ‘b’ are the roots of the equation $x^2$ – 8x + 15 = 0, then find the value of ‘a’ and ‘b’.

The first and last terms of an A.P.are 1 and 11. If the sum of its terms is 36, then the number of terms will be

An open metal bucket is in the shape of a frustum of a cone,mounted on a hollow cylindrical base made of the same metallic sheet. The diameters of the two Circular ends of the bucket are 45 cm and 25 cm, the total vertical height of the bucket is 40cm and that of the cylindrical base is 6cm. Find the area of the metallic sheet used to make the bucket, where we do not take into account the handle of the bucket. Also, find the volume of water the bucket can hold. $(take\pi =\frac{22}{7})$

Evaluate each of the following

$\frac{ta{n}^2{60}^o+4co{s}^2{45}^o+3se{c}^2{30}^o+5co{s}^2{90}^o}{cosec{30}^o+sec{60}^o-co{t}^2{30}^o}$

Compute the area of trapezium PQRS in the figure.

Find all the zeros of $(x^4+x^3-23x^2-3x+60)$, if it is given that two of its zeros are $\sqrt{3}and-\sqrt{3}.$

A military tent of height $8.25$ m is in the form of a right circular cylinder of base diameter $30m$ and height $5.5m$ surmounted by a right circular cone of same base radius. Find the length of canvas used in making the tent, if the breadth of the canvas is $1.5m.$

A pendulum swings through an angle of 30${}^{\circ }$ and describes an arc 8.8 cm in length. Find the length of the pendulum.

Solve for x and y:

$\frac{x}{a}+\frac{y}{b}=2,ax-by=a^2-b^2.$

On comparing the ratios $\frac{a_1}{a_2},\frac{b_1}{b_2}$ and $\frac{c_1}{c_2}$, and without drawing them, find out whether the lines representing the following pairs of linear equation intersect at a point, are parallel or coincide:

(i) $5x-4y+8=0$

$7x+6y-9=0$

(ii) $9x+3y+12=0$

$18x+6y+24=0$

(iii) $6x-3y+10=0$

$2x-y+9=0$

In the equation ax+by+c=0, if $y=\frac{(cx-d)}{b}$ then x =