The sum of the first k terms of a series S is $3k{}^2+5k$. Which one of the following is correct?

The sum of the first 8 terms of a GP is five times the sum of its first 4 terms. If $r$≠$1$ is the common ratio, then what is the number of possible real values of r?

If one root of the equation $x{}^2-kx+k=0$ exceeds the other by $2\sqrt{3}$ then which one of the following is a value of k?

 If $x+\frac{5}{y}=4$, and then $\$y+\backslash frac\{5\}\{x\}=\; -4\$$  what is (x + y) equal to?

If 5th, 7th and 13th terms of an AP are in GP, then what is the ratio of its first term to its common difference?

If p, 1, q are in AP and p, 2, q are in GP, then which of the following statements is/are correct?

I. p, 4, q are in HP.

II. (1/p), (1/4), (1/q) are in AP.

Select the answer using the code given below.

 If $x=(1111){}^2$, $y=(1001){}^2$ and $z=(110){}^2$, then what is x³−y³−z³−3xyz equal to?

If $\Delta = \begin{vmatrix} a & b & c \\ d & e & f \\ g & h & i \end{vmatrix} $ 

and A, B, C, D, G are the cofactors of the elements a, b, c, d, g respectively, then what is $bB+cC-dD-gG$ equal to?

. Consider the following statements in respect of the determinant 

$ \Delta = \begin{vmatrix} k(k+2) & 2k+1 & 1 \\ 2k+1 & k+2 & 1 \\ 3 & 3 & 1 \end{vmatrix} $

I. Δ is positive if $k>0$.

II. Δ is negative if $k<0$.

III. Δ is zero if $k=0$.

How many of the statements given above are correct?

If $ \begin{vmatrix} 2 & 3+i & -1 \\ 3-i & 0 & i -1 \\ -1 &-1 -i & 1 \end{vmatrix} = A + iB $

where i= $\sqrt{-1}$ ,  then what is A+B equal to?

If $A{}^2+B{}^2+C{}^2=0$, then what is the value of the following?

$\begin{vmatrix} 1& cosC& cosB\\ cosC&1&cosA \\ cosB&cosA&1 \end{vmatrix} $

If ω is a non-real cube root of unity, then what is a root of the following equation?$ \begin{vmatrix} x+1 & \omega & \omega^2 \\ \omega & x+\omega^2 & 1 \\ \omega^2 & 1 & x+\omega \end{vmatrix} = 0 $

 

What is $ \left( \frac{\sqrt{3}+i}{\sqrt{3}-i} \right)^3 $ equal to?

 If $x{}^2-x+1=0$, then what is $(x-\frac{1}{x})^2+(x-\frac{1}{x})^4+(x-\frac{1}{x})^8$

How many 7-letter words (with or without meaning) can be constructed using all the letters of the word CAPITAL so that all the consonants come together in each word?

If $z\ne0$ is a complex number, then what is $amp(z)+amp(\bar{z})$ equal to?

How many sides are there in a polygon that has 20 diagonals?

In how many ways can the letters of the word DELHI be arranged, keeping the positions of vowels and consonants unchanged?

What is the number of positive integer solutions of $x+y+z=5$?

What is the number of rational terms in the expansion of $(\sqrt{3}+5^\frac{1}{4})^{12}$

If the sum of binomial coefficients in the expansion of $(x+y){}^n$ is 256, then the greatest binomial coefficient occurs in which one of the following terms?

If $k<(\sqrt{2}+1)^3<k+2,$ where k is a natural number, the value of k?

If

 $\begin{bmatrix} x & 1 & 1 \end{bmatrix} \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{bmatrix} \begin{bmatrix} 1 \\ 1 \\ x \end{bmatrix} = \begin{bmatrix} 45 \end{bmatrix}$

then which one of the following is a value of x?

If

 $A = \begin{bmatrix} y & z & x \\ z & x & y \\ x & y & z \end{bmatrix} $

where x,y,z are integers, is an orthogonal matrix, then what is the value of $x{}^2+y{}^2+z{}^2$?

Consider the following in respect of a non-singular matrix M:

I. ∣M²∣=∣M∣²

II. $|M|=|M{}^{-1}|$

III. $|M|=|M{}^T|$

How many of the above are correct?

If $f(\theta) = \begin{bmatrix} \cos \theta & \sin \theta \\ -\sin \theta & \cos \theta \end{bmatrix}$ then what is (f(π))² equal to?

If $A=\begin{bmatrix}1&2&2 \\ 2&1&2\\2&2&1\end{bmatrix}$ then what is $A{}^2-4A$ equal to?

If the number of selections of r as well as $(n+r)$ things from 5n different things are equal, then what is the value of r?

What is the number of selections of at most 3 things from 6 different things?

If $A=\begin{bmatrix}x&y&z\\y&z&x\\z&x&y\end{bmatrix}$

where x,y,z are integers, is an orthogonal matrix, then what is A² equal to?

What is $(p+q+r)$ equal to?

What is $(pq+qr+rp)$ equal to?

What is (p²+q²+r²) equal to?

What is the minimum value of p?

What is the maximum value of p?

Consider the following statements:

I. The triangle is obtuse-angled triangle.

II. The sum of acute angles of the triangle is also acute.

Which of the statements given above is/are correct?

What is ∠B equal to?

What is the area of the triangle?

What is PN equal to?

What is MN equal to?

What is (p/q) equal to?

What is $(p+q)$ equal to?

What is tan²α equal to?

What is tanα equal to?

What is $2\sin 2\alpha +\cos 2\alpha$ equal to?

One of the angles of the triangle is

Consider the following statements:

I. The triangle is right-angled.

II. One of the sides of the triangle is 3 times the other.

III. The angles A, C and B of the triangle are in AP.

Which of the statements given above is/are correct?

A man at M, standing 100 m away from the base (P) of a chimney of height 50 m, observes the angle of elevation of the highest point (Q) of the smoke to be 45^∘. The highest point of the chimney is at R. Further P, R and Q are in a straight line and the straight line is perpendicular to PM. What is the angle RMQ equal to?

If k is a root of $x{}^2-4x+1=0$, then what is tan⁻¹k+tan⁻¹$\frac{1}{k}$​ equal to?

If tan⁻¹k+tan⁻¹ $\frac{1}{2}$​=$\frac{π}{2} ​ $, then what is the value of k?

Under what condition will the lines $m{}^{2}x+ny-1=0$ and $n{}^{2}x-my+2=0$ be perpendicular?

If p and q are real numbers between 0 and 1 such that the points (p,1), (1,q) and (0,0) form an equilateral triangle, then what is $(p+q)$ equal to?

The vertices of a triangle are A(1, 1),B(0, 0) and C(2, 0). The angular bisectors of the triangle meet at P. What are the coordinates of P?

Let A(3, -1) and B(1, 1) be the end points of line segment AB. Let P be the middle point of the line segment AB. Let Q be the point situated at a distance $\sqrt{2}$ units from P on the perpendicular bisector line of AB. What are the possible coordinates of Q?

ABC is an equilateral triangle and AD is the altitude on BC. If the coordinates of A are (1,2) and that of D are (−2,6), then what is the equation of BC?

What is the equation of the circle whose diameter is 10 cm and the equations of two of its diameters are $x+y=0$ and $x-y=0$?

A square is inscribed in a circle x ² + y ² + 2x + 2y + 1 = 0 and its sides are parallel to coordinate axes. Which one of the following is a vertex of the square?

A tangent to the parabola y² = 4x is inclined at an angle 45° deg with the positive direction of x-axis. What is the point of contact of the tangent and the parabola?

. What is the distance between the two foci of the hyperbola 25x² - 75y ²= 225 ?

If any point on an ellipse is (3sin$\alpha$, 5cos$\alpha$), then what is the eccentricity of the ellipse?

If a line in 3 dimensions makes angles α, β and γ with the positive directions of the coordinate axes, then what is $\cos (\alpha +\beta )\cos (\alpha -\beta )$ equal to?

A(1,2,−1), B(2,5,−2) and C(4,4,−3) are three vertices of a rectangle. What is the area of the rectangle?

$ABC$ is a triangle right-angled at B. If A(k,1,−1), B(2k,0,2) and $C(2+2k,k,1)$ are the vertices of the triangle, then what is the value of k?

If a line  $\frac{x+1}{p} = \frac{y-1}{q} = \frac{z-2}{r}$  where $p=2q=3r$, makes an angle θ with the positive direction of y-axis, then what is cos2θ equal to?

What is the equation of the plane passing through the point (1,1,1) and perpendicular to the line whose direction ratios are (3,2,1)?

A line makes angles α, β and γ with the positive directions of the coordinate axes. If $\$\backslash vec\{a\}=(\backslash sin^2\; \backslash alpha)\backslash hat\{i\}\; +\; (\backslash sin^2\; \backslash beta)\backslash hat\{j\}\; +\; (\backslash sin^2\; \backslash gamma)\backslash hat\{k\}\; \backslash text\{\; and\; \}\; \backslash vec\{b\}\; =\; \backslash hat\{i\}\; +\; \backslash hat\{j\}\; +\; \backslash hat\{k\}\$$ , then what is $\vec{a}.\vec{b}$ equal to?

Consider the following statements with respect to a vector d = (a × b) × c:

I. d is coplanar with a and b.

II. d is perpendicular to c.

Which of the statements given above is/are correct?

The position vectors of three points A, B and C are a, b and c respectively such that $\vec{3a}-\vec{4b}+\vec{c}=\vec{0}$ What is AB:BC equal to?

The position vectors of three points A, B and C respectively, where  $\vec{a} ,\vec{b} $ and $\vec{c} $  respectively, where $\vec{c} = (\cos^2 \theta)\vec{a}+(\sin^2 \theta)\vec{b}$. What is $(\vec{a} \times \vec{b}) + (\vec{b} \times \vec{c}) + (\vec{c} \times \vec{a})$ equal to?

Let $\vec{a},\vec{b} ,(\vec{a}\times\vec{b})$ be unit vectors. What is $\vec{a}.\vec{b}$$\stackrel{equal\; to?}{}$

What is $(\frac{dy}{dx})^2$ equal to?

What  $\left[ \frac{x^2+4}{y^2+4} \frac{dy}{dx} \left( x^2+4 \frac{d^2y}{dx^2} - 16y \right) \right] $  equal to?

What is ∠A equal to if the area of the triangle is maximum?

What is the maximum area of the triangle?

The derivative of y with respect to x

If $p+q=10$, then what is $\frac{dy}{dx}$ equal to?

What is the nature of the curve?

. What is the area bounded by the curve, the x-axis and the line x = 4?

What is  $\lim_{x \to 0} f'(x)$ equal to?

Consider the following statements:

I. The function is continuous at $x=-1$.

II. The function is differentiable at $x=1$.

Which of the statements given above is/are correct?

What is the range of the function?

What is ∫ydx equal to? 

where c is the constant of integration.

What $\lim_{x \to 0} {f(x) g(x)}$ is  equal to?

What is $\lim_{x \to 0} \frac{f(x)}{g(x)}$ equal to?

What is the domain of the function (f(x))?

What is the area bounded by the curve f(x) and y = 3?

If f(x) = px + q then what is the value of (p + q) ?

Consider the following statements:
I. f is one-one function.
II. f is onto function if the codomain is the set of natural numbers.
Which of the statements given above is/are correct?

What is $\lim_{x \to 1} \{f \circ f(x)\}$ equal to?

What is the area bounded by the function f(x) and the x-axis?

What is y equal to?

What is  $\frac{dy}{dx}$ euqal to ?

What is  $\lim_{x \to 0} \frac{\sqrt{f(x)} - 3}{\sqrt{f(x)+7} - 4}$ equal to?

Consider the following statements:
I. f(x) is an increasing function.
II. f(x) has local maximum at x = 0
Which of the statements given above is/are correct?

What is f(16) equal to?

What is f(1)f(4) equal to?

What is f(0) equal to?

What is f(20)+f(-20) equal to?

What  $\int_{\sqrt{2}}^{\sqrt{3}} f(x) dx$ equal to?

$\int_{\sqrt{2}}^{2} f(x) dx$  is equal to ?

What is the total number of students whose height is less than or equal to 165 cm?

What is the height of the class?

The height which occurs most frequently in the class is

The most appropriate graphical representation of the given frequency distribution is

Which one of the following is correct?

Which one of the following statements is correct?

What is the value of k?

What is the value of P * (X = 3) ^ 0

What is the probability that the committee includes exactly 3 gentlemen?

What is the probability that the committee includes at least 2 ladies?

What is the probability that the bonus scheme will be introduced?

If the bonus scheme has been introduced, then what is the probability that the manager appointed was B?

The arithmetic mean of 100 observations is 50. If 5 is subtracted from each observation and then divided by 20, then what is the new arithmetic mean?

The standard deviation of 100 observations is 10. If 5 is added to each observation and then divided by 20, then what will be the new standard deviation?

If $P(A)=1/3$, $P(B)=1/2$ and $P(A\cap B)=1/4$, then what is the value of $P(A|B{}^C)$?

If $P(A)=1/3$, $P(B)=1/2$ and $P(A\cap B)=1/4$, then what is the value of $P(A{}^C\cap B{}^C)$?

If two fair dice are tossed, then what is the probability that the sum of the numbers on the faces of the dice is strictly greater than 7?

The probability of a man hitting a target is 1/5. If the man fires 7 times, then what is the probability that he hits the target at least twice?

Let X be a random variable following binomial distribution whose mean and variance are 200 and 160 respectively. What is the value of the number of trials (n)?

What is the arithmetic mean of 8²,9²,10²,...,15²?