Explore topic-wise InterviewSolutions in Current Affairs.

The maximum number of zeroes the polynomial $x^7$+ $x^5$ + $x^3$ + x + 1 can have is

In a right angled triangle ABC (right angled at B)

The value of tan A tan C=__

The figure shows two concentric circles with centre O. AB and APQ are tangents to the inner circle from point A lying on the outer circle. If AB = 7.5 cm then AQ is equal to:

Which of the following is correct about parabola $y=a{x}^2$ (when a is positive)

Match the object in Column A to the formulae in Column B. Choose the option with correct matches.

"$$\begin{array}{cc}A:& B:\\ 1.VolumeofCone& 1.\pi r^{2}h\\ 2.VolumeofSphere& 2.\frac{4}{3}\pi r^3\\ 3.VolumeofCylinder& 3.\frac{\pi r^{2}h}{3}\end{array}$$

The coefficient of x in the quadratic equation $a{x}^2+bx+c=0$ was wrongly taken as 17 in place of 13 and its roots were found to be –2 and –15, the actual roots of the equation are

In the figure, (3, 4) is the mid-point of AB.

Find: Area of ΔAOB

When divided by ( – 3) the polynomials ³ – ² + + 6 & 2³ – ² – ( + 3) – 6 leave the same remainder. Find the value of ‘’.

Find the values of x and y in the below given pair of equation, where $x\ne 0\&y\ne 0$.
$\frac{2}{x}+\frac{3}{y}=13$
$\frac{5}{x}-\frac{4}{y}=-2$

A(a,b), B(c,d) and C(e,f) are the vertices of a triangle.
i) AB + BC > AC
ii) Area of the triangle = $\left(\frac{1}{2}\right)$[a(c-e)+c(f-b)+e(b-d)]
Which of the following are true?

ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. If $\angle DBC={70}^{\circ },\angle ACD$ is ${50}^{\circ },$ find $\angle ADC$.

If a line passes through the point (1, 2) and cuts off positive intercepts on the x–axis and y–axis in the ratio 2 : 3, find the equation of the line.

In $△ABC$ , B is the right angle and BD is perpendicular to AC, then:

Let GCD $=x+1$ and LCM $=x^6-1$ for two given polynomials $f\left(x\right)$ and $g\left(x\right)$. Then, if $f\left(x\right)=x^3+1$. what is $g\left(x\right)$?

Match the given angles with the corresponding slopes.
$\begin{array}{cc}Positivex-direction& Slopeofline\\ 1.)0^o& p.)0\\ 2.){90}^o& q.)-\sqrt{3}\\ 3.){120}^o& r.)-\frac{1}{\sqrt{3}}\\ 4.){150}^o& s.)Notdefined\end{array}$

The condition for equation ax² + bx + c = 0 to be linear is

Find the equation of line passing through (2, 3) and perpendicular to the line 3x + 4 y - 5 = 0.

CM and RN are respectively the medians of $\Delta ABC$ and $\Delta PQR$. If $\Delta ABC\sim \Delta PQR$, prove that:

(i) $\Delta AMC\sim \Delta PNR$

(ii) $\frac{CM}{RN}=\frac{AB}{PQ}$

(iii) $\Delta CMB\sim \Delta RNQ$
[3 MARKS]

Find the volume of the cuboid with length = 5 km, breadth = 6 m and height = 1.5 m.

Factorise $x^2+8x+16$.

Decide whether 52.123456789 is a rational number or not. If rational (in the form $\frac{p}{q}$), what can you say about the prime factors of q?

The angle between the minute hand and the hour hand of a clock when the time is 04:20, is

The radii of the ends of a bucket of height h cm are r₁ cm and r₂ cm. The capacity of bucket in (cm²) is

If $\left[a_{ij}\right]$ is an element of matrix A then it lies in row of the matrix.

Twice the sum of 5 consecutive odd numbers and thrice the sum of 4 consecutive even numbers is 178. Thrice the sum of 5 consecutive odd numbers and twice the sum of 4 consecutive even numbers is 177. The middle number when all the numbers are arranged in ascending order is

If $sin\theta =\frac{a}{b},$ then find the value of $(sec\theta +tan\theta )$.

$\frac{1}{\sqrt{2}}$ is

(a) a fraction (b) a rational number

(c) an irrational number (d) none of these

If cos $A=\frac{3}{5}$, find the value of sin A+ tan A.

The sum of all zeroes of the polynomial p(x) = $5x^5-20x^4+5x^3+50x^2-20x-40$ is

and the product is

___ multiples of 4 lie between 10 and 250.

For an A.P, first term a = 5 and common difference d = 3. The sum of first 8 terms is ___

Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact. Using the above, do the following:

In fig., O is the center of the two concentric circles. AB is a chord of the larger circle touching the smaller circle at C. Prove that AC = BC

Solve the following quadratic equation by factorization.
$a(x^2+1)-x(a^2+1)=0$

The surface area of a sphere is 2464 $c{m}^2$,Find its volume.

IF $1+4+7+\cdots +x=287,$ find the value of x.

In the given fig, find the perimeter of $\Delta$ABC, if AP = 10 cm

A toy company manufactures two types of toys A and B. Demand for toy B is atmost half of that if type A. Write the corresponding constraint if x toys of type A and y toys of type B are manufactured.

Alpha drives 8 km to the north and 15 km to the east. Find the distance between the starting point and the terminating point

Find the area of the shaded region in the figure, where arcs drawn with centres, A, B , C and D intersect at mid - points P, Q, R and S of the sides AB , BC , CD and DA, respectively of a square ABCD (use $\pi =3.14$)

In a right triangle ABC right-angled at C, P and Q are the points on the sides CA and CB respectively, which divide these sides in the ratio 2:1.


Prove that [4 MARKS]

(i) $9A{Q}^2=9{AC}^2+4{BC}^2$

(ii) $9{BP}^2=9{BC}^2+4{AC}^2$

(iii) $9({AQ}^2+{BP}^2)=13{AB}^2$

Question 1
Visualize 3.765 on the number line using successive magnification.

The area of a sector is one-twelfth that of the complete circle. Find the angle of the sector.

Let say if the mode of a series exceeds its mean by 24, then the mode exceeds median by:

Find the sum of
(i) the first 15 multiples of 8
(ii) the first 40 positive integers divisible by (a) 3 (b) 5 (c) 6.
(iii) all 3-digit natural numbers, which are divisible by 13.
(iv) all 3-digit natural numbers, which are multiples of 11.
(v) all 2-digit natural numbers divisible by 4.