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List of top Mathematics Questions

The mean and variance of the data $4, 5, 6, 6, 7, 8, x, y$, where $x<y$, are $6$ and $\frac{9}{4}$, respectively. Then $x^4+y^2$ is equal to

Let α and β be the roots of the equation x² + (2i – 1) = 0. Then, the value of |α² + β²| is equal to

A tower $PQ$ stands on a horizontal ground with base $Q$ on the ground The point $R$ divides the tower in two parts such that $QR =15 \,m$ If from a point $A$ on the ground the angle of elevation of $R$ is $60^{\circ}$ and the part $PR$ of the tower subtends an angle of $15^{\circ}$ at $A$, then the height of the tower is :

The coefficient of x¹⁰¹ in the expression (5 + x)⁵⁰⁰ + x(5 + x)⁴⁹⁹ + x²(5 + x)⁴⁹⁸ + ……+ x⁵⁰⁰, x > 0, is

The set of values of $k$, for which the circle $C : 4x^2 + 4y^2 – 12x + 8y + k = 0$ lies inside the fourth quadrant and the point $\bigg(1, -\frac{1}{3}\bigg)$ lies on or inside the circle $C$, is

If the mirror image of the point (2, 4, 7) in the plane 3x – y + 4z = 2 is (a, b, c), then 2a + b + 2c is equal to

If A =$\sum_{n=1}^{\infty}$$\frac{1}{( 3 + (-1)^n)^n}$ and B = $\sum_{n=1}^{\infty}$$\frac{(-1)^n}{( 3 + (-1)^n)^n}$ ,
then A/B is equal to :

Let P be the plane containing the straight line$\frac{ x−3}{9}$=$\frac{y+4}{-1}$=$\frac{z-7}{-5}$and perpendicular to the plane containing the straight lines $\frac{x}{2}=\frac{y}{3}=\frac{z}{5}$ and $\frac{x}{3}=\frac{y}{7}=\frac{z}{8}$.If d is the distance P from the point (2, –5, 11), then d² is equal to :

The probability that a randomly chosen one-one function from the set {a, b, c, d} to the set {1, 2, 3, 4, 5} satisfies f(a) + 2f(b) – f(c) = f(d) is :

Let Δε{∧,∨,⇒,⇔} be such that (p∧q)Δ((p∨q)⇒q) is a tautology. Then ∆is equal to

Let S be the sample space of all five digit numbers. It p is the probability that a randomly selected number from S, is multiple of 7 but not divisible by 5, then 9p is equal to

Let $f(x)= \begin{cases} x^3-x^2+10 x-7, & x \leq 1 \\ -2 x+\log _2\left(b^2-4\right), & x>1\end{cases}$ Then the set of all values of $b$, for which $f(x)$ has maximum value at $x=1$, is :

The value of the integral $∫^{ \frac{π}{2}}_{ \frac{-π}{2}} \frac{dx}{(1+e^x)(sin^6x+cos^6x)}$ is equal to

The area of the region bounded by y² = 8x and y² = 16(3 – x) is equal to

Let
$f(x)=\frac{x−1}{x+1},x∈R− \left\{0,−1,1\right\}$
If ƒⁿ⁺¹(x) = ƒ(ƒⁿ(x)) for all n∈N, then ƒ⁶(6) + ƒ⁷(7) is equal to :

Let A be a matrix of order 3×3 and det (A) = 2. Then det (det (A) adj (5 adj (A³))) is equal to ______.

A wire of length 22 m is to be cut into two pieces. One of the pieces is to be made into a square and the other into an equilateral triangle. Then, the length of the side of the equilateral triangle, so that the combined area of the square and the equilateral triangle is minimum, is

Let the system of linear equations \[ x + 2y + z = 2, \quad \alpha x + 3y - z = \alpha, \quad -\alpha x + y + 2z = -\alpha \] be inconsistent. Then $\alpha$ is equal to:

The value of $ tan^{-1}(\frac{cos\frac{15}{4}-1}{sin(\frac{π}{4})} )$ is equal to:

If the tangents drawn at the points $P$ and $Q$ on the parabola $y^2=2 x-3$ intersect at the point $R (0,1)$, then the orthocentre of the triangle $PQR$ is :

If $\lim_{{x \to 0}} \frac{\alpha e^x + \beta e^{-x} + \gamma \sin x}{x \sin^2 x} = \frac{2}{3}$, where $\alpha, \beta, \gamma \in \mathbb{R}$ then which of the following is NOT correct?

In an isosceles triangle ABC, the vertex A is $(6, 1)$ and the equation of the base BC is $2x + y = 4$. Let the point B lie on the line $x + 3y = 7$. If $(α, β)$ is the centroid of ΔABC, then $15(α + β)$ is equal to :

Let R be the point (3, 7) and let P and Q be two points on the line x + y = 5 such that PQR is an equilateral triangle, Then the area of ΔPQR is

The integral $\int_0^{\frac{\pi}{2}} \frac{1}{3 + 2\sin x + \cos x} \, dx$ is equal to

Let Q be the mirror image of the point P(1, 2, 1) with respect to the plane x + 2y + 2z = 16. Let T be a plane passing through the point Q and contains the line
$\vec{r}=−\hat{k}+λ(\hat{i}+\hat{j}+2\hat{k}), λ ∈ R.$
Then, which of the following points lies on T?